Using process capability indices to express process capability has simplified the process of setting and communicating quality goals, and their use is expected to continue to increase. Introduction process capability indices such as, c p, c pk, c pm and c pmk are typically used as measures of process capability in the univariate domain kotz and lovelace1998. Definition of the capability indices a capability index relates the engineering specification determined by the customer to the observed behaviour of the process. The effect of measurement error on process capability indices has been dealt with in.
Measures of process capability process capability indices. Astm e2281 15 standard practice for process capability. However, if the data is nonnormal, measuring process capability using conventional methods can lead to erroneous results. Process capability indices for shape parameter of weibull.
A variety of quality tools including flowcharts process documentation, control charts, process capability indices and experimental design are illustrated throughout the manuscript. Relations among the process capability indices have also been illustrated with examples. A process is a unique combination of machines, tools, methods and personnel engaged in providing a product or service. Process capability calculations with nonnormal data in the medical device manufacturing industry. Cp, cpl, cpu, and cpk are the four most common and timed tested measures of process capability. An origin of process capability indices is in the manufacturing industry. A comprehensive exposition of quality control measures. Samuel kotz is the author of process capability indices in theory and practice 5. Process capability indices pcis, cp, ca, cpk, cpm, and cpmk have been developed in certain. Six sigma process performance is reported in terms of sigma.
English and taylor analyzed nonnormality in pcis and posited. Samuel kotz author of process capability indices in. A number of authors worked on nonnormal distributions which were most notably those of clements, pearn and chen. Below, within the steps of a process capability analysis, we discuss how to determine stability and if a data set is normally distributed. Process capability cp, cpk and process performance pp. Cpk is used to estimate how close you are to a given targe. Encyclopedia and handbook of process capability indices. The distribution of the process considered is normal. Process capability indices for skewed populations chang. A new process capability indexc s, is proposed which extends the most useful index to date, the pearnkotzjohnson c pmk, by not only taking into account that the process mean may not lie midway between the specification limits and incorporating a penalty when the mean deviates from its target, but also incorporating a penalty for skewness.
The comparison is made by forming the ratio of the spread between the process specifications the specification width to the spread of the process values, as measured by 6 process standard deviation units the process width. Residuals based process capability indices for twostage. Process capability compares the output of an incontrol process to the specification limits by using capability indices. Learn the definitions, interpretations and calculations for cp, cpk, pp and ppk. Furthermore, the determination of sample sizes required to achieve a. Process performance is only used when process control cannot be evaluated. Process capability indices based on median absolute deviation kayode s. Statistical methods in process management capability and performance part 4. An overview of theory and practice on process capability indices for. Thus, they emphasize the suppliers responsibility to satisfy those specifications. Process capability indices have been used in the manufacturing industry to.
Process capability indices have been popular for over 20 years, since joseph juran12 popularized the capability ratio cr in his quality control handbook. Process capability analysis and process analytical technology. There is, of course, much more that can be said about the case of nonnormal data. This unique volume provides an uptodate and detailed description of the various process capability indices widely and sometimes misleadingly used in the applications at production sites. In simple words, it measures producers capability to produce a product within customers tolerance range.
Bates 1 discussed robustness of indices based on normal population, pyzdek 2,3 showed that for nonnormal processes standard process capability indices will give false process fallout rates and misled the results. Di erent process capability indices such as clements percentile method and data trans. His research interests include the fields of quality assurance, process capability, process control, and loss functions. Adekeye redeemers university department of mathematical sciences redemption camp mowe, nigeria. Abstract process capability is the performance of a process under normal and incontrol conditions. Sample size determination for the estimate of process. Fred spiring is a senior member of the american society of quality, adjunct professor in the department of statistics, the university of manitoba, and a retired director of pollard banknote ltd in winnipeg, manitoba, canada. Like the capability ratio, all pcis explicitly link process variability to customer specifications. Process capability calculations with nonnormal data in the.
Understanding process capability indices statistics and actuarial. George washington university, washington, dc 20052. The authors, who are internationally recognized experts in this area with numerous contributions to the field, provide a lucid exposition, which covers all. The concept of process capability only holds meaning for processes that are in a state of statistical control. However, if a boxcox transformation can be successfully performed, one is encouraged to use it. Pearn and samuel kotz, an overview of theory and practice on process capability indices for quality assurance, international journal of production economics, 117, 2, 338, 2009. Process capability indices for shape parameter of weibull distribution.
Pdf usage of process capability indices during development. Process capability analysis for nonnormal processes with. Usl, where lsl and usl are the lower and upper tolerance limits. Process capability indices 1st edition samuel kotz. Process capability indices measure the degree to which your process produces output that meets the customers specification. Introduction process capability analysis deals with how to assess the capability of a manufacturing process, where information about the process is used to improve the capability. Basic indices cp, cpk, cpm, cpmk initially developed for normally distributed processes showed inappropriate for processes with nonnormal distributions.
Johnson department of statistics university of north carolina chapei hi11. In process improvement efforts, the process capability index or process capability ratio is a statistical measure of process capability. Finally, section four proposes clear guidelines for the appropriate use of process capability indices. Kotz, samuel and johnson, norman, process capability indices, chapman. Process capability indices crc press book a solid, rigorous, yet comprehensible analysis of process capability indices, this work bridges the gap between theoretical statisticians and quality control practitioners, showing how an understanding of these indices can lead to process improvement. Process capability cp, cpk and process performance pp, ppk. Process capability indices under nonnormality conditions. Cp, cpk and their modifications samuel kotz chapter 3 the cpm index and related indices samuel kotz chapter 4 process capability indices under nonnormality. Process capability index cpk is a statistical tool, to measure the ability of a process to produce output within customers specification limits. If these assumptions are not met, the resulting statistics may be highly unreliable.
The effect of sample size on estimated limits for and x control charts, journal of quality technology, 254 237247. Mar 20, 2007 a new process capability indexc s, is proposed which extends the most useful index to date, the pearn kotz johnson c pmk, by not only taking into account that the process mean may not lie midway between the specification limits and incorporating a penalty when the mean deviates from its target, but also incorporating a penalty for skewness. Rivera 4 discussed c pk index estimation using transformation technique. Cpk works well only for the bellshaped normal gaussian distribution. Kotz and johnson tested properties of the indices, e. Estimating and testing quantilebased process capability indices for processes with skewed distributions cheng peng university of southern maine abstract. Certain standards and tests based on capability indices have validity when the process variation has a normal distribution. For more information on process capability indices kotz and johnson, 1993. Chapter 1 introduction samuel kotz chapter 2 the basic process capability indices. Astm e2281 15 standard practice for process capability and.
A solid, rigorous, yet comprehensible analysis of process capability indices, this work bridges the gap between theoretical statisticians and quality control practitioners, showing how an understanding of these indices can lead to process improvement. There is quit some confusion about the use of these indices. Furthermore, the determination of sample sizes required to achieve a speci. In this article we will discuss the most common used indices cp, cpk, pp and ppk. Pca studies intrigue academics, practitioners, and. Introduction a process capability index is a numerical summary that compares the behavior of a product. Data used in the analyses has been included where permitted. An example of this is for a short preproduction run. To compare a process with customer requirements or specifications, it is common practice to think of capability in terms of the proportion of the process output that is within product specifications or tolerances. Pdf encyclopedia and handbook of process capability indices. But the statistical measurements of cp, cpk, pp, and ppk may provide more insight into the process.
An important part of any spc implementation is the use of process capability indices. Process capability estimation for nonnormal quality. Eagerness to establish a single index to measure process capability has resulted in the proliferation of indices. There are several capability indices cp, cpk, ppk, cpm, ncpk. Pdf encyclopedia and handbook of process capability.
Process capability indices pcis are appropriate tools in order to measure the inherent capability of a process. Because the sample mean and the sample variance s 2 are not unitless, they can be cumbersome as summary statistics for the process location and variance, respectively. However, it has been my experience in the medical device industry that many processes are nonnormal and that the application of the normal theory in these cases can lead one astray. Process capability indices, samuel kotz and norman l. Process capability indices based on median absolute deviation. Cpcpk, vpvpk, ppppk, cpm, tz, %ool, ppm, and more recently. Consider a production process which generates consecutively units of product represented by a sequence of independent n. Pdf process capability and capability index cp and cpk. Process capability indices measure how much natural variation a process. Approximately unbiased estimator for nonnormal process capability index c npk, journal of testing and evaluation, vol. To illustrate the calculation of the estimated capability indices cpk and ppk we present a simple example. Pearn and samuel kotz, an overview of theory and practice on process capability indices for quality assurance, international journal of production economics, 117, 2. Process capability indices in theory and practice request pdf.
Generalized process capability index, defined as the ratio of. Additionally, several extensions and applications to real world problem are also discussed. In a later modules we will discuss capability analysis for nonnormal data. This book therefore covers material essential for quality engineers and applied statisticians who are interested in maximizing process capability. Most capability index estimates are valid only if the sample size used is large enough, which is generally thought to be about 30 or more independent data values. Johnson university of north carolina, chapel hill, nc 27599 we provide a compact survey and brief interpretations and comments on some 170 publications on process capability indices which appeared in widely scattered. Process capability index 179 proceeding as in the case of the index c pcu, one may. Measurement error effects on the performance of process. Samples from the batch may need to be quite large to be representative of the variation in the batch. Pca studies intrigue academics, practitioners, and also students. Pearn and samuel kotz, booktitleseries on quality, reliability. Process capability indices pcis, cp, ca, cpk, cpm, and cpmk have been developed in certain manufacturing industry as. It differs from process capability in that process performance only applies to a specific batch of material. Applications of process capability and process performance.
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