Designing Bayesian Modified Group Chain Sampling Plan for Quality Regions Based on Average Number of Defectives

Abstract

Acceptance sampling provides a mid-way between zero and 100% inspection, which can provide a statistically reliable inference on deciding whether or not to accept the entire lot based on a sample inspection. If the prior information is available then according to experts, Bayesian approach is the best approach to reach a correct decision. Based on the Bayesian approach, this study proposes a Bayesian modified group chain sampling plan (BMGChSP) to estimate the average number of defectives. The Poisson distribution is used to estimate the average number of defectives and gamma as a prior distribution for the average probability of acceptance. Instead of basing a sampling plan one point-wise description of quality like the conventional plans, the proposed plan uses quality range for a wider coverage and offers better protection to both consumer’s and producer’s. In this paper by considering consumer’s risk and producer’s risk, quality regions are estimated for the average probability of acceptance. For all quality regions, acceptable quality level (AQL) and limiting quality level (LQL) are used to find design parameters for BMGChSP. Where AQL is associated with consumer’s risk and LQL is associated with producer’s risk. The values based on all possible combinations of design parameters for BMGChSP are tabulated and inflection points are found. Based on the minimum number of defective the finding exposes that BMGChSP is a better substitute for industrial practitioners. In comparison study by OC curves, it is concluded that the proposed BMGChSP plan gives a smaller number of defective than the existing BGChSP.