2021/09/07 by Jevgeņijs Ivanovs, Ivanovs, Jevgenijs, Kazutoshi Yamazaki +1
Business, Management and Accounting · Decision Sciences · Mathematics · #60G40 #60G51 #62M05 #Advanced Queuing Theory Analysis #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Optimization and Control (math.OC) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2109.03361
openalex publication_date 2021/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new Levy fluctuation theoretic method to analyze the cumulative sum (CUSUM) procedure in sequential change-point detection. When observations are phase-type distributed and the post-change distribution is given by exponential tilting of its pre-change distribution, the first passage analysis of the CUSUM statistic is reduced to that of a certain Markov additive process. We develop a novel series expansion formula of the scale matrix for Markov additive processes of finite activity, and apply it to derive exact expressions of the average run length, average detection delay, and false alarm probability under the CUSUM procedure.