We introduce a new method analyzing 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. By using the theory of the so-called scale matrix and further developing it, we derive exact expressions of the average run length, average detection delay, and false alarm probability under the CUSUM procedure. The proposed method is robust and applicable in a general setting with non-i.i.d. observations. Numerical results also are given.

翻译：我们采用一种新的方法分析相继变化点检测中的累积总和(CUUM)程序。当观测是阶段型分布,而变化后分布则通过变化前分布的指数倾斜进行时,对CUUU统计数据的第一次段落分析将缩减为特定Markov添加过程的分析。通过使用所谓的规模矩阵理论并加以进一步发展,我们得出CUUUM程序下平均运行长度、平均检测延迟和假警报概率的精确表达。提议的方法是稳健的,适用于非i.i.d.观察的一般环境,还给出了数值结果。