Estimating Nonconformance Rates After Zero-Defect Sampling With Rectification

Abstract

Suppose a set of T lots has been subject to zero-defect acceptance sampling with rectification. A lot is accepted if there are no nonconforming units in a sample; otherwise there is 100% inspection of the lot and all nonconforming units are replaced with conforming ones. We introduce an estimator for the number of nonconformances that remain in those lots, using the data observed during acceptance sampling, including the rectification procedure. The estimator proposed is similar to a Horvitz-Thompson estimator in that it weights the number of detected nonconformances in a lot by the inverse of its detection probability. The mean squared error of this estimator is compared with several alternatives. The proposed estimator was found to perform well under a variety of models for the nonconformance process. Confidence interval procedures are given for the proposed estimator. A simulation study shows that coverage is less than the nominal level for few lots and small sample sizes. We observe that the coverage is improved by the use of a transformation.

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