Defect rate estimation and cost minimization using imperfect acceptance sampling with rectification

An important aspect of any quality control program is estimation of the quality of outgoing products. This dissertation applies Acceptance Sampling with rectification to the problem of quality assurance when the inspection procedure is imperfect. The objective is to develop effective rectification sampling plans and estimators based on these plans without making the assumption of a perfect inspection procedure. We develop estimators, under two different sampling plans, for the number of undetected defects remaining after a set of lots has been passed. We compare, by extensive simulation, the proposed estimators with existing ones in terms of Root Mean Squared Error (RMSE). One of our estimators, an empirical Bayes estimator, is seen to consistently obtain substantially lower RMSE overall. We also construct expected cost functions for sampling plans based on fixed sample sizes. We then show how intermediate empirical Bayes estimates of population characteristics can be used to obtain adaptive acceptance sampling plans which vary the sample sizes in order to reduce expected cost. We also compare the two sampling plans on the basis of RMSE and expected cost functions. We show that RMSE comparisons across different levels of machine imperfection can be misleading and propose a measure which accounts for MSE and expected cost simultaneously.