Bayesian EWMA and CUSUM Control Charts Under Different Loss Functions

TL;DR

This paper develops Bayesian versions of EWMA and CUSUM control charts for process monitoring, incorporating different loss functions and priors, and evaluates their performance through extensive simulation.

Contribution

It introduces Bayesian EWMA and CUSUM charts with flexible loss functions and priors, providing a comprehensive performance evaluation and practical recommendations.

Findings

Bayesian charts outperform traditional ones in certain scenarios.

Performance depends on loss functions and prior choices.

Recommendations vary based on process shift characteristics.

Abstract

The Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts have been used in profile monitoring to track drift shifts that occur in a monitored process. We construct Bayesian EWMA and Bayesian CUSUM charts informed by posterior and posterior predictive distributions using different loss functions, prior distributions, and likelihood distributions. A simulation study is performed, and the performance of the charts are evaluated via average run length (ARL), standard deviation of the run length (SDRL), average time to signal (ATS), and standard deviation of time to signal (SDTS). A sensitivity analysis is conducted using choices for the smoothing parameter, out-of-control shift size, and hyper-parameters of the distribution. Based on obtained results, we provide recommendations for use of the Bayesian EWMA and Bayesian CUSUM control charts.