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We introduce a new Levy fluctuation theoretic method to analyze thecumulative sum (CUSUM) procedure in sequential change-point detection. Whenobservations are phase-type distributed and the post-change distribution isgiven by exponential tilting of its pre-change distribution, the first passageanalysis of the CUSUM statistic is reduced to that of a certain Markov additiveprocess. We develop a novel series expansion formula of the scale matrix forMarkov additive processes of finite activity, and apply it to derive exactexpressions of the average run length, average detection delay, and false alarmprobability under the CUSUM procedure.

A series expansion formula of the scale matrix with applications in change-point detection