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 presence 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 considerably different mathematically) is that of quickest detection and transient detection. The former refers to timely notification of a statistical change; the latter, which is the subject of this paper, refers to detection of a temporary change. Much is known about the performance of Page's (1954) test in terms of average run lengths; however, more detailed statistical analysis is required to determine the detectability of a transient change. Techniques to calculate and approximate the probability of detection by Page's test for a transient of a given length and strength are developed through investigation of the probability distribution of the so-called stopping time of Page's test, which is the time between the starting instant of the test and the instant of the first alarm (false- or true-detection).