Bayesian Two-Sided Complete Group Chain Sampling Plan for Poisson Distribution with Gamma Prior

Abstract

For statistical quality assurance based on the inspection of a random sample, acceptance sampling plan help to decide whether the lot should be accepted or rejected. Most traditional plans only focus on minimizing the consumer’s risk, but producer’s risk also should not be ignored in acceptance sampling plan. Therefore, this study focuses on reducing both producer’s and consumer’s risks through the quality region. This study proposes a Bayesian two-sided complete group chain sampling plan (BTSCGChSP) for the average probability of lot acceptance. The Poisson distribution with gamma as prior distribution is used to derive the average probability of lot acceptance. Next, R programing language is used to obtain the average number of defectives according to average probability of acceptance and pre-specified values of design parameters. For selected design parameters in BTSCGChSP, the acceptable quality level (AQL) associated with producer’s risk and limiting quality level (LQL) associated with consumer’s risk are considered to estimate quality regions. In this paper, four quality regions are measured: (i) probabilistic quality region (PQR), (ii) quality decision region (QDR), (iii) limiting quality region (LQR) and (iv) indifference quality region (IQR). Operating characteristic curves (OC) are used for performance comparison with existing Bayesian group chain sampling plan (BGChSP) for the same probability of lot acceptance and other design parameter values. Findings validate that BTSCGChSP provides more ideal OC curve than BGChSP for the same probability of acceptance. For quality regions with the same values of consumer’s and producer’s risks, then the BTSCGChSP region will contain fewer defectives than in the BGChSP region. Hence, the proposed plan is a better substitute for existing BGChSP.