Bayesian new group chain sampling plan for Poisson distribution with gamma prior through quality regions

Abstract

Acceptance sampling is used to make a decision about the lot, either it will be accepted or rejected, based on inspection of a representative sample selected from the same lot. According to experts, when historical information is available the Bayesian approach is the most effective method for making good decisions. The Bayesian approach is used in this study to “estimate an average number of defectives” and proposes a Bayesian new group chain sampling plan (BNGChSP). With gamma prior, the Poisson distribution is used to estimate an average number of defectives. To estimate an average number of defects, the Poisson distribution is combined with the gamma as a prior distribution. By considering both consumer’s and producer’s risks, quality regions are estimated for the average probability of acceptance. For these quality regions, acceptable quality level (AQL) and limiting quality level (LQL) are used to find design parameters for BNGChSP. 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 BNGChSP are tabulated and inflection points are found. For industrial practitioners based on the minimum number of defective the finding exposes that BNGChSP is a better substitute for existing plans. In a comparison study, the operating characteristic (OC) curves are compared for the proposed BNGChSP and the existing Bayesian group chain sampling plan (BGChSP). In the graph, it is represented that the OC curve based on BNGChSP is more ideal than the existing BGChSP. Based on OC curves, it can be concluded that the proposed BNGChSP plan gives a smaller number of defective than the existing BGChSP.