Comparing the sequential and the repetitive Cpk sampling plans

Abstract

Abstract The index Cpk was created to quantify the ability of the process to produce products within the upper and lower specified limits (USL/LSL); but in the last two decades, the sample estimator of the capability index Cpk has also been used to decide whether a lot should be accepted or not; if the value of a sample of size n, randomly taken from the lot, is lower/larger than a threshold, then the lot is rejected/accepted. The sampling plan based on the value is known as the Cpk sampling plan. In recent publications, the Cpk sampling plan has been combined with the repetitive sampling scheme. In short, with the repetitive sampling scheme the Cpk sampling plan might be applied m times, consequently, the lot has m chances to be accepted; if the Cpk sampling plan is applied m times and the lot is not accepted, then the lot is finally rejected. The average number of inspected items per lot (ANI) the repetitive Cpk sampling plan (where m > 1) requires to decide whether the lot should be accepted or not is larger than the sample size n of the standard Cpk sampling plan (where m = 1), because of that the repetitive sampling strategy is not recommended. In this article, we propose the sequential Cpk sampling plan where the is compared with two thresholds (c1; c2) with c1 < c2; if the is lower (larger) than c1 (c2), then the lot is rejected (accepted); otherwise, the decision is left to the next sample. The ANI of the sequential Cpk sampling plan is a function of c1 and c2; depending on the choice of these two design parameters, the ANI of the sequential Cpk sampling plan is substantially lower than the sample size n of the standard Cpk sampling plan.

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