sequential testing; k-out-of-n systems; imperfect tests; sequencing and scheduling
Abstract :
[en] A k-out-of-n system configuration requires that, for the overall system to be functional, at
least k out of the total of n components be working. We consider the problem of sequentially testing the components of a k-out-of-n system in order to learn the state of the system, when the tests are costly and when the individual component tests are imperfect, which means that a test can identify a component as working when in reality it is down, and vice versa. Each component is tested at most once. Since tests are imperfect, even when all components are tested the state of the system is not necessarily known with certainty, and so reaching a lower bound on the probability of correctness of the system state is used as a stopping criterion for the inspection.
We define different classes of inspection policies and we examine global optimality of each of the classes. We find that a globally optimal policy for diagnosing k-out-of-n systems with imperfect tests can be found in polynomial time when the predictive error probabilities are the same for all the components. Of the three policy classes studied, the dominant policies always contain a global optimum, while elementary policies are compact in representation. The newly introduced class of so-called `interrupted block-walking' policies combines these merits of global optimality and of compactness.
Research Center/Unit :
HEC - QUANTOM
Disciplines :
Quantitative methods in economics & management
Author, co-author :
Wenchao, Wei; University of Porto > Faculty of Engineering > INESC > Dr.
Coolen, Kris ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Recherche opérationnelle et gestion de la production > Dr.
Talla Nobibon, Fabrice; Federal Express (FedEx)
Leus, Roel; Katholieke Universiteit Leuven - KUL > Faculty of Economics and Business > ORSTAT > Prof.
Language :
English
Title :
Sequential testing of k-out-of-n systems with imperfect tests
Publication date :
2015
Number of pages :
34
Name of the research project :
COMEX
Funders :
BELSPO - SPP Politique scientifique - Service Public Fédéral de Programmation Politique scientifique
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