In this article, a variables sampling inspection plan for resubmitted lot based on the process
capability index Cpk is developed for normally distributed items with unknown mean and
variance. The three plan parameters, sample size n, critical acceptance value ka 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 a-risk and consumer’s b-risk are provided
and discussed with the help of an application example.