A fully Bayesian approach to sample size determination for verifying process improvement

Abstract

There has been significant growth in the development and application of Bayesian methods in industry. The Bayes’ theorem describes the process of learning from experience and shows how knowledge about the state of nature is continually modified as new data become available. This research is an effort to introduce the Bayesian approach as an effective tool for evaluating process adjustments aimed at causing a change in a process parameter. This is usually encountered in scenarios where the process is found to be stable but operating away from the desired level. In these scenarios, a number of changes are proposed and tested as part of the improvement efforts. Typically, it is desired to evaluate the effect of these changes as soon as possible and take appropriate actions. Despite considerable research efforts to utilize the Bayesian approach, there are few guidelines for loss computation and sample size determination. This research proposed a fully Bayesian approach for determining the maximum economic number of measurements required to evaluate and verify such efforts. Mathematical models were derived and used to establish implementation boundaries from economic and technical viewpoints. In addition, numerical examples were used to illustrate the steps involved and highlight the economic advantages of the proposed procedures.