Backward SPRT failure detection in multivariate observation case

The idea of the backward sequential probability ratio test (SPRT) is applied in the multivariate observation case to detect system degradations which are characterized by the presence of a systematic jump bias in innovations. The results of numerical simulations show its usefulness. It uses the logarithm of likelihood ratio function evaluated in reverse from the current observations to the past ones rather than from the past to the current ones as in A. Wald´s conventional SPRT (1947). By doing this, it is possible to prevent the failure detection system from experiencing the extra time delay caused by the difference of the characteristics of failure processes from Wald´s original SPRT formulation