A comparative study of self-starting CUSUM control charts for location shifts

TL;DR

This paper compares two self-starting CUSUM control charts for detecting mean shifts in normal data, evaluating their performance through extensive simulations and sensitivity analysis.

Contribution

It provides a comprehensive comparison of Bayesian and frequentist self-starting CUSUM charts, highlighting their relative performance and sensitivity.

Findings

Bayesian PRC shows robust detection capabilities.

Frequentist CUSUM performs well under certain conditions.

Sensitivity analysis reveals parameter impacts on PRC performance.

Abstract

In recent years, self-starting methods have garnered increasing attention in Statistical Process Control and Monitoring (SPC/M), as they offer real-time disorder detection without the need for a calibration phase (Phase I). This study focuses on evaluating parametric self-starting CUSUM-type control charts, specifically the Bayesian Predictive Ratio CUSUM (PRC) developed by Bourazas et al. (2023) and the frequentist alternative self-starting CUSUM proposed by Hawkins and Olwell (1998). The performance of these methods is thoroughly examined through an extensive simulation study under various scenarios involving a change in the mean of Normal data. Additionally, a prior sensitivity analysis for PRC is conducted. The work ands with concluding remarks summarizing the findings.