Browsing by Subject "Sequential change detection"

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Open Access
Compound poisson disorder problems with nonlinear detection delay penalty cost functions
(2010) Dayanik, S.
The quickest detection of the unknown and unobservable disorder time, when the arrival rate and mark distribution of a compound Poisson process suddenly changes, is formulated in a Bayesian setting, where the detection delay penalty is a general smooth function of the detection delay time. Under suitable conditions, the problem is shown to be equivalent to the optimal stopping of a finite-dimensional piecewise-deterministic strongly Markov sufficient statistic. The solution of the optimal stopping problem is described in detail for the compound Poisson disorder problem with polynomial detection delay penalty function of arbitrary but fixed degree. The results are illustrated for the case of the quadratic detection delay penalty function. © Taylor & Francis Group, LLC.
Open Access
Sequential sensor installation for wiener disorder detection
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2016) Dayanik, S.; Sezer, S. O.
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%.
Open Access
Wiener disorder problem with observations at fixed discrete time epochs
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2010) Dayanik, S.
Suppose that a Wiener process gains a known drift rate at some unobservable disorder time with some zero-modified exponential distribution. The process is observed only at known fixed discrete time epochs, which may not always be spaced in equal distances. The problem is to detect the disorder time as quickly as possible by means of an alarm that depends only on the observations of Wiener process at those discrete time epochs. We show that Bayes optimal alarm times, which minimize expected total cost of frequent false alarms and detection delay time, always exist. Optimal alarms may in general sound between observation times and when the space-time process of the odds that disorder happened in the past hits a set with a nontrivial boundary. The optimal stopping boundary is piecewise-continuous and explodes as time approaches from left to each observation time. On each observation interval, if the boundary is not strictly increasing everywhere, then it irst decreases and then increases. It is strictly monotone wherever it does not vanish. Its decreasing portion always coincides with some explicit function. We develop numerical algorithms to calculate nearly optimal detection algorithms and their Bayes risks, and we illustrate their use on numerical examples. The solution of Wiener disorder problem with discretely spaced observation times will help reduce risks and costs associated with disease outbreak and production quality control, where the observations are often collected and/or inspected periodically.