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PRE-CONTROL and SOME SIMPLE ALTERNATIVES Stefan H This article was downloaded by: [Canadian Research Knowledge Network] On: 23 November 2010 Access details: Access Details: [subscription number 918588849] Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37- 41 Mortimer Street, London W1T 3JH, UK Quality Engineering Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713597292 PRE-CONTROL AND SOME SIMPLE ALTERNATIVES Stefan H. Steinera a Department of Statistics and Actuarial Sciences, University of Waterloo, Waterloo, Canada To cite this Article Steiner, Stefan H.(1997) 'PRE-CONTROL AND SOME SIMPLE ALTERNATIVES', Quality Engineering, 10: 1, 65 — 74 To link to this Article: DOI: 10.1080/08982119708919110 URL: http://dx.doi.org/10.1080/08982119708919110 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Quality Engineering, 10(1), 65-74 (1997-98) PRE-CONTROL AND SOME SIMPLE ALTERNATIVES Stefan H. Steiner Department of Statistics and Actuarial Sciences University of Waterloo Waterloo, Canada N2L 3G1 Key Words Classical Pre-control refers to the original formulation of Pre-control as described by Shainin and Shainin (I) and Acceptance control charts; Grouped data; Modified he- Traver (3). Two-stage Pre-control is a modification dis- control; Operating characteristic; Process capability; Stop- cussed by Salvia (4) that improves the method's operating light control. characteristics by taking an additional sample if the initial sample yields ambiguous results. Modified Pre-control, on Introduction the other hand, as suggested by Gurska and Heaphy (5), represents a departure from the philosophy of Classical and Two-stage Pre-control. Modified Pre-control attempts to Pre-control, sometimes called stoplight control, was compromise between the design philosophy of Shewhart- developed to monitor the proportion of nonconforming type control charts and the simplicity of application of Pre- units produced in a manufacturing process. Implementation control. is typically very straightforward. All test units are classi- Pre-control schemes are defined by their group classi- fied into one of three groups: green, yellow, or red, where fication procedure, their decision criteria, and their quali- the colors loosely correspond to good, questionable, and fication procedure. The qualification procedure specifies poor quality products (see Fig. 1). The number of green, the required results of an initial intensive sampling scheme yellow, and red units observed in a small sample deter- used to determine if Precontrol is appropriate for the given mines when to stop and adjust the process. The goal of Downloaded By: [Canadian Research Knowledge Network] At: 18:16 23 November 2010 application. For all three versions of he-control, a process Pre-control is to detect when the proportion of noncon- passed the qualification if five consecutive green units are forming units produced becomes too large. Thus, he-con- observed. As all three versions of Pre-control have the trol schemes monitor the process to ensure that process same qualification procedure, it is not discussed in more capability (C,,) remains large. detail in this article. The three versions of Pre-control dif- Pre-control was initially proposed in 1954 (see Refs. 1 fer most substantially in their group classification method. and 2 for more details) as an easier alternative to Shewhart Classical Pre-control and Two-stage Pre-control base the charts. However, since that time, at least three different classification of units on engineering tolerance or specifi- versions of Pre-control have been suggested in the litera- cation limits. A unit is classified as green if its quality ture. In this article the three versions are called dimension of interest falls into the central half of the tol- Classical Pre-control erance range. A yellow unit has a quality dimension that * Two-stage Pre-control falls into the remaining tolerance range, and a red unit falls Modified Pre-control outside the tolerance range. Assuming, without loss of Copyright 1997 by Marcel Dekker. Inc. STEINER The group probabilities given by Eqs. (I) and (2) are the same when p, = 0 and a, = 113. This makes sense because in that case, the control limits and the tolerance limits are the same. It has been suggested that Classical Pre-control and Two-stage Pre-control are only applicable if the current process spread (six process standard devia- tions) covers less than 88% of the tolerance range (3). With specification limits at f I, as defined previously, this con- dition corresponds to the constraint a < 0.29333. The second important difference between the three Pre- Ral Yellow Green Yellow Red control versions is their decision criteria. Classical Pre- -1 -3 J 1 control bases the decision to continue operation or to ad- Measurement LSL USL just the process on only one or two sample units. The Figure 1. Pre-control classification criteria. decision rules are given as follows: Sample two consecutive pans A and B generality, that the upper and lower specification limits If part A is green, continue operation (no need to (USL and LSL) are 1 and -1, respectively, group classi- fication is'based on the endpoints: r = [-I, -0.5, 0.5, I]. measure B). If part A is yellow, measure part B. If part B is Figure 1 illustrates this classification scheme. The colored circle can be used for the ease of the operators as a dial green, continue operation, otherwise stop and adjust indicator overlay (I). process. Let the quality dimension of interest be Y. Then, given If part A is red, stop and adjust process (no need to a probability density function for observations fCy), the measure B). group probabilities for Classical and Two-stage Pre-control The decision procedure for Two-stage Pre-control and are given by Modified Precontrol is more complicated. If the initial two observations do not provide clear evidence regarding the state of the process, additional observations (up to three more) are taken. The decision procedure for Two-stage and Modified Pre-control is given as follows: Sample two consecutive parts. fired) = P, = f(y) dy + f(y) dy. JYi Y-1 If either part is red, stop process and adjust. Modified Pre-control, on the other hand, classifies units If both parts are green, continue operation. using control limits, as defined for Shewhart charts, rather If either or both of the parts are yellow, continue to than tolerance limits. This change indicates a fundamental sample up to three more units. Continue operation Downloaded By: [Canadian Research Knowledge Network] At: 18:16 23 November 2010 difference and makes modified Pre-control much more like if the combined sample contains three green units, a Shewhart chart than like Classical he-control. Equations and stop the process if three yellow units or a single (2) give the group probabilities for the Modified Pre-con- red unit are observed. trol procedure. Note that to avoid confusion, throughout this article the current process mean and standard deviation The advantage of this more complicated decision pro- cedure is that more information regarding the state of the are denoted j~and a, whereas estimates of the in-control mean and standard deviation used to set the control limits process is obtained and, thus, decision errors are less for Modified Pre-control and Shewhart-type charts are likely. The disadvantage is that, on average, larger sample denoted p, and a,. sizes are needed to make a decision regarding the state of the process. Table 1 summarizes the comparison of the three versions of he-control. Clearly, the different versions of Pre-control are not the same in purpose and ease of implementation. By design, Classical Precontrol and Two- stage Pre-control tolerate some deviation in the process mean, so long as the proportion nonconforming does not PRE-CONTROL AND SIMPLE ALTERNATIVES Table 1. Comparison of Pre-control Versions Classical and Two-stage Pre-control are compared with acceptance control charts (ACCs) because both these types GROUP PRE-CONTROL CLASSIFICATION DECISION CRITERIA of monitoring schemes are designed to signal only if the VERSION BASED ON BASED ON proportion nonconforming becomes unacceptably high. An ACC is designed to monitor a process when the process Classical Tolerance limits Two observations variability is much smaller than the specification (tolerance) Two-stage Tolerance limits Five observations spread (7). Under that assumption, moderate drifts in the Modified Control limits Five observations mean (from the target value) are tolerable, as they do not yield a significant increase in the proportion of noncon- forming units. Like Classical and Two-stage Pre-control, become too.large. In this sense, Classical and Two-stage ACCs are based on engineering specification limits. How- Pre-control are very similar to acceptance control charts. ever, ACC limits are derived based on a distributional In addition, Classical and Two-stage Pre-control can be assumption and require a known and constant process stan- quickly implemented because they do not require estimates dard deviation. ACC limits are usually set assuming a of the current process mean and standard deviation to set normal process, although, if justified, other assumptions their grouping criterion.
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