Sequential sensor installation for wiener disorder detection

We consider a centralized multisensor 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 multisensor 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 signals. 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%.