reduces candy defects for a UK food manufacturer

• Recently, a UK-based producer of cough drops tested the effectiveness of the DMAIC approach for cutting manufacturing costs. Tools and Techniques for Quality • Using the DMAIC approach, the company saved £290,000 • The company also reduced its scrap rate from 1 in every 5 cough drops to 1 Control and Improvement in 10,000 or more. Chapter 3 • More importantly the organization now has a much better understanding of the impact of variation.

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Chance and Introduction Assignable Causes of The Quality Variation

Implementing SPC in a The Rest of the Quality Improvement An Application of SPC Learning Objectives Magnificent Seven Program

1. Understand chance and assignable causes of variability in a process 2. Explain the statistical basis of the Shewhart control chart Applications of SPC & 3. Understand the basic process improvement tools of SPC: the or stem - Quality Improvement and-leaf plot, the check sheet, the , the cause-and-effect diagram, the Tools in Transactional defect concentration diagram, the scatter diagram, and the control chart and Service

4. Explain how sensitizing rules and pattern recognition are used in conjunction with Discussion topics Businesses control charts

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1 Introduction Statistical Process Control (SPC)

§ SPC is one of the greatest technological developments of the § A process must be capable of operating with little variability twentieth century because around the target or nominal dimensions of the product’s quality § it is based on sound underlying principles, characteristics in order to meet or exceed customer expectations. § is easy to use, § SPC is a powerful collection of problem-solving tools useful in § has significant impact, and achieving process stability and improving capability through the § can be applied to any process. reduction of variability. § Its seven major tools are § A process is an organized sequence of activities that produces an § Histogram or stem-and-leaf plot output (product or service) that adds value to the organization. § Check sheet § Pareto chart § While we traditionally think of SPC as being applied to § Cause-and-effect diagram manufacturing processes, it can really be applied to any kind of § Defect concentration diagram process including service processes. § Scatter diagram § Control chart 2 – 5 2 – 6

SPC

Chance and § “The Magnificent Seven” are an important part of SPC but they Introduction Assignable Causes of The Control Chart comprise only the technical aspects. Quality Variation

§ The proper deployment of SPC helps create an environment in which all individuals in an organization seek continuous Implementing SPC in a improvement in quality and productivity. The Rest of the Quality Improvement An Application of SPC Magnificent Seven Program § This environment is best developed when management becomes involved in the process. Applications of SPC & Quality Improvement Tools in Transactional and Service

Discussion topics Businesses

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2 Chance and Assignable Causes of Chance and Assignable Causes of Quality Variation Quality Variation § In any production process, regardless of how well designed or § Other kinds of variability in key quality characteristics usually carefully maintained it is, a certain amount of inherent or natural arises from three sources: variability will always exist. § Improperly adjusted or controlled machines, § This natural variability or “Background Noise” is the cumulative effect of § Operator errors, or many small, essentially unavoidable causes. § Defective raw material. § In the framework of statistical quality control, this natural variability is often called a “stable system of chance causes.” § Such variability is generally large when compared to the background noise, and it usually represents an unacceptable level § A process that is operating with only chance causes of variation of process performance. present is said to be in statistical control. § These sources of variability that are not part of the chance cause pattern are referred to as assignable causes of variation.

§ A process that is operating in the presence of assignable causes is said to be an out-of-control process. 2 – 9 2 – 10

Chance and Assignable Causes of Quality Variation

The terminology “chance” and “assignable causes” was developed by Shewhart. Today, some writers use the terminology “common cause” instead of “chance cause” and “special cause” instead of “assignable cause”.

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3 SPC

Chance and § A major objective of statistical process control is to quickly detect Introduction Assignable Causes of The Control Chart the occurrence of assignable causes of process shifts so that Quality Variation investigation of the process and corrective action may be undertaken before many nonconforming units are manufactured. Implementing SPC in a § The control chart is an on-line process-monitoring technique The Rest of the Quality Improvement An Application of SPC Magnificent Seven widely used for this purpose. Program § Control charts may also be used § To estimate the parameters of a production process, and, through this Applications of SPC & information, to determine . Quality Improvement Tools in Transactional § To provide information useful in improving the process. and Service

§ To reduce variability as much as possible. Discussion topics Businesses

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The Control Chart The Control Chart

§ The control chart is a graphical display of a quality characteristic § A point that plots outside of the control limits is interpreted as that has been measured or evidence that the process is out of control, and investigation and computed from a sample versus the sample number or time. corrective action are required to find and eliminate the assignable cause or causes responsible for this behavior. § The chart contains a center line that represents the average value § Even if all the points plot inside the control limits, if they behave of the quality characteristic corresponding to the in-control in a systematic or non-random manner, then this could be an state. indication that the process is out of control. § Two other horizontal lines, called § If 18 of the last 20 points plotted above the center line but below the upper the upper control limit (UCL) and control limit and only two of these points plotted below the center line but the lower control limit (LCL), are also shown on the chart. These above the lower control limit, we would be very suspicious that something control limits are chosen so that if was wrong. the process is in control, nearly all § If the process is in control, all the plotted points should have an essentially of the sample points will fall between them. random pattern.

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4 Control Chart Example Control Chart

§ In semiconductor § manufacturing, an important Every hour a sample of five wafers is taken, the average flow fabrication step is width is computed, and plotted on the chart. photolithography. x=1.5 microns, σ=0.15 microns, n=5 § The developing process is typically followed by a hard σ = σ =0.15/ 5=0.0671 bake process to increase resist x n adherence and etch resistance. § If the process is in control with a mean flow width of 1.5 microns § An important quality § Using Central Limit Theorem, is approximately normally distributed, we x characteristic in hard bake is the would expect 100(1-α)% of the sample means to fall between flow width of the resist x 1.5 + Zα/2(0.0671) and 1.5 - Zα/2(0.0671) § Suppose that the flow width can § Choose Z =3 be controlled at a mean of 1.5 α/2 microns, and it is known that § Therefore, UCL=1.5 + 3(0.0671) = 1.7013 & LCL = 1.5 - 3(0.0671) = 1.2987 the standard deviation of flow width is 0.15 microns.

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Control Chart

§ The width of the control limits is inversely proportional to the sample size n for a given multiple of sigma.

§ Choosing the control limits is equivalent to setting up the critical region for testing the hypothesis

Three Sigma Control Chart H0: μ = 1.5

H1: μ ≠ 1.5 where � = 0.15 (known)

The “Sigma” in the three sigma control chart refers to the § Essentially, the control chart tests this hypothesis repeatedly at standard deviation of the statistic plotted on the chart (i.e. ), σ different points in time. x not the standard deviation of the quality characteristics. σ x

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5 Control Chart Shewhart Control Chart

Note that “sigma” refers to the standard deviation of the § This general theory of control charts was first proposed by Walter σ statistic plotted on the chart (i.e., ), not the standard x A. Shewhart deviation of the quality characteristic. § � - sample statistic that measures some quality characteristic of interest

§ μ� – mean of �

§ �� – standard deviation of �

§ L – “distance” of the control limits from the center line, expressed in standard deviation units.

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Process Improvement using Control Out-Of-Control-Action plan (OCAP) Chart § Most processes do not operate § Developing an effective system for corrective action is an in a state of statistical control. essential component of an effective SPC implementation. § Consequently, the routine and attentive use of control charts § A very important part of the corrective action process associated will identify assignable causes. If with control chart usage is the OCAP. these causes can be eliminated from the process, variability will § An OCAP be reduced and the process will § is a flow chart or text-based description of the sequence of activities that be improved. must take place following the occurrence of an activating event. § The control chart will only § consists of checkpoints, which are potential assignable causes, and detect assignable causes. terminators, which are actions taken to resolve the out-of-control Management, operator, and condition, preferably by eliminating the assignable cause. engineering action will usually § Is a living document in the sense that it will be modified over time as more be necessary to eliminate the knowledge and understanding of the process is gained. assignable causes.

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6 OCAP Example Control Chart as an Estimating Device

§ From a control chart that exhibits statistical control, we may estimate certain process parameters, such as the mean, standard deviation, fraction nonconforming or fallout, and so forth.

§ These estimates may then be used to determine the capability of the process to produce acceptable products.

§ Such process-capability studies have considerable impact on many management decision problems that occur over the product cycle, including make or buy decisions, plant and process improvements that reduce process variability, and contractual agreements with customers or vendors regarding product quality.

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Types of Control Charts Design of Control Charts § Variables Control Chart § This includes the selection of § If the quality characteristic can be measured and expressed as a number on some continuous scale of measurement, it is usually called a variable. § sample size, § In such cases, it is convenient to describe the quality characteristic with a § control limits, and measure of central tendency and a measure of variability. § frequency of sampling § Control charts for central tendency and variability are collectively called variables control charts. § The use of statistical criteria such as these along with industrial experience has led to general guidelines and procedures for § Attributes Control Chart designing control charts. § Many quality characteristics are not measured on a continuous scale or even a quantitative scale. § Recently we have begun to examine control chart design from an § In these cases, we may judge each unit of product as either conforming or economic point of view, nonconforming on the basis of whether or not it possesses certain attributes, or we may count the number of nonconformities (defects) appearing on a unit § considering explicitly the cost of sampling, of product. § losses from allowing defective product to be produced, and § Control charts for such quality characteristics are called attribute s control § the costs of investigating out-of-control signals that are really false alarms. charts 2 – 27 2 – 28

7 Types of Variability Control Chart

§ Another important consideration in § control chart usage is the type of In Fig 3.7 (c) the process is variability exhibited by the process. very unstable in that it drifts or “wanders about” without § Figures 3.7a and 3.7b illustrate stationary behavior. By this we any sense of a stable or fixed mean that the process data vary around a fixed mean in a stable or mean. predictable manner. § In many industrial settings, § This is the type of behavior that Shewhart implied was produced by we stabilize this type of an in-control process. behavior by using § In Fig 3.7 (a) the past values of engineering process control the data are of no help in predicting any of the future (such as feedback control). values. § In Fig 3.7 (b) shows that successive observations in the data are dependent

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Shewhart Control Chart

Chance and § Shewhart control charts are most effective when the in-control Introduction Assignable Causes of The Control Chart process data look like Figure 3.7 (a). Quality Variation

§ With some modifications, Shewhart control charts and other types of control charts can be applied to autocorrelated data. Implementing SPC in a The Rest of the Quality Improvement An Application of SPC § They can also be applied in systems where feedback control is Magnificent Seven Program employed.

§ Control charts are among the most important management Applications of SPC & control tools; they are as important as cost controls and material Quality Improvement controls. Tools in Transactional and Service

Discussion topics Businesses

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8 The Rest of the Magnificent Seven Check Sheet

§ Although the control chart is a very powerful problem-solving and § In the early stages of process-improvement tool, it is most effective when its use is process improvement, it will often become fully integrated into a comprehensive SPC program. necessary to collect § either historical or The magnificent seven are listed below: current operating data § Histogram or stem-and-leaf plot about the process under § Check sheet investigation. § Pareto chart § This is a common activity § Cause-and-effect diagram in the measure step of § Defect concentration diagram DMAIC. § Scatter diagram § A check sheet can be § Control chart very useful in this data collection activity.

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Check Sheet Design Pareto Chart

§ When designing a check sheet, it is important to clearly specify § The Pareto chart is simply a the type of data to be collected, the part or operation number, (or the date, the analyst, and any other information useful in histogram) of attribute data diagnosing the cause of poor performance. arranged by category.

§ If the check sheet is the basis for performing further calculations § Pareto charts are often used or is used as a worksheet for data entry into a computer, then it is in both the measure and important to be sure that the check sheet will be adequate for analyze steps of DMAIC. this purpose.

§ In some cases, a trial run to validate the check sheet layout and design may be helpful.

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9 Pareto Chart Pareto Chart

§ The Pareto chart does not automatically identify the most important defects, but only the most frequent.

§ When the list of defects contains a mixture of those that might have extremely serious consequences and others of much less importance, one of two methods can be used: § Use a weighting scheme to modify the frequency counts § Accompany the frequency Pareto chart analysis with a cost or exposure Pareto chart.

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Types of Pareto Charts Cause-and-Effect (or Ishikawa) Diagram

§ Once a defect, error, or problem has been identified and isolated for further study, we must begin to analyze potential causes of this undesirable effect.

§ In situations where causes are not obvious (sometimes they are), the cause and effect diagram is a formal tool frequently useful in unlayering potential causes. § The cause-and-effect diagram is very useful in the analyze and improve steps of DMAIC.

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10 Cause-and-Effect Diagram Cause-and-Effect Diagram

§ Cause-and-effect analysis is an extremely powerful tool.

§ A highly detailed cause-and- effect diagram can serve as an effective troubleshooting aid.

§ Furthermore, the construction of a cause-and- effect diagram as a team experience tends to get people involved in attacking a problem rather than in affixing blame.

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Defect Concentration Diagram Defect Concentration Diagram

§ A defect concentration diagram is a picture of the unit showing all relevant views.

§ Then the various types of defects are drawn on the picture, and the diagram is analyzed to determine whether the location of the defects on the unit conveys any useful information about the potential causes of the defects. § Defect concentration diagrams are very useful in the analyze step of DMAIC.

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11 Defect Concentration Diagram Scatter Diagram

§ When defect data are portrayed on a defect concentration § The scatter diagram is a useful plot for identifying a potential diagram over a sufficient number of units, patterns frequently relationship between two variables. emerge, and the location of these patterns often contains much information about the causes of the defects. § Data are collected in pairs on the two variables—say, (yi, xi)—for i = 1, 2, . . . , n. Then yi is plotted against the corresponding xi. § We have found defect concentration diagrams to be important § problem-solving tools in many industries, including plating, The shape of the scatter diagram often indicates what type of painting and coating, casting and foundry operations, machining, relationship may exist between the two variables. and electronics assembly.

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Scatter Diagram

§ It is tempting to conclude the Chance and relationship between the two Introduction Assignable Causes of The Control Chart variables is one of cause and effect. Quality Variation § This thinking is potentially dangerous, because correlation does not necessarily imply Implementing SPC in a The Rest of the causality. Quality Improvement An Application of SPC Magnificent Seven Program § This apparent relationship could be caused by something quite different. Applications of SPC & § The scatter diagram is useful for Quality Improvement identifying potential relationships. Tools in Transactional Designed experiments [see and Service

Montgomery (2009)] must be used Discussion topics Businesses to verify causality.

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12 Implementing SPC in a Quality Improvement Program Chance and Introduction Assignable Causes of The Control Chart Quality Variation

Implementing SPC in a The Rest of the Quality Improvement An Application of SPC Magnificent Seven Program

Applications of SPC & Quality Improvement Tools in Transactional and Service

Discussion topics Businesses

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An Application of SPC Cause-and-Effect Diagram

§ This section gives an account of how SPC methods were used to improve quality and productivity in a copper plating operation at a printed circuit board fabrication facility.

§ This process was characterized by high levels of defects such as brittle copper and copper voids and by long cycle time.

§ The long cycle time was particularly troublesome, as it had led to an extensive work backlog and was a major contributor to poor conformance to the factory production schedule.

§ Management chose this process area for an initial implementation of SPC.

§ The DMAIC approach was used.

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13 Measure Step - Check Sheet for Data Pareto Analysis Collection

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Pareto Analysis Improve – Control Chart

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14 Control Chart Tolerance Diagram

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Designed Experiment Designed Experiment

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15 Designed Experiment

Chance and § Factorial Experiment Introduction Assignable Causes of The Control Chart § An experimental design in which all possible combinations of these factor Quality Variation levels would be run.

§ Fractional Factorial Design Implementing SPC in a § An experimental design in which only a portion of all possible combination The Rest of the Quality Improvement An Application of SPC of factor levels is run. Magnificent Seven Program At the conclusion of the team’s initial effort at applying SPC to the plating process, it had made substantial improvements in product Applications of SPC & cycle time through the process and had taken a major step in Quality Improvement improving the process capability. Tools in Transactional and Service

Discussion topics Businesses

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Applications of SPC & Quality Improvement Applications of SPC & Quality Improvement Tools in Transactional & Service Businesses Tools in Transactional & Service Businesses § Many of the examples used to reinforce the SPC principles are in § There seems to be two primary reasons for the difference an industrial, product oriented framework. between Transactional and service industry applications and manufacturing applications: § There have been many successful applications of SPC methods in § Most transactional and service businesses do not have a natural the manufacturing environment. measurement system that allows the analyst to easily define quality. § The system that is to be improved is usually fairly obvious in a § However, the principles themselves are general; there are many manufacturing setting, whereas the observability of the process in a applications of SPC techniques and other quality engineering and nonmanufacturing setting may be fairly low. statistical tools in nonmanufacturing settings, including transactional and service businesses.

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16 Example 1: Preparing Form 1040 Process Flow Chart income tax returns § Flow charts, operation process charts, and value stream mapping are particularly useful in developing process definition and process understanding.

§ Flow charts or process maps must be constructed in sufficient detail to identify value-added versus non- value-added work activity in the process.

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Example 2: Planning Process

The accounting firm was able to use quality improvement methods and the DMAIC approach successfully in their Form 1040 process, reducing the tax document preparation cycle time (and work content) by about 25%, and reducing the cycle time for preparing the client bill from over 60 days to 0 (that’s right, 0!). The client’s bill is now included with his or her tax return.

Example 1 - Result

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17 Check Sheet Summary Check Sheet

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Pareto Analysis Run Chart

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18 Example 3

The common causes were systematically removed from the process, and the long term impact of the SPC implementation in this organization was to reduce planning errors to a level of less than one planning error per 1,000 operations.

Example 2 - Result

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Typical Process Data Value Stream Map

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19 Technical quality improvement tools applied Dealing with Non-Normal data to service & transactional businesses. § Designed experiments, Simulation models, Control charts can all § One alternative to dealing with moderate to severe non- have many applications in the service economy. normality is to transform the original data (say, by taking logarithms) to produce a new set of data whose distribution is § One difference in the service economy is that you are more likely closer to normal. to encounter attribute data. § It also is important to be clear about to what the normality § Even when continuous data is encountered in service and assumption applies. In a regression model, the response is not transactional businesses, such as cycle time, it may not be normally distributed, it is the errors in this model, that need to be normally distributed. approximately normal. § Many statistical procedures (such as the t-tests and analysis of § There are situations in transactional and service businesses variance (ANOVA) are very insensitive to the normality where we are using regression and ANOVA and the response assumption. There are some that are sensitive to the normality variable y may be an attribute. Modeling techniques based on assumption. generalized linear models can handle many of these cases.

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End - Chapter 3

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