Designing the Bayesian single sampling plan through Markov process

Pharmaceutical companies widely use sampling plans to test medications or other relevant components to make sure they are reliable and safe. A sampling plan is used to assess the quality of goods, keep an eye on the quality of the materials, methods, men power and confirm whether or not the yields are defect-free. If prior information about the manufacturing product is available, the Bayesian technique offers a better statistical approach to arriving at an appropriate conclusion. In an acceptance sampling plan under stochastic modelling, the inspected lot is rejected when the number of defective items falls above an upper control threshold value. However, the lot is accepted when it falls below a lower control threshold value, and if it falls within the thresholds, the process of inspecting the items continues, with the help of transition probability matrix. This plan is studied through the Gamma-Poisson model to safeguard both the producer and consumer by minimising the average sample number and total cost. Necessary tables and figures are constructed for the selection of optimal plan parameters, and suitable illustrations are provided that are applicable to the pharmaceutical industry.