2012/05/09 by F. Din-Houn Lau, Lau, F. Din-Houn, Axel Gandy +1
Decision Sciences · Health Professions · Mathematics · #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #Methodology (stat.ME) #Quality and Safety in Healthcare #Scientific Measurement and Uncertainty Evaluation #stat.ME
paper · pdf · doi:10.48550/arxiv.1205.1937
10 pages, 3 figures
arxiv created 2012/05/09 · openalex publication_date 2012/05/09 · arxiv updated 2012/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show optimality, in a well-defined sense, using cumulative sum (CUSUM) charts for detecting changes in distributions. We consider a setting with multiple changes between two known distributions. This result advocates the use of non-restarting CUSUM charts with an upper boundary. Typically, after signalling, a CUSUM chart is restarted by setting it to some value below the threshold. A non-restarting CUSUM chart is not reset after signalling; thus is able to signal continuously. Imposing an upper boundary prevents the CUSUM chart rising too high, which facilitates detection in our setting. We discuss, via simulations, how the choice of the upper boundary changes the signals made by the non-restarting CUSUM charts.