Development of Bayesian Single Sampling Plan Involving Risk Minimization through Minimum Angle Method

Abstract

This chapter presented a procedure and tables for a Bayesian single sampling plan based on the Gamma-Zero Inflated Poisson distribution involving minimum angle method to reduce the producer's risk and consumer’s risk for specified acceptance quality level and limiting quality level. In recent years, every manufacturing industry using technological advancements to detect product defects and rectifying them in the initial stages of production. It is possible to reduce the number of defective products early on using such technologies. Therefore, the occurrence of non-defects would be more frequent in the sampling inspection. However, random fluctuations in the production processes may lead some products to an imperfect state. In this case, one can consider the appropriate probability distribution of the number of defects to be a Gamma-Zero Inflated Poisson (G-ZIP) distribution. The optimal plan parameters for the proposed sampling plan are given to determine its minimum angle values, which are illustrated with suitable examples. Necessary tables are constructed to facilitate quality control engineers.