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