A note on decision making method for product acceptance based on process capability indices Cpk and Cpmk

In this short note, we prove that the derivation of the required sample size and critical acceptance value under the normality assumption of the quality characteristic proposed by 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, is inappropriate. In fact, it leads to a lower probability of acceptance than the one desired by the producer. The same issue also occurs in the case of a variables single sampling plan described in a previous paper by Pearn, W. L., & Wu, C. W. (2007). An effective decision making method for product acceptance. Omega, 35(1), 12–21. Nevertheless, a similar yet less severe inaccuracy is also noticed in 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