Sequential testing of n-out-of-n systems: Precedence theorems and exact methods

Abstract : The goal of sequential testing is to discover the state of a system by testing its components one by one. We consider n-out-of-n systems, which function only if all n components work. The testing continues until the system state (up or down) is identified. The tests have known execution costs and failure probabilities, and are subject to precedence constraints. The objective is to find a sequence of tests that minimizes the total expected cost of the diagnosis. We show how to strengthen the precedence graph without losing all optimal solutions. We examine different formulations for the problem, and propose a dynamic-programming (DP) and a branch-and-price algorithm. Our computational results show that our DP noticeably outperforms the state of the art. Using a novel memory management technique, it significantly increases the size of the instances that can be solved to optimality within given limits on runtime and memory.
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https://hal.archives-ouvertes.fr/hal-02114147
Contributor : Isabelle Celet <>
Submitted on : Monday, April 29, 2019 - 2:05:08 PM
Last modification on : Friday, July 26, 2019 - 11:58:03 AM

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Salim Rostami, Stefan Creemers, Wenchao Wei, Roel Leus. Sequential testing of n-out-of-n systems: Precedence theorems and exact methods. European Journal of Operational Research, Elsevier, 2019, 274 (3), pp.876-885. ⟨10.1016/j.ejor.2018.10.036⟩. ⟨hal-02114147⟩

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