A predictive Bayesian approach to sequential time‐between‐events monitoring

Abstract

AbstractA fundamental problem with all process monitoring techniques is the requirement of a large Phase‐I data set to establish control limits and overcome estimation error. This assumption of having a large Phase‐I data set is very restrictive and often problematic, especially when the sampling is expensive or not available, eg, time‐between‐events (TBE) settings. Moreover, with the advancement in technology, quality practitioners are now more interested in online process monitoring. Therefore, the Bayesian methodology not only provides a natural solution for sequential and adaptive learning but also addresses the problem of a large Phase‐I data set for setting up a monitoring structure. In this study, we propose Bayesian control charts for TBE assuming homogenous Poisson process. In particular, a predictive approach is adopted to introduce predictive limit control charts. Beside the Bayesian predictive Shewhart charts with dynamic control limits, a comparison of the frequentist sequential charts, designed by using unbiased and biased estimator of the process parameter, is also a part of the present study. To assess the predictive TBE chart performance in the presence of practitioner‐to‐practitioner variability, we use the average of the average run length (AARL) and the standard deviation of the in‐control run length (SDARL).