Estimating Cpk Accuracy

Article

Price, Barbara; Price, Kelly   (1992, ASQC)   Wayne State University Business School, Detroit, Michigan

Annual Quality Congress, Nashville TN    Vol. 46    No. 0
QICID: 9810    May 1992    pp. 9-15
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Article Abstract

The capability indices Cp and Cpk are often used by quality practitioners as unitless estimates of process or product performance. These ratios compare product or process sample variation to externally set engineering tolerances. While there is widespread use of these indices as static benchmarks for quality or performance, an important issue that is not always addressed is the accuracy or variability of these sample estimates. Two accuracy issues are examined: the bias in using sample computations as estimates of the population parameters and the variability of the sample estimates. Monte Carlo simulations and the bootstrap methodology are employed as the means to study these two effects for a broad class of probability distributions. Both the Monte Carlo and the bootstrap methods yielded similar results; namely, that Cp and Cpk are biased by the sampling variability. The accuracy of both values based on estimates from random samples is influenced by sample size and properties of the probability distribution. Therefore, using SPC (Statistical Process Control) charting for the mean Cp and Cpk may be the more appropriate technique for comparison, as opposed to static hypothesis testing. (Edited author abstract)

Keywords

Accuracy and precision,Capability study,Estimation,Sampling,Statistical process control (SPC)


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