Backward SPRT Failure Detection System for Detection of Innovation Variance Change

Abstract

It is known that the failure detection system based on the Wald's sequential probability ratio test (SPRT) suffers an extra time delay in detecting system degradation characterized by the presence of a systemstic non-zero mean. Chien and Adams (1976) developed a modified Wald's SPRT system by utilizing a feedback of the logarithm of likelihood ratio function (LLR) for improvement of the detection system. Recently, we proposed a backward SPRT failure detection system to improve the characteristics in detecting the above system degradation (Uosaki (1986)). The system uses the LLR evaluated in reverse from the current observation to hte past ones. Recognizing the fact that system parameter change causes the change in innovation variance rather than in innovation mean, we apply the idea of the backward SPRT to detect degradation characterized by the increase of innovation variance. The mean detection time id derived using the theory of the absorbing Markov chain. This quantity can be used to determine the decision boundary in the system.