Wiener disorder problem with observations at fixed discrete time epochs

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dc.citation.epage785en_US
dc.citation.issueNumber4en_US
dc.citation.spage756en_US
dc.citation.volumeNumber35en_US
dc.contributor.authorDayanik, S.en_US
dc.date.accessioned2016-02-08T09:56:18Z
dc.date.available2016-02-08T09:56:18Z
dc.date.issued2010en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractSuppose 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.en_US
dc.identifier.doi10.1287/moor.1100.0471en_US
dc.identifier.eissn1526-5471
dc.identifier.issn0364-765X
dc.identifier.urihttp://hdl.handle.net/11693/22158
dc.language.isoEnglishen_US
dc.publisherInstitute for Operations Research and the Management Sciences (I N F O R M S)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1287/moor.1100.0471en_US
dc.source.titleMathematics of Operations Researchen_US
dc.subjectOptimal stoppingen_US
dc.subjectSequential change detectionen_US
dc.subjectWiener disorder problemen_US
dc.subjectDiscrete time epochsen_US
dc.subjectDisease outbreaksen_US
dc.subjectExponential distributionsen_US
dc.subjectNumerical algorithmsen_US
dc.subjectNumerical exampleen_US
dc.subjectObservation intervalen_US
dc.subjectOptimal detection algorithmen_US
dc.subjectOptimal stoppingen_US
dc.subjectPiecewise-continuousen_US
dc.subjectProduction qualityen_US
dc.subjectSequential change detectionen_US
dc.subjectWiener disorder problemen_US
dc.subjectAlarm systemsen_US
dc.subjectAlgorithmsen_US
dc.subjectDisease controlen_US
dc.subjectSignal detectionen_US
dc.subjectOptimizationen_US
dc.titleWiener disorder problem with observations at fixed discrete time epochsen_US
dc.typeArticleen_US

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