Sequential sensor installation for Wiener disorder detection

Dayanık, Savaş and Sezer, Semih Onur (2016) Sequential sensor installation for Wiener disorder detection. Mathematics of Operations Research, 41 (3). pp. 827-850. ISSN 0364-765X (Print) 1526-5471 (Online)

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We consider a centralized multi-sensor online quickest disorder detection problem where the observation from each sensor is a Wiener process gaining a constant drift at a common unobservable disorder time. The objective is to detect the disorder time as quickly as possible with small probability of false alarms. Unlike the earlier work on multi-sensor change detection problems, we assume that the observer can apply a sequential sensor installation policy. At any time before a disorder alarm is raised, the observer can install new sensors to collect additional observations. The sensors are statistically identical, and there is a fixed installation cost per sensor. We propose a Bayesian formulation of the problem. We identify an optimal policy consisting of a sequential sensor installation strategy and an alarm time, which minimize a linear Bayes risk of detection delay, false alarm, and new sensor installations. We also provide a numerical algorithm and illustrate it on examples. Our numerical examples show that significant reduction in the Bayes risk can be attained compared to the case where we apply a static sensor policy only. In some examples, the optimal sequential sensor installation policy starts with 30% less number of sensors than the optimal static sensor installation policy and the total percentage savings reach to 12%.
Item Type: Article
Uncontrolled Keywords: optimal multiple stopping; multisensor sequential change detection; Wiener disorder problem
Subjects: Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences > Academic programs > Manufacturing Systems Eng.
Faculty of Engineering and Natural Sciences
Depositing User: Semih Onur Sezer
Date Deposited: 06 Nov 2016 22:13
Last Modified: 06 Nov 2016 22:13

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