Novel Bayesian CUSUM and EWMA control charts via various loss functions for monitoring processes

Abstract

In this work, both the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been reconfigured to monitor processes using a Bayesian approach. Our construction of these charts are informed by posterior and posterior predictive distributions found using three loss functions: the squared error, precautionary, and linex. We use these control charts on count data, performing a simulation study to assess chart performance. Our simulations consist of sensitivity analysis of the out-of-control shift size and choice of hyper-parameters of the given distributions. Practical use of theses charts are evaluated on real data.