Improving the Chain Sampling Plans Based on Cpm Index

ABSTRACT A recent article discusses the design of chain sampling plans based on the Cpm index where a sample is randomly selected from the lot, and the C pm value of the sample is compared with the threshold ( k a ). If the C pm is lower than k a , the lot is rejected, otherwise, the C pm values of previous m lots are examined; if m ‐1 of the C pm values exceed k a and the remaining C pm value exceeds one or both thresholds ( k r , k a ), the lot is accepted, otherwise the lot is also rejected. In this article, we adopted the criteria of C pm s lower than k r (instead of k a ) to reject the current lot. In this way, current lots with C pm s in the interval ( k r , k a ) can still be accepted; in fact, they are accepted if the C pm s of their preceding m lots exceed k a . We found that the original lot sentencing procedure, without the proposed modifications, increase the average sample size required by the CPM‐based chain sampling plan by 18%, 26%, and 28% for m = 1, 2, and 3, respectively. An algorithm has been developed to find the minimum sample size n required by the chain sampling plan to satisfy the producer and consumer risks. It is a very fast ( n , k r ) search algorithm that intelligently exploits the fact that the second threshold k a can be expressed as a function of ( n , k r ).