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

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.