Sequential Detection of Transient Signals with Exponential Family Distribution
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We first consider the sequential detection of transient signals by generalizing the moving average chart to exponential family and study the false detection probability (FDP) and power of detection (POD) in the steady state. Then windowed adjusted signed (or modified directed) likelihood ratio chart is studied by treating it as normal random variable. In the multi-parameter exponential family, the detection of the transient change of one of the canonical parameters or a function of canonical parameters is considered by using the generalized adjusted signed likelihood ratio chart. Comparisons with window restricted CUSUM and Shiryayev-Roberts (S-R) procedures show that the generalized signed likelihood ratio chart performs quite well. Several important examples including the mean or variance change under normal model and a real example are used for illustration.
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