On Designing a New Bayesian Dispersion Chart for Process Monitoring

Statistical quality control is an integral part of modern manufacturing, and control charts are widely used to improve and control the performance of a process. However, much of the work related to process monitoring has been done using frequentist approaches, whereas the Bayesian methodology has a practical advantage in process monitoring; that is, it can be used with a small phase-I dataset. In this article, we considered different symmetric and asymmetric loss functions for designing Bayesian control charts and noticed that the performance of the Bayesian charts is biased, i.e., in-control performance of the charts is not equal to the desired value for some loss functions and comparison among different Bayesian charts can be misleading. Therefore, to get the desired in-control performance under different loss functions, we propose a corrected design of the Bayesian control charts. In addition to posterior charts, we also discuss a predictive control chart to monitor the future observations in this study. Besides a simulation study, we also present two real data examples: the first example is to monitor the surface roughness of reamed holes in a particular metal part while the second is about monitoring the measurements of a diameter.