Developing a family of Bayesian group chain sampling plans for quality regions

Acceptance sampling is used to decide about the lot under inspection, either to accept or to reject. Various acceptance sampling plans under group chain consider only consumer’s risk to develop the plan, but this study focuses on both consumer’s and producer’s risks. If past information about the product is available, then Bayesian approach is the best approach to make a decision. This research aims to develop a family of Bayesian group chain sampling plans. The following plans are developed in this study: Bayesian group chain sampling plan (BGChSP), Bayesian new group chain sampling plan (BNGChSP), Bayesian modified group chain sampling plan (BMGChSP), Bayesian two sided group chain sampling plan (BTSGChSP), Bayesian new two sided group chain sampling plan (BNTSGChSP) and Bayesian two sided complete group chain sampling plan (BTSCGChSP). These plans consider multiple product inspections and use the past information of the product as prior distribution. To estimate the average proportion of defectives, binomial distribution is used with beta distribution as prior distribution. Meanwhile, to estimate the average number of defectives, Poisson distribution is used with gamma distribution as prior distribution. Four quality regions are estimated, namely, probabilistic quality region (PQR), quality decision region (QDR), limiting quality region (LQR) and indifference quality region (IQR). For all quality regions, acceptable quality level (AQL) associated with producer’s risk and limiting quality level (LQL) associated with consumer’s risk, are assessed. Simulated work is done by using R language computer-based programs and operating characteristic (OC) curves are used to monitor the effect of design parameters and for measuring performance between the proposed plans. Findings indicate that all the proposed plans provide a smaller number of defectives compared to the existing non-Bayesian plans. This would be very beneficial to practitioners, especially those involved with destructive testing of high-quality products.