Analytical analysis of effect of sampling plan on Cpk

The use and abuse of process capability indices (PCIs) have become topics of considerable controversy in the last few years. A simulation shows that the difference in Cpk's estimated by three approaches, which are widely used in manufacturing industry, is at least 0.5. In this paper, the authors study analytically the differences in Cpk's calculated by these three different approaches. A few analytical relationships among the Cpk's are derived in this paper and are illustrated with a case study.