A Bayesian approach with double group sampling plan to estimate quality regions for proportion of nonconforming products in industry based on beta prior

Abstract

To succeed in the global market, firms must prioritize quality over individual goals and preferences. One of the two primary approaches for ensuring quality is acceptance sampling, which is employed in statistical process control to inspect attributes of the product for acceptance. In acceptance sampling, the lot is either accepted or not-accepted based on predetermined acceptance criteria for inspection. This paper presents a proposed Bayesian double group sampling plan (BDGSP) for estimating quality regions. The binomial distribution is used to construct the likelihood function for both nonconforming and conforming products based on acceptance criteria. To calculate the average probability of acceptance, the beta distribution is used as a suitable prior distribution of the binomial distribution. Four distinct quality regions are predicted for various indicated producer’s and consumer’s risk levels. Based on various combinations of values for design parameters, the suggested plan generates variation point values. Risks for producers and consumers are related to acceptable quality level and limiting quality level. To track the effects of changes in the values of the specified parameters, operating characteristic curves are utilized. The applicability of the proposed plan for current industrial strategies is demonstrated using a real dataset.