Multiple Optimality Properties of the Shewhart Test

• Published in: Sequential analysis Vol. 33; no. 3; pp. 318 - 344
• Main Author: Moustakides, George V.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis Group 03.07.2014; Taylor & Francis Ltd
• Subjects: Change detection; Computer engineering; Delay; Exact solutions; False alarms; Formulations; Mathematical analysis; Minimization; Optimization; Probability; Sequential analysis; Sequential detection; Shewhart test; Statistics
• DOI: 10.1080/07474946.2014.916927
• ISSN: 0747-4946

For the problem of sequential detection of changes, we adopt the probability maximizing approach in place of the classical minimization of the average detection delay and propose modified versions of the Shiryaev, Lorden, and Pollak performance measures. For these alternative formulations, we demonstrate that the optimum sequential detection scheme is the simple Shewhart rule. Interestingly, we can also solve problems that under the classical setup have been open for many years, as optimum change detection with time-varying observations or with multiple postchange probability measures. For the latter, we also offer the exact solution for Lorden's original setup involving average detection delays, for the case where the average false alarm period is within certain limits.