Source:Lloyd. R. Quality Health Care: A Guide to Developing and Using Indicators CHAPTER 9 2nd Edition, Jones & Bartlett Learning, 2019. Understanding Variation with Shewhart Charts
e details related to these di erences are dis- ▸ Run Charts versus cussed in the remaining sections of this chapter. Shewhart Charts For many teams just beginning their quality mea- ▸ What Is a Shewhart surement journey (QMJ) the run chart provides an excellent starting point. It is easy to construct Chart? with paper and pencil, it does not require a so - Like run charts, Shewhart charts are graphic ware package in order to make one, and it can displays of process variation as it lays itself out be used with any type of data (i.e., time, money, over time. FIGURE 91 shows the basic elements of counts of errors, percentages, rates, scores, or days a Shewhart chart and one of the tests to identify between adverse events). Also, the four run chart a special cause (i.e., a data point exceeded the rules are easy to understand and apply. So, why upper control limit [UCL], signaling too much would I want to use a Shewhart chart instead of a variation in the data, which, by the way, you run chart?1 ere are basically three reasons why should recognize as an astronomical data point Shewhart charts are preferable over run charts: on the run chart). A run chart and a Shewhart 1. Shewhart charts are more sensitive chart look similar in that the indicator of interest than run charts. and its values are plotted on the vertical or y 2. Shewhart charts have the added axis and the chronological order of the data are feature of control limits and zones, organized by what are called subgroups (e.g., which run charts do not have. by individual patients, by day, week, or month) 3. Shewhart charts allow us to more along the horizontal or x axis. e data points accurately predict process behavior, are then connected by a line and the mean of the future performance, and process data points is then plotted as the centerline (CL) capability than do run charts. on the Shewhart chart. e presence of control
© Michal Ste ovic/Shutterstock
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Signal of a Upper Control special Limit
60.0
50.0 UCL=46.910
40.0 Data are plotted in time order 30.0 CL=23.381 20.0 Centerline (the mean) 10.0
Number of Patient Complaints Number of Patient 0.0 LCL=0.148 Lower Control -10.0 Limit 12345678910 11 12 13 14 15 16 17 18 19 20 21 Week
The unit of time is plotted along the horizontal axis
FIGURE 91 Elements of a control
limits on Shewhart charts are major points that data point actual values. By using the mean we separate it from a run chart. are ensuring that the absolute value and the Shewhart charts are more sensitive than distance of each data point from the CL will be run charts because the run chart cannot detect considered in determining the variation in the special causes that result from point-to-point indicator and if special cause variation exists. variation. is is because the CL on the run Another reason why Shewhart charts are chart is the median (i.e., the 50th percentile). more sensitive than a run chart is that Shewhart e run chart basically allows you to classify charts have the added feature of control limits, the data points as being only above or below which run charts do not have. e control the median. e actual distance a data point limits are properly referred to as the UCL and is from the CL is not an issue on a run chart. the lower control limit (LCL). ey are also erefore, if one data point is 2 units above referred to as sigma limits. You will probably the median and another point is 22 units hear someone refer to control limits, however, above the median, they will both be treated as con dence intervals, con dence limits, or the same because they are both on the same even standard deviation (SD) limits, which they side of the median. e logic for this decision are not (Blalock, 1960; Carey, 2003; Daniel & is related to the de nition of the median and Terrell, 1989; Provost & Murray, 2011). of a run (i.e., one or more data points on the e UCL and LCL basically de ne the same side of the median). If these same two boundaries of process variation around the data points (i.e., 2 and 22) were placed on a mean. e developer of the chart does not set or Shewhart chart, however, you would notice a de ne the UCL and LCL. ese are determined discernable di erence because the CL on the by mathematical formulae and the width of these control chart is the mean or average of all the limits is dependent on the inherent variation
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that lives within the data. e only thing the UCL is 47 minutes, the lower control limit is developer of the chart can place on the Shewhart 23 minutes and there are no special causes chart is a target or goal and annotations as to detected. is means that the process is a stable when improvements were introduced. and predictable. erefore, if we do nothing e control limits enable the Shewhart to change how this process works we can charts to have increased precision over the run predict that patients will wait on the average chart. A run chart will miss certain nonrandom 35 minutes with the possibility that the wait patterns that would be detected on a Shewhart time could go up as high as 47 minutes or as chart as special causes. According to Perla, low as 23 minutes. In light of the target of Provost, and Murray (2011, p. 47), “ e three having all patients seen by their doctor within probability-based (run chart) rules are used to 20 minutes or less, however, you can see that objectively analyze a run chart for evidence of we have our work cut out for us!” non-random patterns in the data based on an is scenario provides a summary of how α error of p < 0.05.” is means that run charts process capability for the wait time in a clinic could miss a nonrandom pattern in the data can be based on the parameters calculated for a approximately 5% of the time. Shewhart chart Shewhart chart (i.e., the UCL, LCL, and mean). rules, on the other hand, will not miss detecting Classically, process capability is de ned as, “ e a special cause. is is why it is recommended calculated inherent variability of a characteristic that the terms special and common cause as well (indicator) of a product or service. It represents as stable or unstable should be reserved for use the best performance of the process over a period only with Shewhart charts and that the terms of stable operation” (ASQ, 2005, p. 78). Process random and nonrandom patterns be applied capability is essentially aimed at determining to run charts. whether under current operating conditions the Shewhart charts also allow us to more process can meet the predetermined speci cations accurately predict process behavior and future or achieve the target or goal we have established performance than do the run charts. On a (Blank, 1998; Carey, 2003; Kume, 1985; Provost & run chart, if the variation is random the best Murray, 2011; Western Electric, 1985; Wheeler & prediction of the future performance of an Chambers, 1992). indicator is the median value. For example, Besides a verbal summary of the Shewhart if a team is trying to improve the wait time chart parameters using the UCL, LCL, and mean to see a doctor and have plotted the data on as described previously, process capability can a run chart the median is the best estimate of also be de ned statistically by “a single number future performance. Let’s say that the median assessment of the ability of the process to meet wait time is 27 minutes. If you were present- speci cation limits on the quality characteris- ing this data to a team or a committee all you tic(s) of interest (ASQ, 2005, p. 78). When you could say would be, “Ladies and gentlemen, the move to the statistical indices that capture pro- median wait time is 27 minutes. e process cess capability it is necessary to have an upper reects only random variation. erefore, if speci cation limit (USL) and a lower speci - we do nothing to change the current process cation limit (LSL), which are then compared we can expect to have patients wait about 27 to the performance of the process as de ned minutes to see the doctor.” On a Shewhart by the UCL, LCL, and the mean.2 Although chart, however, because we have the UCL, these indices have not been used extensively LCL, and the mean as the CL, we have more in healthcare settings I believe that they have precision. In this case, when you present the great utility. We have many physiological tests data to the team or a committee you would be that have upper and lower preferred levels of able to say, “Ladies and gentlemen, the average performance (i.e., speci cation limits). ese wait time to see a doctor is 35 minutes, the include such indicators as temperature, blood
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pressure, hematocrits, neutrophils, white and the interpretation of the chart and what can be red blood cell counts, platelets, and clotting learned from it must come from the dialogue factors.3 that emerges when people with subject matter ere are many useful books and articles on knowledge interpret the chart. is requires the statistical theory behind Shewhart charts, how knowledge not a computer. to construct them, and how to interpret the results. I have provided only a brief introduction to the key principles behind the Shewhart charts. is is ▸ Key Questions about a very rich eld of study that has been developed over the past 100 years. Readers interested in Shewhart Charts the detailed aspects of statistical process control (SPC) and in particular Shewhart charts should ere are three basic questions people typically consult the rich variety of books and articles on ask as we start them on the road to using She- this topic. Ones I have found particularly useful whart charts: include Benneyan (2001); Benneyan, Lloyd, and 1. How many data points do I need to Plsek (2003); Blank (1998); Carey (2003); Carey make a Shewhart chart? and Lloyd (2001); Duncan (1986); Ishikawa 2. What is a sigma limit? And, why do (1989); Mohammed, Worthington, and Woodall I need three of them? (2008); Montgomery (1991); Provost and Murray 3. Do I apply the run chart rules to (2011); Pyzdek (1990); Western Electric (1985); Shewhart charts? Wheeler (1993, 1995); Wheeler and Chambers (1992); and Woodall (2006). Each of these is discussed next. If you wish to build a rm foundation in Shewhart charts and SPC in general, I would How Many Data Points Do I Need recommend that you read widely on this topic and read what di erent authors have written. If to Make a Shewhart Chart? one item you read seems too academic or math- As soon as the team begins to gather data they ematical, read another author’s description and should start plotting the data points (dots) on a use of SPC. As you read more of the literature chart. At rst this will simply be a line graph. A and di erent authors at some point there will be run chart requires less data because the median a moment when you say, “Okay, I get it.” Fur- as the CL is not as sensitive to point-to-point thermore, if you do not have a reasonably solid variation as is a Shewhart chart. Also the run working knowledge of the theory and mechanics chart rules start to come into play with di erent of Shewhart charts and how they are constructed, amounts of data. e trend rule can be detected it will be rather dicult to successfully apply when you have ve or six data points. As Provost them to your improvement work. is becomes and Murray point out (2011, p. 87) “a trend even more problematic when people say “No will remain a trend no matter the amount of problem with the charts. We have so ware that additional data added to the graph.” e run makes the charts for us.” is orientation creates chart rules related to a shi and too many or several problems. Although it is easy to push too few runs, however, require more data to be a few buttons on your computer and “make a detected. e general rule is that a minimum of chart” this does not necessarily mean it is the 10 data points is necessary to properly determine most appropriate chart for the indicator you are whether a shi has occurred on the run chart or tracking. More important, the SPC so ware does whether too many or too few runs are present. not help at all with interpreting what the chart When we move to using Shewhart charts more is trying to tell you. e chart can come from data are usually required because (1) the mean the machine in front of you with a keyboard but is now used as the CL and the absolute value of
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any data point enters into the calculations of the pulled from the process when it is stable UCL and LCL, and (2) the rules for detecting and predictable. special causes of variation are more rigorous ■ If you have less than 20–30 subgroups of and precise than the four rules for run charts. data you can still create a Shewhart chart but But, the simple answer to the question of how the UCL and LCL should be referred to as much data I need to make a Shewhart chart “trial” control limits (Carey, 2003; Carey & is . . . it depends. I know some readers will Lloyd, 2001; Provost & Murray, 2011). be thinking, “What kind of a lame answer is e trial limits can be used for learning this? Just tell me how many data points I need but the use of the word “trial” is to remind to make a Shewhart chart!” Because there are those using the chart that these limits may many types of Shewhart charts, which are dis- change as more complete data are obtained cussed in the next section, it must be realized and make the limits more reliable and stable. that the di erent charts can be produced with e issue here is that when you have less di ering amounts of data. e subgroup, that than the recommended amount of data is how you have organized your data along (i.e., 12–15 data points) the control limits the x or horizontal axis of the chart, is key and CL (i.e., the mean) can change rather to determining how much data you need to quickly and dramatically with the addition make a particular type of Shewhart chart. For of each new data point. With a fewer num- example, if you want to track the wait time of ber of subgroups you also run the risk of each patient at a family practice clinic to see the committing a type II error (i.e., concluding doctor then the subgroup is one patient and the that the chart indicates no special causes one bit of data for this patient will be her wait when in fact one or more special causes do time to see the doctor. If, on the other hand, exist). When you start to have more than you decide that you want to track wait time by the recommended 20–30 subgroups of data, day then the horizontal axis of your chart will say 40–50, you run the risk of committing have Monday, Tuesday, Wednesday, etc. rather a type I error (i.e., nding special causes than patient 1, patient 2, patient 3, etc. as the by chance alone). Additional detail on the subgroup. Selecting day as the subgroup for theory and use of the type I and type II a clinic could now provide upwards of 30–40 error concepts can be found in Carey and patients’ wait times as possible observations (bits Lloyd (2001), Carey (2003), and Provost and of data) within a single day. Having multiple Murray (2011). In summary, the underlying data points in a subgroup or only one will play question here is how much data do you a major role in deciding which Shewhart chart need to create a reasonably stable distri- you can make. is is why it is very important bution? Di erent disciplines recommend to make sure you have a well-thought-out data di erent amounts of data needed to form collection plan. Again, more will be said about a distribution (e.g., from only a few data these issues in the next section when I discuss points to over 500) but generally speaking the types of Shewhart charts. a reasonably stable distribution of data for All this being said, I do know that many improvement purposes occurs when you people still want to have at least some general have 20–30 subgroups of data. guidelines for organizing their data, so here are ■ As a general rule I also recommend not a few that I o er to improvement teams as we using quarterly data for your improvement begin to work on developing Shewhart charts:4 e orts. ere is just too much variation being aggregated in quarterly data to be ■ It is usually recommended that you have useful for improvement e orts. A quarter 20–30 subgroups of data before construct- consists of 3 months approximately 90 days ing a Shewhart chart. ese data should be and over 2100 hours. During this time a
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great deal of variation can occur. So when (i.e., the normal bell-shaped curve), skewed to someone begins making conclusions about the le , or skewed to the right in which case the the quarterly average or SD you should ask distribution will have a tail that is longer on one them to provide the actual variation that side than the other. A distribution with a long produced these summary statistics by day, tail skewed to the right will have a mean that is week or at a minimum by month. greater than the median whereas a le -skewed distribution will have the mean be less than the median. Kurtosis, on the other hand, refers to What Is a Sigma? And Why Do how spread out or peaked the distribution is. For additional details on measures of central I Need Three of Them? tendency, dispersion, and distribution shape ese two questions probably pose the most you can consult any basic stat book. Some of challenging technical aspects of Shewhart chart the books I have on this topic come from my construction. Some of you will really enjoy this undergraduate days and are just as relevant as a issue and want to learn more whereas others statistics book published last year (Blalock, 1960; of you will say, “I really don’t care about this Daniel & Terrell, 1989; Gonick & Smith, 1993; statistical distinction just make the chart that is Levine & Stephan, 2005). ese principles are most appropriate for my indicator and tell me fundamental and have not changed over the years. what it means.” Either position is ne. I do not FIGURE 92 provides examples of distributions intend to go into great detail on this topic but with di erent characteristics of center, dispersion, I do want to frame it properly so that you can and shape. Note that the normal (or Gaussian) decide if you want to learn more or accept the distribution, which is popularly referred to as the fact that these statistical principles have been bell curve, is typically not found in the real world discussed, debated, and written about extensively of data collection and analysis. In a theoretical for many decades. normal distribution, the mean, median, and Let’s start with the basics. Whenever you mode are all at the same position and the data have an array of data you need to consider three are distributed randomly and symmetrically characteristics of the distribution these data about the mean. But it needs to be pointed out create: the central tendency of the distribution, that not all symmetrical bell-shaped curves are the dispersion or spread of the distribution, normal (Blalock, 1960, p. 80). You can have, and the shape of the distribution. You were for example, three normal curves that have the acquainted with these characteristics when same SDs but di erent means. Similarly, you you took your rst statistics class, which was could have several curves that have the identical probably a number of years ago. So, this should means but very di erent SDs that in turn create all sound rather familiar even if you have not di erent shapes for the distributions. used the concepts in a while. Measures of central It is important that you have a comfort level tendency include the mean (i.e., the arithmetic with the characteristics of distributions so that average), the median (i.e., the midpoint of the you can more fully understand the character- distribution or 50th percentile), and the mode istics of the data you have collected and their (i.e., the most frequently occurring number). potential limitations. Although the Shewhart Measures of dispersion include the minimum charts can accommodate both normally and and maximum values, the range (i.e., the absolute nonnormally distributed data (Wheeler, 1995) di erence between the min and max values), having knowledge of the data you have gathered the sum of the deviations, the mean deviation, is the rst step toward creating and interpreting the sample variance, and the SD. e shape of Shewhart charts. a distribution is determined by skewness and With a few of the basics about distributions kurtosis. A distribution can be symmetrical in hand it is now time to address in a little more
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FIGURE 92 Examples of distributions with different centers, spreads and shapes
detail the topic of sigma limits. As was mentioned Chambers, 1992, p. 60). Wheeler also earlier in this chapter, the UCL and LCL are prop- points out that the common dispersion erly referred to as sigma limits or alternatively, statistic for a distribution (i.e., the SD) estimates of the SD (Provost & Murray, 2011, needs to be converted into sigma units by p. 115; Wheeler, 1993, 1995). Although some the use of speci c formulas. He concludes: writers will call the UCL and LCL SD limits “By shi ing from measurement units (i.e., and not even reference the term sigma, I think SD of a distribution) to sigma units, it is it is important to use the term sigma to refer to possible to characterize how much of the the estimates of variation in a Shewhart chart data will be within a given distance on rather than SDs for several reasons: either side of the average. us, the sigma ■ is is how Dr. Shewhart (1980, 1986) units express the number of measurement originally described the limits on the charts units which correspond to one standard he developed. unit of dispersion” (p. 61) ■ e SD of a distribution is calculated dif- A nal point to acknowledge is that if you ferently than a sigma. e SD is a single calculate the SD of a distribution using the number that represents the average distance traditional formula that you will nd in any individual data point in a distribution many so ware packages, multiply this is from the mean. It cannot be a negative number by 3, and then add and subtract this number and it will go, theoretically, from value (i.e., 3 SDs) to the mean, you will get zero to a rather large positive value (but the incorrect UCL and LCL for a Shewhart generally speaking the SD usually does chart. is becomes even more important not go much beyond double digits). A when you realize that each type of Shewhart sigma unit, on the other hand, is a “mea- chart has its own formula to compute sigma sure of scale for the data” (Wheeler and values and that none of these formulae use
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the traditional SD formula for a sample based standard deviation is used to describe the on the following formula: units of variation on a Shewhart chart or the UCL and LCL in healthcare settings con- n 2 fusion occurs conceptually and statistically. xx− ∑ = ()i S = i 1 I would strongly encourage you, therefore, x n −1 to use the proper terms when constructing and explain Shewhart charts. 5 n = e number of data points x = The mean of the xi Now that we know a little more about what xi = Each of the values of the Data a sigma is, the next question is, “Why do we need three of them?” e answer to this question is Note that if you were calculating the SD for found partially in statistical theory and partially a de ned population the formula would in practicality. According to Wheeler (1995, p. 14) use N as the denominator (i.e., the total Shewhart’s use of 3 sigma limits (i.e., three above number of observations in the population the mean and three below the mean for a total of being observed) rather than n - 1, which is 6 sigma units) as opposed to any other multiple typically used when calculating a SD for a of sigma did not stem from any speci c math- sample. ematical computation. Rather Shewhart said If you do not use the appropriate formula that three “seems to be an acceptable economic for computing a particular chart’s limits, you value,” and that the choice of 3.0 was justi ed by will produce limits that are too wide or too “empirical evidence that it works” Provost and narrow. is will then lead you to make the Murray (2011) provide a succinct summary of wrong decision about the variation in your the rationale for using Shewhart’s 3 sigma limits: data (i.e., you will see special causes when ■ they do not exist and miss them when they e limits have a basis in statistical theory. ■ are actually present). e limits have proven in practice to distin- ■ e third reason I prefer using the terms guish between special and common causes sigma units and sigma limits with Shewhart of variation. ■ charts rather than SD units or SD limits is In most cases, use of the limits will ap- to avoid confusion. A majority of health- proximately minimize the total cost due to care professionals have been exposed to overreaction and underreaction to variation the concept of a SD but not to a sigma. We in the process. ■ have all been in meetings where someone e limits protect the morale of the workers in presenting data has proudly said, “We have the process by de ning the magnitude of the analyzed the data from last month for pro- variations that has been built into the process. cedure X and discovered that the average Provost and Murray’s point about overreaction length of stay is 4.3 days and the SD is 2.6 and underreaction to variation deserves a few more days.” When this occurs most participants comments. ere are basically two mistakes or in the meeting either nod their heads and errors that you need to avoid when interpreting say nothing or mumble a few words to the data. e rst mistake (a type I error) is a risk person sitting next to them about this is just of concluding that a data point requires special what we heard last month. e SD is a very action when it is actually reecting common cause popular statistic presented in healthcare (random) variation. is leads to tampering with management meetings. People hear the a process that is in fact stable and predictable. number but most could not explain what Tampering (i.e., reacting one way a data point it is, how it was calculated, or how to inter- then reacting another way to the next data point pret it. But, it is a regular part of healthcare when they are part of a process that is stable and management meetings. So, when the word predictable) leads to increases variation in a
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High
The combine total risk of a Type I and a Type II Error is minimized when 3 sigma limits (SLs) are used. Risk
Low
+/- 1SL +/- 2SL +/- 3SL +/- 4SL +/- 5SL +/- 6SL FIGURE 93 Balancing the risk of a Type I and Type II error
nonlinear manner making things worse. (See the and Leavenworth (1988), Montgomery (1991), reference to Rule 4 of the funnel demonstration Shewhart (1931), Wheeler (1995), and Wheeler in Chapter 7 for more detail on tampering.) Type and Chambers (1992). I errors happen most o en when you decide to use sigma limits on a Shewhart chart that are less than three. On the other hand, the second mistake Do I Apply the Run Chart Rules (a type II error) occurs when you basically do to Shewhart Charts? the opposite of a type I error. In this case, you e simple answer to this question is no. e would conclude that a data point indicates no four run chart rules (a shi in the data, a trend need for action when it fact it reects a special in the data, too many or too few runs in the data, cause. Type II errors lead to under controlling an astronomical data point) should be applied or what Provost and Murray call underreacting. only to the run charts. Shewhart charts have is happens most o en when you decide to use their own rules to determine whether special sigma limits that are wider than plus and minus 3 causes are present. ese rules ae explored next. around the mean. As Carey and Lloyd (2001, p. 67–68) point out, “ e challenge, therefore, is to balance the risk of tampering against the risk of under controlling. In the rst case, you will ▸ Deciding Whether see special causes when they do not exist, and in the second case, you will miss special causes a Special Cause Is when they are present. e combined total risk Present of type I and type II errors is minimized when 3 sigma limits are used.” FIGURE 93 provides a Much of the beauty of the Shewhart charts lies visual of how the total combined risk of two types in their simplicity. ey require just enough data of error is minimized when the limits are set at (about 20 data points) to construct a reliable chart, +/− 3 sigma. ose of you interested in exploring are easy to read, and allow you to determine these issues further should refer to the works very quickly whether special cause variation is of Blumenthal (1993), Deming (1994), Grant present in your data. Shewhart charts, according
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to Pyzdek (1990, p. 90), “are an operational de - ■ Irving Burr recommended using no more nition of a special cause,” which I think is a very than Detection Rules One and Four. appropriate way to summarize the purpose of ■ Ellis Ott recommended the use of Detection the charts. Shewhart (1931, p. 6) also captured Rules One, Two, and Four. the purpose of the charts nicely when he wrote, ■ Lloyd Nelson recommends the routine use “A phenomenon will be said to be controlled of Detection Rules One and Four, along when, through the use of past experience, we can with Test 3 (trends) and Test 4 (sawtooth). predict, at least within limits, how the phenome- non may be expected to vary in the future.” is e selection of the most appropriate rules, acknowledges the fact that no one can predict however, should be linked to the subject matter the exact value of the next data point. But, if you being analyzed, the types of data being collected, understand the di erences between a process and the ability of those who own the processes being in control (i.e., merely random variation) that produce the outcomes to actually move and out of control (i.e., detecting special causes the relevant indicators in the desired direction. in the data) then you will be well on your way to e application of the rules for special understanding Shewhart’s notion of prediction causes to a Shewhart chart begins by dividing within limits. He basically argued that in order the chart into zones. e area between the cen- to understand the variation in a process you terline (CL) (the CL or otherwise known as the needed to move away from static and aggregated mean or average) and the UCL is divided into displays of data and look at the process from a three equal areas or zones. Because the control more dynamic view by plotting the data over limits are referred to as sigma limits, each zone time and understanding the inherent variability is the equivalent of 1 sigma. e area from the in the process. Figure 7-3 (Chapter 7) depicts CL to the LCL is divided in a similar manner. what Shewhart was recommending. ese zones are labeled C, B, and A, respectively For decades the Western Electric Statistical and emanate outward from the CL. FIGURE 94 Quality Control Handbook (1985) has served as provides an example of how a Shewhart chart the standard reference for the special cause rules. is divided into six zones. e creation of zones In fact, in many circles and even in several SPC is a very simple process that can be achieved so ware packages the rules are frequently referred easily with any reputable SPC so ware program. to as the “Western Electric tests for detecting A natural or random pattern of data will special cause.” Although there are dozens of tests bounce around across the zones, between the or rules to detect special causes, most experts in UCL and LCL, and include the following three the eld of SPC maintain that only a few of the characteristics: tests are essential for a basic understanding of what the charts are trying to tell you. Wheeler Note: Each zone is equal to 1 sigma (1995) and Wheeler and Chambers (1992) provide excellent summaries and critique of the Western UCL Electric rules and the variations that have been Zone A +3 SL proposed by leading SPC experts. Consider the Zone B +2 SL Zone C +1 SL following passage from Wheeler (1995, p. 139) X (CL) on this issue: Zone C -1 SL Measure Zone B -2 SL ■ Zone A -3 SL Shewhart used Detection Rule One. LCL ■ David Chambers remarked that “No data set could stand up to the scrutiny of all of Time the detection rules in the Western Electric Handbook.” FIGURE 94 Dividing the Shewhart chart into zones
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■ Most of the data points are near the CL A 3 sigma violation ■ A few of the data points spread out and approach the UCL and LCL ■ None of the data points (or at least only a UCL very rare and occasional point) exceeds the A control limits (Western Electric, 1985, p. 24) B C A natural pattern or random distribution of data CL will exhibit these three characteristics simulta- C neously. One of the rst signals that a process B A has special causes, therefore, is the absence of LCL any one of these characteristics. Because these rules for detecting special causes have grown primarily out of industrial A 3 sigma violation and manufacturing applications, however, we need to evaluate them in light of which rules FIGURE 95 Rule #1: A single data point that are most appropriate in health, education, and exceeds the upper or lower control limit social services settings. We have done this at the Institute for Healthcare Improvement (IHI) statistical way to determine whether, in fact, it is with our colleagues from Associates in Process astronomical. is is the only test that Shewhart Improvement (API)6 and decided that ve of the used to identify special causes and the reason rules for detecting special causes on a Shewhart why Wheeler (1995) stated that “Shewhart used chart are most appropriate for these disciplines. Detection Rule One.” Some texts refer to a single e ve IHI/API rules for detecting special causes data point that exceeds 3-sigma as a “freak” point on a Shewhart chart are: (Pyzdek, 1990). Irrespective of the term being used, a 3-sigma violation is a clear signal that Rule 1: 1 point outside the +/− 3 sigma limits the variation of this single point is very di erent Rule 2: 8 successive consecutive points above from the variation demonstrated by the rest of (or below) the CL the data points on the chart. When you detect a 3-sigma special cause do Rule 3: 6 or more consecutive points steadily not overreact. e rst thing you should do is increasing or decreasing check the data to make sure that the data point Rule 4: 2 out of 3 successive points in Zone is legitimate. For example, if someone used a A or beyond di erent operational de nition for this data point it may in fact be a false positive. is data point Rule 5: 15 consecutive points in Zone C on might also be due to a data collection procedure either side of the CL that sampled the population di erently than Each of these rules is discussed next. the other data points. Finally, it could be due to a strati cation problem. In this case, data may Rule 1: 1 Point Outside the +/− have been pulled from the a ernoon shi when the rest of the chart was based on data sampled 3 Sigma Limits (FIGURE 95) from the day shi . My point is that before you is is usually referred to as a 3-sigma violation and see a 3-sigma violation as a true special cause, is classi ed as a signal of instability in a process. investigate the methods used to gather that data It is also one of the most easily recognized of all point. If the data point was based on the same the tests because it is based on a single data point. operational de nition as the rest of the data and On the run chart this was a visual determination there were no sampling or strati cation issues of the “astronomical data point.” Now we have a then you do in fact have a special cause that
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requires investigation. Why is this data point are observed as a gradual movement of the data statistically di erent from the rest of the data? over time, which is demonstrated as a shi in the e presence of a true special cause provides the process. Ideally this shi would be in the desired opportunity for learning. direction but the shi could also be in the oppo- site direction. e data are neutral. ey do not know if they are in the direction of goodness or Rule 2: 8 Successive Consecutive away from it. is is why it is important that you Points Above (or Below) the apply the statistical decision rules that allow you to know when there is a true signal in the data of a Centerline (FIGURE 96) special cause and when it is just random variation. People generally nd it easy to detect a 3-sigma Although the rule of 8 is a classic Western violation (Rule 1). But, as the Western Electric Electric rule you will see other alternatives o ered Statistical Quality Control Handbook points out (e.g., 7 in a row, 9 in a row or even one approach (1985, p. 26) the data can reect instability even that favors a spread of 8 to 10 in a row). Wheeler when all the data points fall between the UCL and (1995) lists all the various options de ning a LCL. A shi in the process is one such indication of shi that have appeared over the years and o ers instability. Most writers refer to this rule as “eight commentary on which ones he has seen used most consecutive data points on the same side of the o en. My point in even mentioning these alterna- centerline.” When such a pattern is observed, it tives is that you will hear a variety of opinions on signals that there has been a shi in the process. the number of data points used to de ne a shi Another way to think of this rule is that it reects and also on what constitutes a trend (rule 3). e a run of data that has lingered too long above or challenge is if you de ne a shi with say seven data below the mean, which indicates a nonrandom points you may see special causes when they do pattern. is test is a variation on the run chart not exist (i.e., a type I error). If, on the other hand, shi rule but you will notice that it requires eight you choose to use 9 or 10 data points as a shi you data points in a run whereas the run chart rule may fall prone to a type II error, which is missing required six data points to determine a shi . a special cause when it is present. e rule of 8 has is test is one of the original Western Electric been regarded as a solid practical rule and it is the four primary tests and it is a frequent signal on one I and my colleagues at IHI have decided to healthcare charts. As teams work continuously use. It is neither too lenient nor too conservative on improvement strategies, their work typically for health and social service application. Unless produces results that are not immediate and dra- you like to get into rather heavy statistical theory matic in nature (i.e., the 3-sigma rule) but rather debates about which rule is “the best” I’d suggest that you accept a set of rules that are practical and UCL appropriate for your work. A B C CL Rule 3: Six or More Consecutive C Points Steadily Increasing or B A Decreasing (FIGURE 97) LCL is rule detects a trend in the data that Provost and Too many data points in a row below the Murray (2011, p. 117) de ne as “a small, consistent centerline signals a downward shift in the process. dri in a process.” When deciding if a trend exists, duplicate points (i.e., repeating values) should be FIGURE 96 Rule #2: 8 successive consecutive points ignored. is rule engenders considerable debate. above (or below) the centerline First, there is the popular de nition of a trend. We
9781284023077_CH09_211_258.indd 222 31/07/17 5:59 PM Deciding Whether a Special Cause Is Present 223
UCL A
B
C CL C
B
A LCL
Downward trendUpward trend
FIGURE 97 Rule #3: 6 or more consecutive points steadily increasing or decreasing
see a trend in fashion, a trend in food, a trend in is detected when there is “a series of consecutive the stock market, which is usually referring to data points without a change in direction.” At the the fact that the stock market closed higher than IHI we have decided to use the rule of 6 as initially it started the day. I regularly hear the weather de ned by Nelson (1985) and then by Pyzdek reporter on the Chicago TV stations referring to (1990) as a common practical basis for detecting a “trend in the temperature.” In this case, the trend an upward or downward trend in the data. e is usually a comparison of today’s temperature nal point I will make about this particular rule to the average temperature for the past week or is that like Rule 2 this rule engenders considerable month or the comparison of today’s temperature debate. Wheeler (1995, p. 137), for example, states to the temperature on the same day a year ago. that “all of these tests (for a trend) are problem- e point is that there are very popular usages atic.” He o ers a number of reasonable statistical of the word trend and then there are statistical principles as to why he maintains this perspective. de nitions. As we analyze Shewhart charts we Others will argue with you about a trend because de nitely should be using a statistical de nition. they are (1) wanting to see a trend, (2) are using But, I have been in many meetings where people a popular de nition of a trend, or (3) have some interpreting either static or dynamic displays of other statistical reference that says their trend is data have devised their own de nitions of a trend. preferred over the one you propose. So, once again, Over the next week make a mental note of how unless you are ready for these debates I would o en you hear your coworkers or people in the suggest that you accept the rule of 6 as a trend and media look at data and declare a trend is present. see how well it ts with your analysis of the data. People will conclude that there is a “trend” in the data when in fact they are merely comparing two data points. If the second data point is higher than Rule 4: Two out of Three the rst and in the direction of goodness then this Successive Points in Zone A gets labeled as an upward trend. Deming (1992) had a very good bit of guidance: when you have or Beyond (FIGURE 98) two data points, “it is very likely that one will be Another of the classic Western Electric rules for di erent from the other.” instability is when two out of three consecutive e Western Electric handbook does not data points are more than 2 sigmas away from the specify how many data points are needed in order CL. In this particular case, the single data point to identify a trend. ey merely indicate that a trend not in Zone A or beyond can be anywhere on the
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Rule #2: Two out of three consecutive data points that fall in Zone A or beyond
UCL A
B
C CL C
B
A LCL
Rule #2: Two out of three consecutive data points that fall in Zone A or beyond
FIGURE 98 Rule #4: 2 out of 3 successive points in Zone A or beyond
chart. e deciding criterion is whether two out of tail(s) of the distribution when you should in the three successive data points are in Zone A or fact be observing less and less the further you beyond on the same side of the CL. is is one of go out. ere certainly are more complex sta- the rules that is more dicult to explain in words tistical explanations of why this rule detects a than pictures. Observing Figure 9-8 will help in special cause. But as Wheeler points out (1995, understanding this rule. e primary question I p. 135) “this rule provides a reasonable increase get with this rule, however, is “so what?” “Why in sensitivity without an undue increase in the is it that two out of three data points in Zone A false alarm rate.” constitutes a special cause?” First, envision the static normal curve. Slightly over two thirds of the data (68.26%) will fall within ± 1 SD of the Rule 5: 15 Consecutive Points mean. When you go out to ± 2 SDs of the mean in Zone C on Either Side of the you will nd 95.46% of the data. is means that by the time you are out to ±3 SDs from the Centerline FIGURE 99 mean you should be observing 99.73% of all the is test is generally described as reecting an data in the distribution. But, because the normal issue with strati cation. Strati cation usually curve theoretically extends in nitely in either indicates that two or more di erent causal sys- direction you do not account for 100% of the tems are present in every subgroup. is pattern data. Now let’s get back to the two out of three of strati cation is also known as “hugging the data points in Zone A of a Shewhart chart. As centerline” because there is a run of 15 or more you go out the tails of the normal distribution data points within 1 sigma of the CL (i.e., in Zone you should expect to see less data. e two out C above or below the CL) and the variation is of three rule, therefore, is signaling that you relatively small for these data points compared are observing too much data bunching in the to the width of the UCL and LCL. Strati cation
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UCL A
B
C CL C
B
A LCL FIGURE 99 Rule #5: 15 consecutive points in Zone C on either side of the centerline
occurs most o en because the data collection plan was awed. For example, you will nd a ▸ Deciding Which strati cation pattern when two separate distri- butions of data have been collected (e.g., day shi Shewhart Chart turnaround time was combined with night shi Is Most Appropriate turnaround time) or the sample of data points was drawn from two di erent distributions of data. Although there is only one way to make a run Even though we have these rather speci c chart, there are numerous ways to make a She- statistical rules for determining special cause whart chart. e basic design and look of any variation that are grounded in decades of testing in Shewhart chart is essentially the same as shown manufacturing settings, I think it is important that in Figure 9-1 (i.e., data plotted over time, the when we apply these rules to healthcare situations mean of the indicator as the CL and the calcu- we apply them with a serious dose of common lation of the UCL and LCL). Furthermore, the sense. For example, if we are trying to improve charts are all grounded in established statistical food tray delivery time we may be willing to fully theory and are all interpreted in terms of the accept six data points constantly increasing as a fundamental ideas related to common and trend. But, on the other hand, if we are dealing special causes of variation. But, there are many with wrong site surgeries we may not want to di erent types of Shewhart charts and the user wait until we have six occurrences of wrong site needs to know which one is most appropriate surgery to declare a trend and then take action. As for the indicator being studied. e variety of my colleague Dr. Ray Carey (2003, p. 19) wrote: Shewhart charts is summarized by Benneyan “When the well-being of patients is at risk, a case et al. (2003, p. 16): can be made for using 2-sigma limits as ‘early warning limits’ or for using 6 rather than 8 points ere are at least a dozen di erent to detect a shi .” In these situations, clinicians types of control charts in common use would still be looking for signals of special cause in manufacturing and other industry, so they do not over react to a single data point. with three or four new types being But, they would use the data not necessarily to developed each year. e various types justify changing the system but rather as a basis di er by the statistic plotted (e.g., av- to investigate potential instability in their process erages, percentages, counts, moving that could cause harm to patients. Wheeler and averages, cumulative sums, etc.) and Chambers (1992) refers to this as having a process the distribution assumed (e.g., normal, on the “brink of chaos.” Statistical decisions must binomial, Poisson, geometric, etc.). All be moderated with and ltered through a healthy have di erent formulae for calculating dose of common sense and rational thinking. centerlines and control limits.
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If there are all these di erent types of Shewhart ■ Blood glucose readings charts how do you decide which one is the most ■ e number of procedures or tests performed appropriate for your data? e decision involves ■ e number of surgeries done each day two rather simple steps: (1) deciding on the ■ Financial measures such as revenue, oper- type of data you have collected and (2) deciding ating margin, or expenses which of the various Shewhart charts is the most ■ Duration of a surgical procedure in minutes appropriate for this type of data. or hours
Attribute data are essentially counts of events that can be placed into discrete categories. Unlike ▸ Types of Data measuring a patient’s weight on a continuous scale, attribute data are looking at characteristics that e rst step in selecting a Shewhart chart is to can be classi ed and placed into categories or determine the type of data you are collecting. “buckets.” For example, any time you are measuring ere are basically two types of data: (1) variables mortality you are using attribute date (the patient data (also known as continuous, interval, ratio, is either alive or dead). Similarly, pregnancy is an or measurement data depending on your back- attribute indicator. ere are only two outcomes: ground and training) and (2) attributes data the woman is either pregnant or not pregnant. (also known as classi cation or count data). e A woman does not proudly announce that she term used to identify the type of data is a matter is 53.9% pregnant. is is essentially a binomial of taste and preference. Most SPC books will outcome. Attribute data can be further divided use the terms variables or continuous data and into two subdivisions, defectives and defects. attributes, classi cation, or count data. What is Defectives (also known as nonconforming more important than the terms you choose to units) require that you have a count of the total use are the concept the terms are capturing and number of items or events being observed or how you apply them to your data. In this text, produced and the number of items from this total I use the terms variables and attributes data as that were not acceptable. e unacceptable items or the primary categories. FIGURE 910 provides events become the numerator and the denominator examples of these two types of data. is the total number of items or events observed. Variables data can be measured along a When you know how many items out of the total continuous scale. In Figure 9-10 this type of data is are unacceptable you can either plot the number depicted as money, time, weight, length, and tem- of defective items on your Shewhart chart or you perature. Consider the ruler as a form of variables can compute the percent of defectives. When we data. It has equal appearing intervals that can be compute a percentage, therefore, we are basically divided into as many subdivisions as your calibration determining what proportion or percentage the instruments will permit. With variable data you numerator is of the denominator. e standard can perform all the mathematical function. Data terminology used in most SPC books to de ne measured this way can be either counts of whole defectives is that you know both the occurrence numbers or they can have decimals or fractional of the defective product or service (the numer- parts. Examples of variables data include: ators) and the nonoccurrences (defectives plus ■ Wait times in the emergency department (ED) nondefectives which when added together form ■ Turnaround time for a lab test the denominator). Knowing these two pieces ■ Blood pressure readings allows you to calculate a percentage or proportion ■ Newborn weight (measured in grams or of defectives. Keep in mind that when you use pounds and ounces) percentages you are comparing the same types of ■ international normalized ratio (INR) and items, products, or services. If you are looking at prothrombin times (PTs) the percentage of food trays delivered late to the
9781284023077_CH09_211_258.indd 226 31/07/17 5:59 PM Types of Data 227
Variables Data
© Pedjami/Shutterstock
© Ultrashock/Shutterstock
© Butterfly Hunter/Shutterstock
© Paul Velgos/Shutterstock © Lipskiy/Shutterstock
Attributes Data
Defectives Defects (occurrences only) (occurrences plus Nonconformities non-occurrences) Nonconforming Units
© HeinzTeh/Shutterstock
FIGURE 910 Examples of variables and attributes data
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patient, for example, you will have the number of report that she just stuck herself. A er you try to late food trays as the numerator and total number calm her down and explain the next steps you will of food trays produced as the denominator. In take, you do not say, “Oh by the way, how many this case, you have trays divided by trays—like times didn’t you stick yourself today?” Similarly, if divided by like. e only attribute that is di erent a nurse asked a patient, “How many times didn’t for classi cation purposes is whether the food you fall today?” she would probably get a rather tray was delivered late to the patient. is is an confused look from the patient. important distinction to keep in mind because When you are dealing with defects you need as we move next to de ne defects, this condition to remember that a count of the number of falls, will not hold. In summary, data classi ed as de- needle sticks, or medication errors gives you a fective can be divided into one of two categories numerator but you do not have a denominator. So (i.e., a binomial situation) when you know both you cannot compute a percentage. So, you either the occurrences and the non-occurrences of an just count the number of defects as whole numbers event. Examples of this form of classi cation in- (e.g., the total number of falls today was eight) clude conforming/not conforming to standards, or you create a falls rate. A rate is a ratio (i.e., it harm/no harm, go/no-go, pass/fail, OK/not OK, has a numerator and a denominator just like a complete/ incomplete or present/absent. proportion or percentage) but the two numbers Defects pose an interesting challenge. Defects you are using to form this ratio are not alike. For occur and can be counted. But, how do you count example, when we compute an inpatient falls rate all the nondefects? Stated di erently, you know by month we have the number of inpatient falls when a defect occurs (the occurrence of an event) (including multiple falls) for the month as the but you do not know when the nondefects or numerator and the denominator is usually the nonoccurrences happen. I know, at this point you total number of inpatient days for the month. Now are thinking, “ is makes no sense.” When I rst we have falls divided by days, two unlike things. heard this statement it did not make a lot of sense e resulting number is reported as so many to me either. Examples should help to clarify this falls per 1,000 patient days. Any time you report concept. Look down at the rug in your oce or that there are so many defects per 1,000, 10,000 in your family room. How many spots, stains, or or 100,000 units (e.g., inpatient days, medication snags do you nd in the carpet? For argument’s orders, lab tests, or surgeries) you have just created sake I’ll imagine that you found three dirt spots, a rate. Note that when you see the little word per two co ee stains, and four snags on the carpet. included with the name of a measure you know Now, count the number of nonstains on the carpet? that it is a rate and not a percentage. Most of the How did you do? You cannot count the nonstains patient safety indicators as well as epidemiology or blemishes on the carpet. is is an unknown. indicators are constructed as rates (e.g., patient Similarly, when the highway department records fall rate, restraint rate, surgical site infection trac accidents they do the same thing. ey can rate, ventilator-associated pneumonia (VAP) count how many accidents occurred today on a rate, needle stick rate, or medication error rate). particular segment of the highway but they have e other characteristic of a rate is that the no idea how many nonaccidents there were today. numerator of a rate can be larger than the denom- ere are times, therefore, when we know the inator. For example, if you had a 20-bed unit and occurrence of an event when the nonoccurrences each patient fell two times you would have 40 falls are unknown and unknowable. for 20 patients. What do you call this? Is it 200% In health care, we experience this situation with falls? No. If you wanted to use a percentage you patient falls, needle sticks, nosocomial infections, would have to make a di erent indicator, which medication errors, and liability cases. We know would be the percent of patients who fell once or only when the event happens. ink of needle more while they were with us. In this case, we do sticks. A sta member comes into your oce to not care about the total number of falls, which
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OK? If Ye s, then the car is fit to be shipped out!
Not OK? If No, then the car is classified as being “defective” but we do not know why it is defective (not fit to be shipped) until we inspect it and count the number of specific “defects” that make the car “not OK” or defective.
FIGURE 911 Defectives versus Defects Ed Aldridge/Shutterstock
includes duplicates. All we are concerned with is defects: one headlight does not come on (defect at the time of discharge did this patient fall once 1), the driver’s side door does not close ush with or more, yes or no? Basically if the indicator is the the body (defect 2), and the driver’s seat moves percentage of patients who fell we do not care if backwards but not forward (defect 3). e entire they fell more than once. But, because patients car is classi ed as defective but three defects have can fall more than once, and we are concerned been discovered. e next car is also classi ed as about this problem, we generally do not use the defective but it has only one defect (the oil pressure percentage of patients who fell as a binomial in- warning light on the dashboard does not go out dicator (i.e., fell/did not fall). If we are concerned a er the speci ed period of time). In summary, about the magnitude of the falls and severity we defects or nonconformities are the speci c things typically track all falls, which means that we have that make a product or service defective. Once you the possibility of having a numerator that is larger understand the distinctions between defectives and than the denominator. When this can occur, we defects you will be well on your way to selecting normalize the total number of falls by creating a the most appropriate Shewhart chart. To help you rate (e.g., 3.2 falls per 1,000 inpatient days). A nal in building your skills in di erentiating between point about defects is that they usually occur less defectives and defects refer to EXERCISE 91. For each o en than indicators measured by a percentage. indicator listed decide if it is describing a defective FIGURE 911 provides an easy way to remember or defect. e answers to this exercise can be found the di erences between defectives and defects. When at the end of this chapter. cars come o the assembly line they get inspected. If the car is determined to be acceptable by the inspectors it is t to be shipped to a dealer. But, if the inspectors nd one or more things wrong with ▸ Types of Shewhart the car it is not t to be shipped. In this case, the car Charts would be classi ed as being defective. is t to ship determination is a binomial decision: the car is okay A er determining whether your data are variables or the car is not okay to be shipped. At the end of or attributes, the next step is to decide which She- the shi the inspectors take all the defective cars and whart chart is most appropriate for the type of data provide a summary of why each car was classi ed you have collected. Seven basic control charts are as defective (i.e., as a nonconforming unit). is is regularly described in the literature and taught in where the defects come into the picture. e rst most classes and seminars on SPC. A er working defective car has a summary report pasted to the with the charts for over 15 years, however, I have windshield. It reads that this defective car has three found that ve of the seven charts are the most
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EXERCISE 91 Defective or defect? You make the call!
Defective Defect Indicator (Classification) (Count)
1. Number of accidents per 1,000 employee days
2. Number of errors per 25 food trays
3. Percentage of acute myocardial infarction (AMI) patients receiving aspirin within 24 hours of arrival in ED
4. Percentage of inpatient deaths each month
5. Number of surgical complications per 1,000 surgeries performed
6. Proportion of hand hygiene observations done incorrectly
7. Number of falls per 1,000 patient days
8. Number of medication errors per 10,000 doses dispensed
relevant and frequently used with healthcare, that you read beyond what I summarize in this social services, and educational indicators. I focus chapter. As I mentioned earlier in this chapter, on these ve Shewhart charts but encourage you by reading the explanations of di erent authors to explore the full range of charts as discussed in describing Shewhart charts and their uses you the Western Electric Statistical Quality Control will build knowledge on how to use them with Handbook (1985), Wheeler (1993, 1995), Wheeler your own improvement e orts. and Chambers (1992), Carey and Lloyd (2001), Carey (2003), Duncan (1986), Pyzdek (1990), Kume (1996), and Provost and Murray (2011).7 ▸ Defining the Key Terms FIGURE 912 presents the Shewhart chart decision tree with the ve control charts that Before addressing the details related to each of have the most relevance to health care, social the reviewing the ve basic Shewhart charts service and educational indicators. Two of the shown in Figure 9-12, however, is it necessary ve charts are used with variables data (i.e., X-bar to review three key terms that play a critical and S chart and the XmR chart) and three of the role in helping you work your way successfully charts are used with attributes data (i.e., p-chart, through the Shewhart chart decision tree shown u-chart, and c-chart). Each of the ve charts is in Figure 9-12. ese key terms are subgroup, described next and examples of how to apply observation, and area of opportunity and are the charts are o ered. I would suggest, however, summarized in FIGURE 913.
9781284023077_CH09_211_258.indd 230 31/07/17 6:00 PM Defining the Key Terms 231
Variables data Decide on the type of Attributes data data
More than one Occurrences and observation per Ye s No nonoccurrences? subgroup? No Ye s
Is there an equal Ye s area of No opportunity?
X-bar & S XmR c-chart u-chart p-chart
Average and Individual The number of The defect The proportion Standard measurement defects rate or percentage of deviation defectives
FIGURE 912 The Shewhart chart decision tree
Subgroup Observation Area of Opportunity
How you organize your data (e.g., The actual value (data) you Applies to all attributes or by day, week, or month) collect counts charts The label of your horizontal axis The label of your vertical Defines the area of frame in Can be patients in chronological axis which a defective or defect order May be single or multiple can occur Can be of equal or unequal sizes points Can be of equal or unequal Applies to all the charts Applies to all the charts sizes
FIGURE 913 Defining Subgroup, Observation, and Area of Opportunity
Subgroup axis of the chart. e subgroups will be arranged in chronological order of occurrence. When deciding e subgroup de nes how you have organized your on a subgroup you should strive to select them so data and usually captures some dimension of time that if special causes exist the chances for di erences such as when patients show up for an appointment, between subgroups will be maximized, whereas the day of the week, week, or month. e subgroup chances for di erences due to special causes within will be the label you place on the horizontal or x
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a subgroup will be minimized (Duncan, 1986; month we have 30 or 31 days, upwards of Montgomery, 1991). e traditional subgroups 90 shi s in a hospital, and approximately for Shewhart charts have been: 720 hours in which to deliver care. Why would we want to aggregate all this activity ■ An individual patient as the subgroup in into a monthly average or monthly total? which case you would order the patients Monthly data frequently lead people down along the x axis of the chart in the order the path of judgment or accountability not that they presented themselves in the oce. quality improvement (QI). In my view, a Patient 1 arrived at 9:00 a.m., patient 2 at primary reason we have so many health- 9:25 a.m., patient 3 at 9:50 a.m. and so on. care indicators structured around monthly ■ A day as your subgroup in which case you subgroups is that this is how nancial and would have Monday, Tuesday, Wednesday, etc. resource allocation systems are organized. across the x axis. en each day you would In health care, work is being produced select either all of the patients or a sample of every minute of the day not in monthly them and record their wait times. blocks. Patients are waiting to be seen, ■ A week the subgroup and you would label the have tests performed, or surgery started. x axis as Week 1, Week 2, Week 3, etc. You eir focus is on minutes or possibly hours would then have to decide if you were going not months. Administrators and managers to track the wait time for all the patients in a think in terms of months but patients think week or just a sample. Usually when a week about the here and now not in monthly or even a 2-week period is selected as the aggregates.8 e other challenge with using subgroup and patient wait time is the indicator month as a subgroup is that the variation of interest you would probably want to draw in the indicator of interest is usually not a sample of the patients. A total enumeration visible because the data is aggregated into would probably provide more data than you an average. Although administrators, man- need and create data collection challenges. agers, and policy makers frequently rely on ■ A month is a frequently used period of aggregated data and summary statistics to time for a subgroup. But it is not always make decisions, no customer, patient, or the best block of time in which to think service user cares about the average. ey about improvement or understanding are concerned about why they or their loved variation. Remember that the Shewhart one are not getting service or treatment charts are designed to help you understand now. A patient takes no comfort in being the variation in a key process indicator as told that the average wait time to see the close to the production of the indicator as doctor last month was only 49 minutes. Or possible. In manufacturing, they evaluate a physician waiting for her stat lab result to products and services on an hourly, shi , come back will rightfully be irritated if she or daily basis. Although they may aggregate is told “We don’t have your result quite yet the key indicators for management reports but don’t worry, the average time to get a by month or quarter the ability to improve result last month was only 63.5 minutes.” quality and insure reliability does not come My point is that although we have a ten- by looking at monthly or quarterly averages. dency to fall back on making month the It comes by looking at production almost subgroup for many healthcare indicators as it happens. In health care and many there is no reason to do so. I have made social services, there is a strong tendency many charts for teams that are collecting to track indicators by month or even quar- monthly data. But each time this happens ter. is is what I refer to as the tyranny I make sure we have a discussion about of monthly data. ink of it this way: in a what is the smallest unit of time that we
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could gather data on. Using month as a occurrence and nonoccurrences of the events subgroup should be a fallback option not being studied. If you answer “yes” to this question the rst choice. you will be able to calculate either the proportion ■ Finally, it is probably quite evident at this or percentage of defectives and proceed to make point that it is not advisable to use quarters a p-chart. If you respond that you do not have as a subgroup choice because quarterly data the occurrences and nonoccurrences you are represent a very long time period and the le with having only the occurrence of an event variation you are interested in understanding when the nonoccurrences are not know. As was has been aggregated and therefore severely mentioned previously, this gives you a count of dampened. Quarterly data can lead only to the defects and you will make either a c-chart or judgment not improvement. a u-chart. e decision to make a c- or u-chart is based on your answer to the following question: “Is there a relatively equal area of opportunity Observation for the defect to occur?” If you respond “yes” to As the term implies this is the actual piece of data this question you will make a c-chart, which is or the measurement that you record or observe a plot of the number of defects occurring within (e.g., turnaround time for a lab test or medication each subgroup (e.g., a count of the number of order, blood glucose readings for a patient, or falls occurring each day). If you respond “no” to time to administer beta blockers to heart attack this question (i.e., there is not an equal area of patients in the ED). e vertical axis label on the opportunity for a fall to occur) then you would chart de nes the observation and the units of make a u-chart, which would be a plot of the measurement along the y axis show the potential defect rate by subgroup (e.g., 3.2 falls per 1,000 distribution of these values. An observation patient days). So, it really does not matter if you can be classi ed as either variables or attribute respond “yes” or “no” to the area of opportunity data (e.g., time, money, weight, a percentage of question. Consider it essentially a ltering ques- defectives, a count of defects, or a defect rate). tion that will help you select the correct chart for For example, if your indicator is wait time to see your indicator. As each chart type is explained the doctor in a clinic your observation will be the use of these terms is demonstrated. the actual wait time in minutes that occurs from e terms used in the Shewhart decision tree when the patient checks in at the registration (Figure 9-12) and summarized in Figure 9-13 are desk until she is seen by the doctor. is amount not only central to understanding SPC theory but of time will be what gets plotted on the chart. also from a practical perspective, understanding erefore, the dot on the chart, or the “doink” the terms subgroup, observation, and area of as I like to refer to it, represents the quantitative opportunity are essential in the operation of SPC aspect of the indicator you are observing during so ware packages. Many of the SPC so ware the de ned period of time (i.e., the subgroup). packages I have used explicitly ask you to identify the subgroup and the observation or some variant of these terms. Although most so ware appli- Area of Opportunity cation do not ask you the “area of opportunity” All Shewhart charts must have a subgroup and an question, understanding this concept is critical observation clearly de ned or the chart cannot to selecting the most appropriate chart for your be constructed. When we move to the right side indicator. With these basic terms in mind, we of the decision tree (Figure 9-12) and consider can start using the Shewhart chart decision tree the attributes charts, discussed in detail later, a to understand the conditions that will lead us to third term comes into play. Notice that the rst select each chart. We will start on the le side of decision point when dealing with attributes the decision tree and address the variables data charts is determining whether you have both the charts then move over to the attributes charts.
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X-Bar and S Chart If the subgroups are of unequal size, however (e.g., on Monday, we sample 10 patient wait e le side of the Shewhart decision tree times, on Tuesday, we had 15, and Wednesday, (Figure 9-12) follows a pathway to two charts. we collected 20 wait times) the UCL and LCL e rst one is referred to as the average (X-bar) will not be straight lines. Instead, they will be and SD (S) chart. It is the most powerful of the what are called “stair-step” control limits as ve Shewhart charts because it has multiple shown in FIGURE 915. With an unequal sub- observations of continuous data that have been group size the amount of data varies within organized into subgroups. In this case, the “doink” each subgroup and so the dots on the chart on the chart (i.e., the plotted dot) has multiple (i.e., the observations) each have their own “doinkettes” (i.e., observations) going into it. For individual UCL and LCL calculated. With more an X-bar and S chart the subgroups can be of data the limits are tighter and with less data in equal size or unequal size. If the subgroups are each subgroup the limits are wider as shown in of equal size (e.g., a strati ed random sample of Figure 9-15. Day 4 in Figure 9-15, for example, 15 patients is selected each day and their wait has tighter limits indicating that there is more times to see the doctor are recorded) then the day being collected on this day. Day 9, on the UCL and LCL on the chart will be straight lines other hand, has wider limits due to less data FIGURE 914 as shown in . being collected on this day.
X-bar chart: patient wait time 60.0 UCL 50.0
40.0
30.0 LCL 20.0
Wait time in minutes Wait 10.0
0.0 123456789101112 13 14 15 16 17 18 19 20 21 22 23 24 Week
S chart: patient wait time 18.0 16.0 UCL 14.0 12.0 10.0 8.0 6.0 4.0 Standard deviation Standard 2.0 0.0 123456789101112 13 14 15 16 17 18 19 20 21 22 23 24 Week
FIGURE 914 X-bar and S chart with straight control limits due to equal subgroup sizes
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140
137 UCL = 135.22 134
131
128 CL = 127.333
124 Average (mmHg) Average 121 LCL = 119.44 118
115
20 16 12 UCL = 12.071
Sigma 8 CL = 6.129 4 0 LCL = 0.186 12345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Day FIGURE 915 X-bar and S chart with stair-step control limits due to unequal subgroup sizes
When you make an X-bar and S chart most In Figure 9-15 the indicator of interest is a so ware programs will give you the option of patient’s systolic blood pressure. e patient re- producing two charts as shown in Figures 9-14 corded several blood pressure readings each day and 9-15. e top chart is the X-bar chart or (a minimum of three and a maximum of ve each average chart and the bottom chart is the S chart day). As a result the subgroups are of unequal sizes, or SD chart. e X-bar chart is considered to which produces the stair-step control limits. If the be the primary chart. Both charts have three patient had recorded exactly the same number main components: (1) the CL or average, (2) of blood pressure readings (observations) each the UCL, and (3) the LCL. e X-bar chart day (e.g., four) then the UCL and LCL would be will show the average of the data within each straight lines. As you will see in subsequent ex- subgroup and the lower chart (the S chart) amples, stair-step control limits will also be found shows you the SD for each subgroup (i.e., each on p- and u-charts. As was mentioned above, on dot) plotted on the X-bar chart. In Figure 9-14, those days when more data were collected (e.g., for example, Week 1 on the X-bar chart has an Day 4 in Figure 9-15) the control limits will be average wait time of 38 minutes and an SD of 5 tighter. On days when fewer data were collected minutes (seen on the bottom chart). On Week (e.g., Day 9) the limits will be wider. 2 the average wait time is 39.7 minutes and the e upper chart in Figure 9-15 reveals SD is 7.2 minutes. So for each week we can see the average systolic blood pressures by day what the average wait time is and the amount and the overall average. e lower chart shows of spread around that average for this week as the SD for each day as well as the average SD measured by the SD. across all 25 days.9 e average systolic blood
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pressure shown in the top chart for the patient (1992), Western Electric (1985), and Provost and in Figure 9-15 is 127. Note that the decimal Murray (2011). places on the chart can be ignored in this case because this is entirely too nite a reading for blood pressure results. e degree to which you XmR chart or the I-chart can control the decimal places on a chart will e XmR chart is also known properly as the depend on the so ware being used. e average Individuals and Moving Range chart. But it UCL is 135 whereas the average LCL is 119. can also be referenced as the Individuals chart Because this chart reveals only common cause or simply the I-chart. e key characteristic of variation, the way to describe the performance of this chart is that each subgroup contains one this patient’s systolic blood pressure this chart is and only one individual observation or bit of data as follows: “On the average this patient’s systolic (i.e., the “doink” on the chart has only 1 bit of blood pressure is 127. It could go up as high as data and no “doinkettes” as we discovered in the 135 on any given day or down to 119 and that X-bar and S chart). In the Shewhart decision tree is the natural rhythm of this patient’s systolic (Figure 9-12), this decision point is identi ed blood pressure process.” by the question “More than one observation e lower chart is the S-chart. is chart for each subgroup?” When the answer is “no” has two primary purposes. First, it helps you then the chart of choice is the XmR chart. Like to understand the variation that exists within the X-bar and S chart, you will typically get each subgroup (i.e., day). For example, the SD two charts when you request this type of chart for Day 4 is around 4. On Day 9 the standard from your SPC so ware. e X chart shows the deviation is about 3 mmHg. As you look at values for the individual data points as well as the each day, therefore, you will see that there is a average for all the individual data points. e mR di erent average and standard deviation which chart documents the “moving range.” e XmR reects the variation in this patient's blood chart is typically used when you are interested pressure over time. e second purpose of the in answering questions such as: S-chart (i.e., the bottom chart) is that the av- ■ How many surgeries do we do each week? erage SD (the CL) is used in the calculation of ■ What is the cost of each knee replacement the control limits for the average (upper) chart. surgery? In this case, the average systolic blood pressure ■ How long does each patient wait before (i.e., CL) is 127. What is important to realize is being seen by the doctor? that if the SD chart reveals wide variation, then ■ How many home care visits do we conduct the average SD will likewise be large. Because each week? the average SD is used to compute the UCL and ■ How many calories do I eat each day? LCL, a large SD will also contribute to making ■ What is the length of stay for each coronary the control limits of the top chart (the average artery bypass gra (CABG) patient? chart) wider. e relationship of the two charts must be understood together. is chart is used frequently to address questions I do not intend to elaborate on the statistical related to volume, frequency of events, or nancial formulae for the calculation of the control limits. issues. Note that you are not interested in nding It is important to realize, however, that each out what percentage of surgeries started late (this Shewhart chart has a di erent set of formulae to would be considering a late surgery start classi ed calculate the chart’s UCL and LCL. For additional as a defective, which would require a p-chart), details on calculating the statistical parameters but rather you merely want to know how many for the various Shewhart charts readers should surgeries are done in the course of a day or a refer to Wheeler (1995), Wheeler and Chambers week. In this case, the day or week becomes the
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subgroup (x axis label) and the total number of dashed lines that divide the chart into three areas surgeries completed each day or week becomes above and below the CL. As was discussed earlier the individual observation for that week (i.e., the in this chapter, the zones are used to assist in dot on the chart). In short, the XmR chart can identi cation of special causes. Typically, and you be used in many situations. Remember, however, will see exceptions to this point, the zones are used that the indicator being placed on the XmR chart when you have a chart with equal subgroup sizes. is not being classi ed as a defective or defect. e bottom chart is referred to as the moving When you use the XmR chart you will usually range chart. e moving range is derived by calculating be asking a more neutral question such as “How the simple di erence between two successive data many of procedure X do we do?” points on the Individuals chart and then plotting FIGURE 916 provides an example of an XmR this di erence on the mR chart. is is also referred chart. In this particular example, the indicator of to as creating an arti cial subgroup of 2 since each interest is the total number of U.S. dollars saved subgroup on the chart initially contains only 1 bit each month as a result of implementing a new of data. ese steps are highlighted in Figure 9-16 transcription system for radiology. Note that like by the circles drawn around each neighboring data the X-bar and S chart there are two charts. e point on the top chart and the corresponding arrows top portion of the chart provides a plot of the that point to the mR value between the coupled individual data points along with the average of data points on the lower chart. Notice that the rst all the data points and the UCL and LCL. is three data points on the mR chart (Months 2–4) chart also has the zones identi ed. ese are the are relatively close together. is is due to the fact
5750.0
5500.0 UCL = 5470.10 5250.0 A 5000.0 B
d 4750.0 ve 4500.0 C 4250.0 CL = 4360.90 C Dollars sa 4000.0 3750.0 B
3500.0 A 3250.0 LCL = 3251.70 3000.0
1500.0 UCL = 1362.79 1000.0
500.0 CL = 17.20
Moving range Moving 0.0 LCL = 0.00 123456789 10 11 12 13 14 15 16 17 18 19 20 21 Month FIGURE 916 XmR chart for the total amount of dollars saved each month in radiology transcription
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that there are small di erences between the rst does not have a neighboring data point to be com- four data points that have been coupled together pared with until the data for Month 2 is posted. on the Individuals chart. If you look at data points erefore, there is no moving range for Month 1 for Months 15 and 16, however, you see a very on the mR chart, which is identi ed by the triangle di erent picture. e di erence (i.e., the range) surrounding Month 1. is will always be the case between Months 15 and 16 is much larger ($938 when you use an XmR chart. to be exact) than any of the ranges found when the EXERCISE 92 (You make the call: Is it an X-bar rst four data points were compared. In short, the and S chart or XmR chart?) will test your ability to individual values when coupled together produce determine whether a particular indicator should an arti cial subgroup of two, which you must have be placed on an X-bar and S chart or an XmR in order to calculate a range and subsequently the chart. Answers to this exercise may be found at moving ranges. One nal thing to note about the the end of this chapter. XmR chart. e mR chart will always have one less When we move to the Attributes side of the data point on it than the Individuals chart. is Shewhart chart decision tree (Figure 9-12), we is due to the fact that the rst data point (Month 1) need to address two questions:
EXERCISE 92 Is it an XmR (I) or X-bar and S? You make the call!
X-Bar and XmR Indicator S Chart (I Chart)
Time to clean an inpatient room (in minutes)
Patient satisfaction scores for subgroups of 15 patients in the outpatient clinic
Average turnaround time for all STAT labs done each day
Cost for each normal delivery
A diabetic patient’s 3x a day blood sugar readings
Average length of stay for a subgroup of 20 intensive care unit (ICU) patients
The distance (in feet) that a sample of 10 knee replacement patients can walk in 15 seconds
■ Do we have the occurrence and nonoccur- equal opportunity for a defect to occur?” rences of an event? If “yes” then we make a If we have an equal opportunity for a p-chart (i.e., a percentage chart) defect to occur we make a c-chart. If not, ■ If the answer is “no” meaning that we then we make a u-chart. e details are have only the occurrence of an event (i.e., explained next. a defect when we do not know the non- We start with the rst question and address the defects) then we need to ask, “Is there an use of the p-chart.
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P-Chart denominators for each dot on the chart are not equal and spread from a minimum of 326 cases e p-chart derives its name from the fact that (Month 3) to a maximum of 1,041 (Month 15). either a percentage or a proportion is what you Notice that the smallest denominator (326 for actually are plotting on the chart. Most of the Month 3) has the widest control limits whereas time the percentage will be the statistic of interest the largest denominator (1,041 for Month 15) has rather than the proportion. When you make a the tightest set of control limits. e numerators p-chart, or any other attributes chart, you will get go from a low of 75 readmissions (Month 3) to a only one chart (unlike the variables charts which high of 249 in Month 16. If the distance or spread gives you two charts). e p-chart is used to between the stair-step limits is relatively small monitor the proportion or percentage of defectives this means that the denominators are relatively when you know the occurrence of the defective close in size. product, unit, event, or service (the numerator) Finally, it should be noted that if the sub- and the nonoccurrences (the denominator, groups (the denominators) were of equal size, the which is the total being observed). is chart is control limits on the p-chart would be straight. used frequently in healthcare settings because But because most healthcare indicators that we track many indicators that look at accuracy, are de ned as percentages di er from one sub- completeness, errors, or the percentage of some- group (i.e., time period) to another (e.g., we do thing done or not done (e.g., cesarean sections, not have the same number of deliveries each completed history and physical reports, proper month, produce the same number of food trays hand washing, or compliance with a standard each day, or have the same number of patients FIGURE 917 protocol). provides an example of visit at clinic each day) we usually do not have a p-chart with stair-step control limits. In this equal subgroups when calculating percentages case, the indicator is the percentage of hospital or proportions. erefore, most p-charts will readmissions for home healthcare patients. e generally have stair-step control limits.
35.0
30.0
25.0 UCL = 24.59
20.0 CL = 20.64
LCL = 16.68 15.0
10.0 Denominator = 1041 (tightest limits) Percentage of readmissions Denominator = 326 5.0 (widest limits)
0.0 12345678910111213141516171819 Month
FIGURE 917 p-chart on the percent of hospital readmissions for home healthcare patients
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C-chart ■ Medication errors ■ Central line infections e c-chart and the u-chart are the Shewhart charts of preference when you are tracking defects. Figure 9-1 was used to show the elements of a e c-chart is the appropriate chart when you Shewhart chart. It also provides an example of have an equal area of opportunity for a defect a c-chart. In this example, the customer service to occur. As shown in Figure 9-13, an area of manager of a large medical group is interested in opportunity has the following characteristics: charting the total number of patient complaints received each week at 17 sites of care. Because ■ It applies to all attributes or count charts each patient could le more than one complaint, (c, u, and p) complaints are viewed as defects. e alternative, ■ It de nes the frame or area in which a considering the registration of a complaint as defective (i.e., a nonconforming unit) or a defective, is not selected because this would a defect (i.e., a nonconformity) can occur preclude counting more than one complaint from ■ It can be of equal or unequal sizes. an individual patient. Remember that defectives A manufacturing example may help clarify this are based on the binomial distribution (i.e., the concept. Imagine that you work on a paint line at patient complained or did not complain). If you an automobile manufacturing plant. If you were approached this indicator as a defective you assigned to paint the hoods of a single model would not be concerned with the magnitude of of a car (e.g., a Ford Taurus) there would be an the complaint problem (i.e., the total number equal area of opportunity for a paint blemish of complaints) but rather with the fact that a because all Ford Taurus hoods are the same size. patient complained or did not complain and In this case, we would make a c-chart and plot you do not care if a patient complained more the total number of paint blemishes (defects) than once. Measuring complaints as a defective on each hood you paint. Because each hood has would produce a percentage of patients who the same number of square inches of surface complained (a p-chart). As a defect, however, area there is a constant area of opportunity for we are concerned with the magnitude of the a paint blemish. problem so we count the total number of com- e challenge now becomes determining plaints, including multiple complaints from the when this equal area of opportunity condition same patient. e c-chart is selected because the exists in healthcare settings. One of the more volume of patients seen at the 17 clinics Monday frequently used examples of how this might occur through Friday remains fairly constant each week is with monitoring patient falls. If you conclude and the number of sites included in the study that there is basically an equal opportunity for does not change. ese two conditions allow the a patient to fall each day of the week at your manager to assume an equal area of opportunity hospital, rehabilitation facility, or long-term care for a complaint to occur. She merely counts the facility, then you would merely count the num- total number of complaints received each week ber of falls occurring each day, week, or month and plots this number on a c-chart. e chart and plot the number of falls on a c-chart. Other produces a CL (average number of complaints) indicators that could be placed on a c-chart if and a UCL and LCL. the equal area of opportunity assumption was A frequent challenge with using the c-chart met include the number of: for healthcare applications is that the condition of equal area of opportunity may not be met. ■ Patient restraints Frequently in healthcare settings there are few ■ Lawsuits indicators that have equal areas of opportunity. ■ Patient complaints e severity of a patient’s condition can change ■ Needle sticks
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quickly, the census can show uctuations, the actually means. An example should help clarify clinic is not a 7 days a week operation, the volume how these are opposite sides of the same coin. If of orders may change rapidly, and the ED may we have 21 inpatient falls, this number becomes have to go on bypass because there are no more the numerator of the rate-based statistic. When we inpatient beds available on a Friday or Saturday place this count of 21 falls over the total number night. So if the assumption of an equal area of of patient days for the month (e.g., 4,775) we have opportunity is violated, what do we do next? e a ratio of two di erent numbers that produces answer is simple—you make a u-chart. a result of 0.00439 (i.e., 21/4775 = 0.00439). Because the number of inpatient days is in the thousands we multiple the resultant value of U-Chart 0.00439 by 1000 to produce the inpatient falls rate is chart is used frequently in health care, of 4.4 falls per 1,000 inpatient days. e number especially now that there has been a more con- of spots you slip the decimal point on the resultant centrated e ort to track patient safety indicators. ratio depends on how large your denominator is. e u-chart, like the c-chart, is used to track In this case, we had 4,775 inpatient days so we defects. e di erence is that the u-chart is slip the decimal point three places to the right selected when you conclude that there is not an by multiplying the value of 0.00439 by 1000. If equal area of opportunity for the defect to occur. you had patient days in the tens of thousands you Let us return to the paint line at the Ford plant would slip the decimal point four places to the for a moment. Although you have in the past right and have 43.9 falls per 10,000 inpatient days. painted one model of car at a time, today you Or you could go out to 100k inpatient days and have been told that the line will have a mixture say “I’m sorry but we had 439 inpatient falls per of cars and a mixture of hood sizes. So, how do 100,000 inpatient days.” Or if you really wanted you count the paint blemishes on the hoods to depress the senior management team or board of a Ford Escort, a Taurus, a Mustang, and an you could report 4,397 inpatient falls per 1 million Expedition? Each hood has a di erent number inpatient days. You can adjust the result of the ratio of square inches, takes a di erent volume of of 21/4,775 very easily for any value you place in paint to cover the surface of the hood, and has the denominator position. e general rule for a varying probability of experiencing a paint rates, however, is that the denominator you use blemish. e u-chart takes care of this problem should be based on the volume you are observing very quickly by computing a defect rate. e on a regular basis. In the case of inpatient falls, number of paint blemishes is used as the nu- most hospitals are dealing with inpatient days merator and the number of square inches of the that are in the thousands so this is what should hood’s surface is used as the denominator. e be used to calculate the nal rate-based statistic resultant ratio provides the number of blemishes of 4.4 falls per 1,000 inpatient days. If, on the per so many square inches of hood area. e other hand, you were tracking medication errors rate essentially normalizes the di erences in you would most likely be justi ed in making the denominator size (i.e., the area of opportunity number of errors per 10,000 doses dispensed or for a blemish to occur). scripts written because an average-size hospital One technical point about rates. Explaining will general dispense 10,000 or more doses each a rate-based statistic can be a little challenging. It month. Finally, if your measure was the neonatal is much easier to say, “ is past month we had death rate for a state, province, or region then the 21 inpatient falls” than to say, “ is past month proper denominator size might be per 100,000 we experienced an inpatient falls rate of 4.4 falls live births. per 1,000 inpatient days.” Some in your audience Because it is an extremely rare to have the may struggle with what this rate-based statistic same number of medication orders each week,
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the same patient census, or the same number on SPC. e ASQ, for example, o ers public of central line days in the ICU, the u-chart is seminars on SPC. You may want to check with used more o en in healthcare settings than the your local ASQ chapter to see when such courses c-chart. Furthermore, because epidemiologists will be o ered. e IHI also o ers workshops frequently produce rate-based statistics (e.g., on building e ective measurement systems and the neonatal death rate or the VAP rate) the SPC. e various program o erings that I and use of terms associated with the u-chart should my colleagues teach throughout the year can be sound familiar to many healthcare professionals. reviewed on the IHI home page (www.ihi.org). Examples of u-chart applications are provided Finally, if you have the opportunity to attend a in the case study chapter (Chapter 10). local or national quality conference (e.g., the TABLE 91 provides an overview of the ve IHI National Forum on Quality Improvement charts just described and o ers examples of in Healthcare or the IHI-BMJ International indicators that could be placed on each type Forum on Quality and Safety in Healthcare), of chart. Other useful tables that summarize make sure that you sit in on sessions that are how charts should be set up and their various discussing Shewhart charts and SPC. Hearing uses can be found in Statistical Quality Control about control charts from multiple sources will Handbook (Western Electric, 1985) and Benneyan be very bene cial. (2001).10 Readers wishing to gain additional You can also test your knowledge of the var- insights about the selection of control charts ious charts by completing the You Make the Call should consult Wheeler (1995), Montgomery exercise found in EXERCISE 93. When I teach my (1991), Pyzdek (1990), Ishikawa (1989), Duncan classes on Shewhart chart applications, I give the (1986), Carey and Lloyd (2001), Carey (2003), participants this exercise at the end of the class and Provost and Murray (2011). to provide a nal test of their understanding of the selection of appropriate Shewhart charts. It gives them a chance “make the call!” and tests ▸ You Make the Call their control chart knowledge. e indicators listed in this exercise are taken from actual teams Now that you are familiar with the basic ideas I have had the opportunity to facilitate or coach. behind the Shewhart charts, the next step is to Start the exercise by determining the subgroup. apply this knowledge to your own indicators. Remember that the subgroup is the label for e study questions in BOX 91 will serve as a the horizontal axis and reects how you have quick overview of some of the central issues organized your data (e.g., by day or week). Next related to Shewhart chart development and as decide if you have variables or attributes data. a test of your current knowledge. If you struggle Finally, list the chart you think is most appropriate with some of the questions you can review the for this situation. You may want to refer to the material presented in this chapter and then Shewhart Decision Tree shown in Figure 9-12 to explore some of the listed references for addi- assist you in thinking through the chart options. tional explanations. Another way to enhance e answers to the You Make the Call exercise your knowledge base is to attend workshops can be found at the end of this chapter.
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TABLE 91 Shewhart chart summary
Type of Data and Data Examples of Indicators Type of Control Chart Collection Issues Used on This Type of Chart
X-bar and S chart Variables data ■ Actual turnaround time This is known as the Average The X-bar and S chart usually for five lab tests or three (X-bar) and Standard Deviation involves drawing a sample of pharmacy orders each day (S) chart. Most SPC software observations (e.g., 3–10 per ■ Blood pressure readings programs will give you two subgroup). Rational subgrouping (e.g., three to five per day) charts when you select this is frequently used with this ■ Diabetes monitoring (e.g., chart: one for the X-bar portion chart. The statistical principles three fasting blood sugar and one for the S portion. This behind this chart are based readings each day) is considered to be the most on the assumptions of the ■ Anesthesia time for a statistically powerful of all the normal (Gaussian) bell-shaped sample of cases each day charts. The X-bar and S chart distribution. ■ Patient satisfaction scores can have straight or stair-step control limits.
XmR chart Variables data ■ Patient wait time to see This chart is known as the The XmR chart is used when you the physician or to be Individual values (X) and have a single observation for each seen in the ED moving range (mR) chart. subgroup (i.e., n = 1). Sampling ■ The number of days to Sometimes it will be referred typically is not done but might be mail a patient bill after to as the Individuals or I-chart. if the process being monitored discharge It does not have the statistical has an extremely large volume. ■ The number of calls rigor or power of the X-bar Because this chart frequently uses coming into a clinic each and S chart because each dot aggregates as the plotted number day on the chart is representing (e.g., days in accounts receivable ■ Average length of stay only one observation. This this month), it is important to by week for a particular chart is used frequently to make sure that the data are diagnosis-related group answer questions related to consistently collected from one (DRG) volume, for example, “How time period to the next. This chart ■ The number of surgeries many surgeries did we do this is used to evaluate questions done each week week?” The XmR chart does related to process outcomes ■ Operating margin by not address the question as to (volumes), with no concern as month whether these surgeries were to whether the outcomes of the ■ Pounds of laundry started on time (this would process are acceptable or not each day require a p-chart). Instead, acceptable. ■ Average turnaround time the XmR chart is answering a by day neutral question, “How many?” ■ The number of food trays or “How much?” The XmR produced chart will always have straight ■ Patient satisfaction score control limits.
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TABLE 91 Shewhart chart summary (continued)
Type of Data and Data Examples of Indicators Type of Control Chart Collection Issues Used on This Type of Chart
p-chart Attributes data ■ Percentage of cesarean The p-chart is used frequently These data are classified as sections in health care to compute the defectives or nonconforming ■ Percentage of late food trays percentage (or proportion) units because they reflect the ■ Percentage of incomplete of defective products or percentage (or proportion) of charts services. The p-chart requires things or events that do not meet ■ Percentage of late surgery being able to count both specifications or criteria (the starts the numerator and the numerators). The denominators ■ Percentage of bills that are denominator. The p-chart is usually (but not always) are of inaccurate the weakest of the attributes varying sizes, which produce ■ Percentage of mortality charts because it is based on stair-step control limits. Data of ■ Percentage of staff the binomial distribution (i.e., this type reflect the binomial turnover there are only two outcomes distribution. The denominators ■ Percentage of patients such as yes/no, acceptable/ need to be sufficiently large (e.g., responding “Very Good” to not acceptable, or complete/ usually greater than 12) to enable a survey question not complete. The p-chart a reasonable percentage to be ■ Percentage of x-rays that can have straight or stair-step calculated yet not too large (e.g., had to be redone control limits. over 5,000). ■ Percentage of did not attends (DNAs) at an outpatient clinic
c-chart Attributes data ■ The number of falls The c-chart is used to count The key to using a c-chart is that ■ The number of restraints the number of defects that there should be an equal area of ■ The number of needle occur within an equal area opportunity for a defect to occur. sticks of opportunity when the This condition frequently makes it ■ The number of lawsuits nondefects are unknown. difficult to use this chart in health filed In this case, each observed care because the conditions under ■ The number of ventilator- unit (e.g., a patient) can have which we provide care do not associated pneumonias multiple defects (e.g., falls). always remain constant. One way ■ The number of Generally speaking, defects to address this inequality in the nosocomial infections are the specific reasons why a area of opportunity is to apply ■ The number of product or service is classified stratification. For example, if the medication errors as defective (i.e., a defective conclusion is that there is not an ■ The number of returns to product or service will suffer equal area of opportunity for an surgery from one or more defects). inpatient fall because the hospital ■ The number of surgical Generally speaking, indicators functions differently on weekends site infections appropriate for a c-chart than weekdays then separating the ■ The number of violent should be considered “rare data by weekdays versus weekends events in a mental health events.” The c-chart will always may be sufficient to conclude that ward have straight control limits. there is a relatively equal area of ■ The number of central line opportunity for a fall during each of infections these periods. The c-chart is based on the Poisson distribution.
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TABLE 91 Shewhart chart summary (continued)
Type of Data and Data Examples of Indicators Type of Control Chart Collection Issues Used on This Type of Chart
u-chart Attributes data ■ Medication errors per The u-chart is used to track The Poisson distribution is also 10,000 doses dispensed defects when the area of used as the frame of reference for ■ VAP per 1,000 vent days opportunity is not equal. For this chart. The u-chart presents ■ Total falls per 1,000 patient this reason, the u-chart is rates (e.g., so many falls per 1,000 days typically used more often in patient days). Knowledge of how ■ Total readmissions per health care than the c-chart. to collect data to form rates is 1,000 discharges This chart is based on rates essential. ■ Bloodstream infections rather than simple counts. The per 1,000 line days u-chart can have straight or stair-step control limits.
BOX 91 Shewhart charts study questions
■ When is it appropriate to use Shewhart charts? Should I use them in place of descriptive statistics? ■ What is the relationship between Shewhart charts and tests of significance? ■ How many data points do I need to make a Shewhart chart? What do I do if I do not have enough data? ■ Which is better, attributes or variables data? ■ What is a subgroup? Do I have to have one to make a Shewhart chart? ■ Can I make a Shewhart chart with only single data points? ■ Do my subgroups have to be of equal size when I make Shewhart charts? ■ Much of the data I get does not have the date on it. So, does it really matter if the data points are not in chronological order? ■ I still don’t get this distinction between a SD and a sigma limit. Why aren’t they the same? Does it really matter? My spreadsheet software will give me a SD. Why can’t I just multiple this number by 3 and then add and subtract this product from the mean to get the control limits? ■ Why do I have to use 3 sigma control limits? Why can’t I use two or maybe 1.5 sigma limits? ■ Do defects add up to make defectives or is the other way around? ■ When I make a p-chart, does the size of the denominator make a difference? Can I have, for example, 4 or 5 in my denominator? ■ What is the difference between a proportion, a percentage, and a rate? ■ Should I view common cause variation as “good” variation and special cause variation as “bad” variation? ■ Do I really have to investigate a special cause? Can’t I just remove the data point from the chart and get on with making changes?
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EXERCISE 93 You make the call! Selecting the right chart
Type of Type of Situation Subgroup? Data? Chart?
1. Each day you record the number of films processed in V or A the radiology department.
2. Each day you record the number of films requested V or A and the number that cannot be found in the radiology library.
3. The number of inpatient restraints each month is V or A placed over the total inpatient days each month.
4. Each day you pull a stratified random sample of V or A 15 complete blood counts (CBCs) and record the turnaround time (in minutes) for each CBC.
5. The number of minutes it takes to get a stat med V or A order administered to the patient (order time to administration time).
6. Every 2 weeks you pull a sample of 30 medication V or A orders and count the total number of orders that have one or more errors.
7. The wait time in the ED (door to discharge) is tracked V or A for each patient.
8. The clinic receptionist notes the time of check-in for V or A each patient. The physician notes the time when he/ she first sees the patient in the exam room. An analyst compiles the data daily and reports the percentage of patients who had to wait more than 30 minutes.
9. The director of surgery keeps track of the total number V or A of surgical procedures performed each week.
10. The dietary department records the number of food V or A trays that come back uneaten each day and the total number of trays they produced for that day.
11. You are interested in the average time patients spend V or A in your waiting area, so every day a student randomly picks eight patients and measures their actual waiting time in whole minutes.
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EXERCISE 93 You make the call! selecting the right chart (continued)
12. The ICU nurses want to evaluate the ventilator- V or A associated pneumonia (VAP) rate. So every 2 weeks they record the total number of pneumonia episodes and the total number of vent days.
13. Each week patient satisfaction scores for three units V or A are compiled and an average is calculated for the three units.
14. The finance department tracks the total number of V or A business days it takes to process a vendor’s request for payment. Process time starts when the request for payment is received in the finance department and ends when the payment is sent (electronically or posted in the mail) to the vendor.
15. Every week each medication order is checked against V or A five potential types of errors. The total number of errors for the week is divided by the total number of orders submitted that week.
16. You know the number of people who come to the ED V or A complaining of chest pain and the number who are actually diagnosed with an AMI or unstable angina.
■ Multivariate Shewhart-type Charts ▸ Additional Shewhart ■ P primed chart (p′-chart) Charts ■ U primed chart (u′-chart) Provost and Murray (2011) do a very good job of In addition to the ve basic Shewhart charts not only describing these alternative charts and described previously, there are many other charts provide examples of their use. I do not intend to that have their roots in manufacturing but have go into depth about these various charts but I do proven to be very useful in certain healthcare want to make a few comments about the t- and situations. Some of these alternative Shewhart g-charts that are being used more and more in charts include: healthcare improvement work. ■ Median chart e t- and g-charts are designed to address ■ t-chart the occurrence of rare events. I know, you are ■ g-chart wondering, “What is the operational de nition ■ Moving average chart of a rare event?” When I was rst learning ■ Cumulative Sum chart (CUSUM) about these charts the instructor used a simple ■ Exponentially weighted moving average example. He would ask, “What is the probability chart (EWMA) of looking out the window and seeing a car go ■ Standardized Shewhart Chart by?” Everyone would respond, “High.” en he
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would ask, “What is the probability of looking happens (e.g., a fall, a pressure ulcer, a surgical out the window and seeing an accident occur?” site infection) you basically reset the counter and Everyone would respond, “Low.” He then would begin counting the number of days again until proudly announce, “You now understand a rare the next fall occurred. is is the same approach event.” Now this is a pretty casual explanation of that factories use to track the number of days that a rare event but I think it helps to set the context have gone by without an accident in the factory. for thinking about rare events. If you wish to get If you never had an event you would never have very statistical about rare events you can study a dot on the chart. Because you are counting the what is called the “rare event rule for inferential number of days that have gone by since the last statistics.” Within this body of statistical theory event (i.e., a defective or a defect) the horizontal you will be reacquainted with probability theory axis will not have Monday, Tuesday, Wednesday that you were exposed to relatively early in your or January, February, March, etc. marked. When statistical training. Most of the time this is ex- an event occurs this is when you place the date plained by using the probabilities associated with of the event on the horizontal axis, which will rolling various combinations on dice or getting not be occurring in equal periods of time. e a particular combinations of cards while playing indication of improvement on a t-chart is when blackjack or poker or betting on a roulette wheel. you observe an ever-increasing run of days At the IHI we use a practical approach to without the occurrence of an event. de ning rare events that is grounded in statistical As healthcare providers have become more theory but does not require detailed compu- focused on safety indicators and reducing harm tations. Simply stated, if you have more than the t-chart has become increasingly popular. 25% of the data on a p-, c-, or u-chart at zero But a word of caution is in order. The statistical (or conversely at 100%) you need to consider basis for properly calculating the limits on a moving to a t- or g-chart. With 25% or more of t-chart are a little involved. First, you need to the data points at zero the use of the traditional realize that a distribution of rare events does not rules for detecting special causes on a Shewhart follow a normal Gaussian bell curve. A Poisson chart become questionable (Provost & Murray, distribution is a better referent for rare events. 2011). It also is a practical issue. If you do not The Poisson distribution is appropriate as a have sucient nonzero data for an attribute referent for the c- and u-charts as well as the chart the LCL may not exist, which makes the time between chart. In the case of the t-chart, interpretation of the chart dicult. In these however, the form of the Poisson distribution situations, you should consider moving to the is actually an exponential distribution, which time between chart (t-chart) or the cases between is in turn highly skewed. Second, the skewness chart (g-chart). e t-chart (the t part of the of the exponential distribution is not a major name refers to “time”) or time between chart problem and is addressed by transforming the shows you how much time has gone by since the time between events (i.e., days gone by) into last adverse event. Nelson (1994) provided the a quasi-normal or symmetric distribution by details on how this chart is constructed. When performing what is called a Weibull transfor- you use this chart you have to reorient the way mation. Third, once the data are more or less in which you explain the chart. For example, the approximating a normal distribution the UCL horizontal axis on the t-chart is a discontinuous and LCL can be calculated by using the formulae time sequence. If you start next Monday to begin for the XmR chart. Finally, after the limits and tracking patient falls but a fall does not occur CL are calculated they are transformed back until Wednesday then you would place a dot to their original state for plotting on the chart. on the chart’s vertical axis at 2 (i.e., 2 days have I know, this all sounds rather complicated. gone by before a fall occurred). When an event The detailed steps for constructing the t-chart
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are clearly discussed by Provost and Murray sudden proclaim, “I think I get it!” Once you (2011) and Nelson (1994). Also take heart reach this point it is now time to start applying in knowing that any reasonably good SPC this knowledge to actual improvement oppor- software package will do all the calculations tunities. But be careful. I have seen some people for a t-chart quickly and easily once you cre- become so enthusiastic about the various charts ate the time between data file. Your biggest that they start making graphs on any process that challenge will be to explain how to interpret produces data. It is at this stage that I remember the t-chart. But because its use is growing an old adage—if you give a child a hammer, the in popularity in healthcare setting, it is well whole world looks like a nail! e charts play a worth your time to gain more knowledge of valuable and central role in all QI e orts. It is the time between chart. important to realize, however, what they can do e g-chart (or geometric chart) is similar in and what they cannot do. principle to the t-chart. It too is a chart for rare First, appreciate the fact that the charts do tracking events except that instead of plotting not answer the following questions: the amount of time (e.g., days) between a rare ■ What is the reason for a special cause? event, the g-chart plots the number of cases ■ Should a common cause process be improved? that are regarded as being successful against ■ What should I do to improve the process? cases considered to be failures. A failure in this situation might be a surgical site infection, e answers to these questions do not come patients experiencing a medication error, or from the charts or statistics. ey come from a return to surgery within 24 hours. Like the the will, ideas, and ability of the team to execute t-chart success is determined by having a long tests of change. I have seen too many teams feel run of successful cases with no failures or ad- that once they have created a chart their work verse events. Although the t-chart is modeled is nished. I think that this occurs because the a er an exponential distribution the g-chart chart is a tangible thing that can be pointed to referent is a geometric distribution. Again, and shown to others. Improvement strategies, the steps for computing the limits and the CL on the other hand, are not as nite or discrete. on a g-chart are nicely laid out in Provost and Developing improvement strategies is actually Murray (2011). ere is also a considerable much more dicult than mastering control body of literature on both the exponential and chart theory and construction because you are geometric distributions that can be found in the dealing with people, behaviors, and culture ASQ's Journal of Quality Technology. e g-chart not numbers. is also becoming a standard o ering in most Second, a er you make a chart and decide SPC so ware packages. Once again, however, whether the process exhibits common or special the challenge is making sure you have at least cause variation, you then need to decide how a moderate foundation in being able to explain you are going to approach the variation you the chart and how to interpret it. have identi ed. Do you need to merely reduce variation in the process or fundamentally redesign the process and change the way in which work is envisioned and delivered? All improvement ▸ Using Shewhart Charts strategies emanate from an understanding of Effectively variation. If the process exhibits special cause variation the appropriate decision is to investigate At some point a er reading various books on the special cause(s) and determine why they have run and Shewhart charts and listening to others made the process unstable and unpredictable. explain control chart theory, you will all of a Just as we would investigate a patient safety event
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(i.e., a sentinel event) by conducting a root Notes cause analysis, we also need to do the same thing when a special cause is detected on a run 1. Historically these charts have been known or Shewhart chart. Ignoring a special cause will as control charts. Shewhart himself even guarantee that it will rear its ugly head at some referred to them as control charts as have point in the future. We cannot predict exactly many writers since Shewhart’s time. But as when a special cause will occur but you can Blank (1998, p. 1) points out, “It is important be sure that it will pop up again if you choose to understand that SPC does not control to ignore it.11 processes. People control processes. SPC e other aspect of a special cause is that not is merely a tool that provides you with every special cause is negative and undesirable. information you need to reduce variation Remember that special causes are not bad and and tell you whether or not your processes common causes are not good. e key point can meet the customer’s expectations.” In is the special causes make a process unstable more recent times, the charts have been and unpredictable. It is very likely that you will referred to more and more as Shewhart observe a special cause that you want to emulate charts (Provost & Murray, 2011, p. 113) (e.g., when lab turnaround time is much faster to emphasize their use primarily in un- than it has been or the past 15 days). In this derstanding variation and to facilitate case, you want to investigate why the process learning about process capability rather worked so well on those days and see whether conveying images of “control.” e term these conditions can be replicated. Common Shewhart chart is also used to recognize the causes on the other hand are not inherently signi cant contributions of Dr. Shewhart to good. Common cause variation merely means the eld of SPC. A nal note on the use of that the process is stable and predictable (i.e., the word “control.” e ASQ was originally predictable within the boundaries of the UCL called the American Society for Quality and LCL). Just as you can have a special cause Control (ASQC). In 1997, the membership that you might want to emulate, you can also voted to drop the word “control” from the have common cause variation that is unac- organization’s name. is was to recognize ceptable (e.g., when a patient’s blood pressure that quality was becoming a broader con- is running at a very high level and staying cept and used in many other elds besides there or when the wait time to see your family manufacturing where initially in the early physician is consistent and predictable but it 1900s control was used as a key operative is at such a high level that it is predictably bad word. Shewhart’s book, Economic Control and unacceptable). of Quality of Manufactured Product (1931) QI starts with making the correct decision provides a classic reference to the initial about the variation that lives in your data. Walter use of the term “control.” So for a variety Shewhart introduced the control chart and the of reasons I use the term Shewhart chart (s) notions of common and special causes of variation in this text rather than control charts. in 1924 (Hare, 2003). Since then SPC has become 2. e USL and LSL are frequently referred the foundation for all successful QI initiatives. to in manufacturing as “tolerance limits” It is a key component of the Baldrige criteria, Six and are also frequently referred to as the Sigma, Lean, and International Organization for voice of the customer (VOC, i.e., what the Standardization (ISO). Without a clear under- customer wants, needs, or expects from standing of variation and its causes, however, the product or service). ere are many individuals and organizations will continue to di erent types of indices that have been su er from numerical illiteracy. developed to capture statistically process
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capability. e three basic process capability precision for many of its indicators as the indices are the process capability index manufacturing industry. So, when I use the (Cp), the minimum process capability term process capability I am using it in a index (Cpk), and the process capability general sense to describe the variation in index to the mean (Cpm). e traditional the process as de ned by the mean (CL) statistical use of process capability (Cp) and the UCL and LCL. ese numbers is to indicate whether or not the process de ne how well the process is performing can meet the predetermined speci ca- relative to the target or goal. tions (Blank, 1998). ere are numerous 4. Some of my colleagues may disagree with variations on the Cp statistic, all of which these guidelines. I have found over the years are designed to help the quality control that there are two general issues that need (QC) researcher investigate special causes to be balanced against each other: statisti- and get the process to perform as closely cal purity and practicality. e science of as possible to the expectations of the improvement (SOI) is as Shewhart referred customer (i.e., the speci cations). to it an “applied science.” erefore, in my 3. I have calculated a Cp and Cpk statistics work I have always tried to balance the only once for a healthcare indicator. It precision of statistical requirements with was when I was helping to set up an out- a heavy dose of practicality. For example, patient clinic designed to manage patients I have worked with wonderful people in on anticlotting medication (i.e., warfarin the National Health Service (NHS) of sodium). Several key indicators are used Scotland for over 12 years. During this in assessing clotting issues. e PT, along time we have developed a variety of health with its derived measures of prothrombin and social service measurement systems. ratio (PR) and INR, are assays evaluating Most of the data are collected monthly and the extrinsic pathway of coagulation. many of the indicators were not collected is test is also called “ProTime INR” historically. So, we were starting out with and “PT/INR” (MedlinePlus medical no data on selected indicators and had encyclopedia, https://medlineplus.gov/ to build charts as we went along. In this ency/article/003652.htm). Because there case, trail control limits were essential. are de ned therapeutic limits associated We also made a very practical decision to with these measures they can be regarded use the rst 6 months of data as baseline as USL and LSL. ese values would be set for indicators that had no history. Again on the Shewhart charts as reference lines. some would argue that this is not enough en the patient’s actual results on the PT data to establish a baseline but it was and INR would be plotted on the chart, sucient to get us started on the road to and the UCL and LCL of the patient would improvement. then be compared to the USL and LSL. 5. In one of my measurement workshops, Because we had both an USL and a LSL and a few years ago this confusion was high- control limits the capability statistics could lighted very clearly. A young woman be calculated to determine how well the near the front of the room raised her patient was conforming to the therapeutic hand a er I was done explaining that a limits (USL and LSL) of the drug. But in sigma was not equivalent to a SD. She most instances in healthcare settings, there had a bit of a wrinkled brow and looked is only a single target or goal rather than concerned. She said, “I was told that the the USL and LSL. Healthcare simply does UCL and LCL were calculated as SD. Is not currently function at the same level of this not correct?” I drew the formula for
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the SD on a ipchart and asked her if this for his 4-day seminars. ey have written is what she used to calculate the three a number of key books on QI including sigma control limits. She said “Yes, that is e Improvement Guide (Langley, Moen, what I was told to use.” I then proceed to Nolan, Nolan, Norman, & Provost, 2009), politely tell her that the control limits on Quality Improvement rough Planned her charts were wrong. e UCL and LCL Experimentation (Moen, Nolan, & Provost, would either be too wide or too narrow 2012), and e Health Care Data Guide if she used the SD of the data. She got a (Provost & Murray, 2011). very strange look on her face, was quiet 7. When Dr. Ray Carey and I rst started for a moment, then burst out, “But this teaching control chart applications to means I have been giving the charts to healthcare professionals in 1992, we the senior management team and to the taught the traditional list of seven control board! What am I going to do?” I asked charts. In 1995, we wrote a book that her if anyone had ever noticed or com- described these seven charts and their mented on the fact that the limits were not use (Carey & Lloyd, 2001). In December, properly calculated. She responded, “No.” 2002, Dr. Carey and I taught a minicourse I suggested that she learn how to make and two workshops on control charts the charts correctly with SPC so ware at the 14th National Forum on Quality (she was merely using Excel with no SPC Improvement in Health Care sponsored add-on so ware that properly computes by the IHI. is was the rst time in the sigma limits) and then submit the correct 12 years that we had been teaching for charts to the senior management team the IHI that we reduced the number and board the next time around. She still of charts we taught from seven to ve. looked a little perplexed, however. She was e sessions were well received, and the concerned that she would lose credibility participants found the more simpli ed with the management team when they approach to be appealing. e two charts found out the charts were wrong. I told her we dropped were the X-bar and R chart that unless she tells them that her original and the np-chart. Our reasoning for doing charts had the wrong limits it does not this was that the X-bar and S chart can sound like anyone on the board or the be used in any situation that calls for the senior management team had sucient X-bar and R chart (when the subgroup grounding in Shewhart charts to actually is greater than 2). e np-chart, which discern that the charts were di erent. I is a count of the number of defectives, told her to let me know how it went when requires equal subgroup sizes (i.e., the she showed them the correct charts. She denominators), which do not happen very wrote back and said that no one asked o en in healthcare settings. e p-chart any questions. can be used e ectively, however, in any 6. API develops methods, works with leaders situation where an np-chart could be used. and teams, and provides education and If there are equal subgroup sizes then the training to help organizations improve their p-chart will have straight control limits. products and services and to build their If, on the other hand, the measure has capability for ongoing improvement. e unequal subgroups then the p-chart will principals of API have worked in industrial, have what is known as “stair-step” control educational, health, and social service limits. In this case, the control limits are settings. ey have worked extensively di erent for each data point. e closer with Dr. Deming and provided support in size the denominators the smaller the
9781284023077_CH09_211_258.indd 252 31/07/17 6:00 PM Answers to the Chapter 9 Exercises 253
“steps” between each of the control limits. 11. ere are many good examples of how If there are large di erences between the people have ignored special causes when denominators the “steps” will be greater they rst occurred and then decided to between the individual data points. deal with them when they popped up 8. I wrote a commentary in JAMA a few again. e terrorist attacks on our nation years ago titled “A Matter of Time” (Lloyd on September 11, 2001 provide a classic & Goldmann, 2009) highlighting how example. Several years prior to 9/11 clinicians, researchers, patients, and the World Trade Center was bombed improvement specialists all have very by terrorists. Although this seemed to di erent views of time. To these four draw the nation’s attention for a while, categories I could add management time, interest in this special cause soon faded which focuses on monthly aggregates into the “old news” category and steps of data. were not taken to extricate the factors 9. e control chart examples presented that led to the special cause. e condi- in this chapter have been developed to tions for 9/11 were still existing within demonstrate the ve di erent charts. e our system. e September 11 special substantive importance of the various cause, however, generated a completely charts is not the focus of this chapter. e di erent reaction. Our nation mobilized charts have been developed for heuristic not only to investigate the special cause purposes, and the clinical or operational but also take steps to literally try to impacts of the indicators presented on eliminate the origin of the special cause. the charts are not the primary objective Every day there are stories in the news in this chapter. Analysis and interpreta- that should prompt a discussion as to tion of control charts are addressed in whether the event is a special cause or Chapter 10. part of a common cause system. All too 10. e idea for creating this table came from o en, however, we overreact to a special Dr. James Benneyan of Northeastern cause and want to change the system University in Boston. In a paper titled without fully investigating the reasons “Design, Use, and Preferences of Statistical why it occurred. Other times, however, Control Charts for Clinical Process Im- we ignore a special cause and “hope” that provement” (September 16, 2001), he used it will not happen again. Hope is not a a table to summarize the various charts. plan. Knowing how to appropriately react A er reading this paper, I realized that to common and special causes is a much the table was something I had not used better approach than hoping a special to summarize the control charts. I believe cause will not pop up again. a table format works nicely to augment the utility of the decision tree shown Answers to the Chapter 9 in Figure 9-12 and the textual details. Dr. Benneyan has written extensively Exercises on the topic of control charts in health is section provides the answers to the exer- care and I would encourage readers to cises presented earlier in this chapter. e rst review his work. He can be reached at the EXERCISE 91 deals with di erentiating defectives following address: MIME Department, 334 from defects. EXERCISE 92 provides indicators Snell Engineering Center, Northeastern that could be placed on either an X-bar and University, Boston, MA 02115; phone 617- S chart or an XmR chart. e answers to these 373-2975; email [email protected]. two exercises are shown here.
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EXERCISE 91 Defective or defect? You make the call! (Answers)
Defective Defect Indicator (Classification) (Count)
1. Number of accidents per 1,000 employee days *
2. Number of errors per 25 food trays *
3. Percentage of AMI patients receiving aspirin within * 24 hours of arrival in the ED
4. Percentage of inpatient deaths each month *
5. Number of surgical complications per 1,000 surgeries * performed
6. Proportion of hand hygiene observations done incorrectly *
7. Number of falls per 1,000 patient days *
8. Number of medication errors per 10,000 doses dispensed *
EXERCISE 92 You make the call: Is it an X-bar and S chart or XmR chart? (Answers)
X Bar and S XmR Indicator Chart (I Chart)
Time to clean an inpatient room (in minutes) *
Patient satisfaction scores for subgroups of 15 patients in the * outpatient clinic
Average turnaround time for all STAT labs done each day *
Cost for each normal delivery *
A diabetic patient’s 3x a day blood sugar readings *
Average length of stay for a subgroup of 20 ICU patients *
The distance (in feet) that a sample of 10 knee replacement * patients can walk in 15 seconds
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The final EXERCISE 93 brings together the of this situation is that if the target is to have key issues related to selecting the most appro- all patients be seen in 30 minutes or less, the priate Shewhart chart for different measurement 30-minute target actually needs to be the UCL situations. In this exercise, the subgroup, type of of the X-bar and S chart not the average. If 30 data, and type of chart all need to be specified. minutes is the average on the chart you will Depending on how you interpret the word- naturally have some patients waiting more ing describing the situations in Exercise 9-3, than 30 minutes and some waiting less. A you might think that a type of chart other target is useful on a chart but it needs to be than that I have listed could be selected. A understood in light of the actual variation in key leaning point for this exercise is that slight the process and the capability of the current changes to the wording of the situation could process to achieve the target. The Shewhart lead you to selecting a different chart. For chart can help you determine the magnitude example, take a close look at situations 8 and of improvement needed to achieve the target 11 in Exercise 9-3. The wording for situation and but in the case of improving wait time, this 8 points you to select a p-chart because they is best accomplished by not turning variables decided to focus on patients who had to wait data into attributes. more than 30 minutes. Even though they had e most appropriate chart for each situation variables data (i.e., time) they basically turned described in Exercise 9-3 is shown here. Note it into attributes data because of the 30-minute that situation 16 is a trick question. Did you target. They have taken the more powerful determine that a chart cannot be identi ed? form of data (variables data) and relegated it Why? Because there is no subgroup identi ed in to a binomial condition, over 30 minutes and the situation description. Remember, a Shewhart under 30 minutes. They will never understand chart must have a subgroup and an observation the true variation in wait time. What is the as minimum requirements. In this situation, longest wait? You have no idea. All we know is there is no subgroup. But if the situation had that a certain percentage of patients had to wait been worded as follows then we would have more than 30 minutes. The longest wait could a subgroup: “You know the number of people be 31 minutes or 13,184 minutes. The more who come to the ED complaining of chest appropriate approach is found in situation 11. pain EACH MONTH and the number who are Here they are taking a sample of eight patients actually diagnosed with an AMI or unstable each day and recording their actual wait times. angina.” Now you would be able to determine The chart of preference in this situation is which chart is most appropriate. In this situ- the X-bar and S chart. We will now have the ation, the Shewhart chart of choice would be average wait time for a given day and the SD the p-chart because we know the denominator from this average. We can lay a separate line (i.e., the number of people coming to the ED of the chart showing the target of 30 minutes. complaining of chest pain) and the numerator This gives us much more information about (i.e., the number who were actually diagnosed the process variation and how capable it is of with an AMI or unstable angina). Without a achieving the target, which cannot be deter- subgroup, however, we cannot make a decision mined by using the p-chart. The final aspect about which chart is most appropriate.
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EXERCISE 93 You make the call!: Selecting the right chart (Answers)
Type of Type of Situation Subgroup? Data? Chart?
1. Each day you record the number of films processed in Day V XmR the radiology department.
2. Each day you record the number of films requested Day A p-chart and the number that cannot be found in the radiology library.
3. The number of inpatient restraints each month is Month A u-chart placed over the total inpatient days each month.
4. Each day you pull a stratified random sample of Day V X-bar & S 15 CBCs and record the turnaround time (in minutes) for each CBC.
5. The number of minutes it takes to get a stat med Stat med V XmR order administered to the patient (order time to order administration time).
6. Every 2 weeks you pull a stratified sample of 30 Two weeks A p-chart medication orders and count the total number of orders that have one or more errors.
7. The wait time in the ED (door to discharge) is tracked Patient V XmR for each patient.
8. The clinic receptionist notes the time of check-in for Day A p-chart each patient. The physician notes the time when he/ she first sees the patient in the exam room. An analyst compiles the data daily and reports the percentage of patients who had to wait more than 30 minutes.
9. The director of surgery keeps track of the total Week V XmR number of surgical procedures performed each week.
10. The dietary department records the number of food Day A p-chart trays that come back uneaten each day and the total number of trays they produced for that day.
11. You are interested in the average time patients spend Day V X-bar & S in your waiting area, so every day a student randomly picks eight patients and measures their actual waiting time in whole minutes.
9781284023077_CH09_211_258.indd 256 31/07/17 6:00 PM References 257
EXERCISE 93 You make the call!: Selecting the right chart (Answers) (continued)
Type of Type of Situation Subgroup? Data? Chart?
12. The ICU nurses want to evaluate the ventilator- Two weeks A u-chart associated pneumonia (VAP) rate. So every 2 weeks they record the total number of pneumonia episodes and the total number of vent days.
13. Each week patient satisfaction scores for three Week V XmR units are compiled and an average is calculated for the three units.
14. The finance department tracks the total number of A request V XmR business days it takes to process a vendor’s request for payment for payment. Process time starts when the request for payment is received in the finance department and ends when the payment is sent (electronically or posted in the mail) to the vendor.
15. Every week each medication order is checked against Week A u-chart five potential types of errors. The total number of errors for the week is divided by the total number of orders submitted that week.
15. You know the number of people who come to the Unknown* A Unknown* ED complaining of chest pain and the number who are actually diagnosed with an AMI or unstable angina.
*NOTE: Item 16 is a trick question. A subgroup is not specified. Without a subgroup you cannot make a decision about the most appropriate chart. If this description indicated that “You know the number of people who come to the emergency department EACH MONTH . . .” you would have a subgroup. The chart of choice would then be a p-chart.
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