Some methods to evaluate the performance of Page's test as used to detect transient signals

In the "classical" detection problem, a decision is to be made about the pr esence or absence of a target based on an observation sequence. Since this data is of a given length, we refer to this as fixed-sample-size testing. A pair of problems that are similar in spirit (but turn out to be considerab ly different mathematically) is that of quickest detection and transient de tection, The former refers to timely notification of a statistical change; the latter, which is the subject of this paper, refers to detection of a te mporary change. Much is known about the performance of Page's test in terms of average run lengths; however, more detailed statistical analysis is required to determi ne the detectability of a transient change. In this paper, techniques to ca lculate and approximate the probability of detection by Page's test for a t ransient of a given length and strength are developed through investigation of the probability distribution of the so-called stopping time of Page's t est, which is the time between the starting instant of the test and the ins tant of the first alarm (false- or true-detection).