Sequential Detection of Transient Changes

• Published in: Sequential analysis Vol. 31; no. 4; pp. 528 - 547
• Main Authors: Guépié, Blaise Kévin, Fillatre, Lionel, Nikiforov, Igor
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis Group 01.10.2012; Taylor & Francis Ltd; Taylor & Francis
• Subjects: Algorithms; Change detection; Computer Science; Criteria; Decision theory; Detection algorithms; Drinking water; Environmental monitoring; Failure detection; False alarms; Mathematical analysis; Monitoring; Optimization; Probability; Signal and Image Processing; Signal detection; Signaling; Statistical analysis; Transient signals; Upper bounds; Water pollution
• ISSN: 0747-4946; 1532-4176
• DOI: 10.1080/07474946.2012.719443

This article addresses the transient change detection problem. It is assumed that a change occurs at an unknown (but nonrandom) change-point and the duration of post-change period is finite and known. A latent detection-that is, a detection that occurs after signal disappearance-is considered as a missed detection. A new optimality criterion adapted to the detection of transient changes involves the minimization of the worst-case probability of missed detection under constraint on the false alarm rate for a given period. A suboptimal sequential transient change detection algorithm is proposed. It is based on a window-limited cumulative sum (CUSUM) test. An upper bound for the worst-case probability of missed detection and a lower and an upper bound for the false alarm rate are proposed. Based on these bounds, the window-limited CUSUM test is optimized with respect to the proposed criterion. The developed algorithm and theoretical findings are applied to drinking water distribution network monitoring.