Bibliographic Information: Bourazas, K. (2024). A comparative study of self-starting CUSUM control charts for location shifts. arXiv preprint arXiv:2410.12736v1.
Research Objective: This paper compares the performance of two self-starting control charts, the frequentist Self-Starting CUSUM (SSC) and the Bayesian Predictive Ratio CUSUM (PRC), in detecting location shifts in normally distributed data.
Methodology: The study employs an extensive simulation study to evaluate the performance of SSC and PRC under various scenarios involving changes in the mean of normally distributed data. The performance is assessed using the Conditional Expected Delay (CED) metric, which measures the average delay in detecting a shift after it occurs. The study considers different magnitudes of shifts, change point positions, and design parameter values for both methods. Additionally, a prior sensitivity analysis is conducted for PRC using a non-informative reference prior and a weakly informative prior.
Key Findings: Both SSC and PRC exhibit effective detection of larger shifts compared to smaller shifts. Their performance improves with a larger IC data history, meaning when the change point occurs later in the process. The prior information in PRCi positively impacts detection, especially with limited data points early in the process. However, as the IC data volume increases, the performance of PRCi converges with PRCn and SSC, diminishing the impact of the prior. PRCn and SSC demonstrate similar performance overall, with SSC showing a slight advantage for small design parameter values and early change points, while PRCn performs slightly better for larger design parameter values.
Main Conclusions: The study concludes that both SSC and PRC are viable options for online change point detection in the mean of univariate Normal data without a Phase I calibration phase. The choice between the two methods might depend on factors like the expected magnitude of shifts, the availability of prior information, and the desired sensitivity to early change points.
Significance: This research contributes to the field of Statistical Process Control and Monitoring (SPC/M) by providing a comparative analysis of two prominent self-starting control chart methods. The findings offer valuable insights for practitioners and researchers in selecting and implementing appropriate methods for online change point detection, particularly in scenarios where a Phase I calibration phase is impractical or infeasible.
Limitations and Future Research: The study focuses on univariate Normal data and specific types of shifts in the mean. Future research could explore the performance of these methods for other data distributions, shift types, or multivariate data. Additionally, investigating the robustness of these methods to deviations from normality assumptions and exploring adaptive schemes for dynamically adjusting design parameters could be valuable extensions of this research.
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by Konstantinos... um arxiv.org 10-17-2024
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