Numerical comparison of popular quickest change point detection procedures

In this paper, we study the problem of sequential detection of the moment of change in the properties of a random process that occurs in various fields of science and technology. The article provides a comparative analysis of the three most popular procedures: Shiryaev, Shiryaev-Roberts, cumulative sums (CUSUM) for a problem with Gaussian observation (signal to white noise). In the same observation characteristics are obtained from Fredholm second kind integral equations by numerically solving the integral equations by the collocation method. The study shows that in this statement of the problem, the most popular in practice CUSUM procedure works noticeably worse than the Shiryaev and Shiryaev- Roberts procedures.