Bayesian double group sampling plan for assessing the average number of nonconforming products in manufacturing: a Poisson-Gamma distribution approach

To succeed in the global market, firms must prioritize quality over individual goals and preferences. Acceptance sampling is one of the two primary approaches for ensuring quality, which is used in statistical process control for attributes inspection of the product. In acceptance sampling based on predetermined acceptance criteria for inspection the lot is either accepted or not accepted. This research introduces a Bayesian double group sampling plan (BDGSP) for estimating average number of nonconforming products. Based on acceptance criteria the Poisson distribution is used to construct the likelihood function for both nonconforming and conforming products. To calculate the average probability of acceptance, the gamma distribution is used as a suitable prior distribution of the Poisson distribution. For various suggested producer's and consumer's risk levels four distinct quality regions are calculated. The producer's risk is related to acceptable quality level and consumer's risk is related to and limiting quality level. Operating characteristic curves are utilized to track the effects of changes in the values of the specified parameters. The applicability of the proposed plan for current industrial strategies is demonstrated using a real dataset.