A generalized change detection problem

The purpose of this paper is to give a new statistical approach to the change diagnosis (detection/isolation) problem. The change detection problem has received extensive research attention; however, the change isolation problem has, for the most part, been ignored. We consider a stochastic dynamical system with abrupt changes and investigate the multiple hypotheses extension of Lorden´s (1971) results. We introduce a joint criterion of optimality for the detection/isolation problem and then design a change detection/isolation algorithm. We also investigate the statistical properties of this algorithm. We prove a lower bound for the criterion in a class of sequential change detection/isolation algorithms. It is shown that the proposed algorithm is asymptotically optimal in this class. The theoretical results are applied to the case of additive changes in linear stochastic models