A Sequential Hypothesis Test for the Process Capability Index Cpk

In this work we propose a sequential test for the process capability index . We study the statistical properties of the sequential test by performing an extensive simulation study with regard the average of the sample sizes for correctly deciding, for H0 and H1 , the maximum allowable sample size required to achieve a pre-set power level and for ensuring that the empirical type I error probability does not exceed the nominal alfa-level of the test. We compared the performances of the sequential procedure with two non-sequential tests. The results show that the proposed test allows on average smaller stopping sample sizes as compared with the fixed sample size tests while maintaining the desired alfa-level and power. Furthermore, the maximum allowable sample sizes required by the sequential test to achieve the desired power level are smaller than, or at most equal to, the sample sizes required by the non-sequential tests: this means that even in the worst cases the sequential procedure uses a sample size that does not exceed the sample size of the non-sequential tests with the same power level (under H1) or without exceeding the type I error probability (under H0). Summarizing, the proposed sequential procedure has several interesting features: it offers a substantial decrease in sample size compared with the non-sequential tests, while type I and II error probabilities are correctly maintained at their desired values.