ENBIS-17 in Naples

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

A Note on the Minimum Sample Size and Critical Acceptance Value for Variables Sampling Inspection Scheme Based on Process Capability Indices Cpk and Cpmk

11 September 2017, 17:50 – 18:10


Submitted by
Biagio Palumbo
Antonio Lepore (University of Naples Federico II), Biagio Palumbo (University of Naples Federico II), Guido Cesaro (University of Naples Federico II)
Mathematical insights into the use of process capability indices (PCIs) Cpk and Cpmk are discussed in order to support managerial decision-making via hypothesis testing and avoid misleading conclusions [1]. In view of those arguments, inappropriate approximations found in the literature concerning producer’s α-risk and consumer’s β-risk corresponding to a sampling inspection scheme based on those PCIs are highlighted. In particular, in the case of Cpk, we demonstrate the approximation proposed in [2] gives required sample size and critical acceptance value that are not (even asymptotically) conservative with respect to the α-risk. Some counter examples illustrate that such approximation leads to substantial deviations from the actual α-risk and thus, should be not used in practice. Moreover, we point out that there is no need of particular computer programs and tables to numerically determine the exact solution. Nevertheless, the same issue occurs in [3] and a similar yet less severe inaccuracy with respect to the case of the Cpmk is also noticed in [4].

[1] 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. https://doi.org/10.1002/qre.1713
[2] Wu, C. W., Aslam, M., & Jun, C. H. (2012). Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk. European Journal of Operational Research, 217(3), 560–566. https://doi.org/10.1016/j.ejor.2011.09.042
[3] Pearn, W. L., & Wu, C. W. (2007). An effective decision making method for product acceptance. Omega, 35(1), 12–21. https://doi.org/10.1016/j.omega.2005.01.018
[4] Wu, C. W., & Pearn, W. L. (2008). A variables sampling plan based on Cpmk for product acceptance determination. European Journal of Operational Research, 184(2), 549–560. https://doi.org/10.1016/j.ejor.2006.11.032

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