A Fixed-Size Sample Strategy for the Sequential Detection and Isolation of Non-Orthogonal Alternatives

Abstract

The comparison between the optimal sequential and repeated fixed-size sample (FSS) strategies in the problem of abrupt change detection and isolation is discussed. The general case of non-orthogonal Gaussian hypotheses is considered. Each hypothesis is characterized by its mean vector (the change signature) and it is desirable to detect/isolate a change subject to the constraints on a pre-assigned time between false alarm and a maximum probability of false isolation. It is established that the performance of the proposed FSS algorithm is directly related to the mutual geometry between the hypotheses through the Kullback–Leibler information. This algorithm is less efficient than an optimal sequential one but in contrast to the sequential strategy, the FSS strategy can be easily used for monitoring in the case of variable structure systems.

Keywords:

• Repeated fixed-size sample test
• Sequential change detection/isolation
• Variable structure systems

Subject Classification:

• 62L15
• 62H15
• 62F03
• 62C99

ACKNOWLEDGMENT

We appreciate the valuable comments and suggestions of the anonymous Referee and the Associate Editor.

Notes

Recommended by A. G. Tartakovsky