ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

A Sequential Hypothesis Test for the Process Capability Index Cpk

11 September 2017, 17:30 – 17:50


Submitted by
Michele Scagliarini
Michele Scagliarini (University of Bologna)
In this work we propose a sequential test for the process capability index Cp. 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.

Hussein, A., Ahmed, S.E., Bhatti, S. (2012). Sequential testing of process capability indices. Journal of Statistical Computation and Simulation, 82(2), 279-282.
Lepore, A. Palumbo, B. (2015). New Insights into the Decisional Use of Process Capability Indices via Hypothesis Testing. Quality and Reliability Engineering International, 31(8), 1725-1741.
Pearn, W.L., Chen, K.S. (1999) Making decision in assessing process capability index Cpk. Quality and Reliability Engineering International, 15(4), 321-326.
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