A generalized Shiryayev sequential probability ratio test for change detection and isolation

We derive an online multiple hypothesis Shiryayev sequential probability test (SSPRT) by adopting a dynamic programming approach. It is shown that for a certain criterion of optimality, this extended Shiryayev SPRT detects and isolates the occurrence of a failure in the conditionally independent measurement sequence in minimum time, unlike the Wald SPRT, which detects the presence/absence of a failure in the entire measurement sequence. We consider the measurement cost, the cost of a false alarm and the cost of a miss-alarm in our dynamic programming analysis. The algorithm is shown to be optimal even in the asymptotic sense and the theoretical results have been extended to the detection and identification of changes with unknown parameters, Finally, the performance of the algorithm is evaluated by using a few examples. In particular, we implement the algorithm in a fault detection and identification scheme for advanced vehicle control systems.