Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items

In this article, a variables sampling inspection plan for resubmitted lot based on the process capability index C_pk is developed for normally distributed items with unknown mean and variance. The three plan parameters, sample size n, critical acceptance value k_a and the number of resubmissions m, are determined simultaneously by minimizing average sample number (ASN) with two conditions specified by the producer and the consumer. The advantages of the proposed resubmitted sampling plan over the variables single sampling plan are also discussed. Tables of plan parameters for selected values of acceptable quality level (AQL), limiting quality level (LQL), producer’s α-risk and consumer’s β-risk are provided and discussed with the help of an application example.