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

Author

Listed:
  • Salim Rostami

    (IESEG - School of Management (LEM))

  • Stefan Creemers

    (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

  • Wenchao Wei
  • Roel Leus

    (KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven)

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.

Suggested Citation

  • Salim Rostami & Stefan Creemers & Wenchao Wei & Roel Leus, 2019. "Sequential testing of n-out-of-n systems: Precedence theorems and exact methods," Post-Print hal-02114147, HAL.
    • Handle: RePEc:hal:journl:hal-02114147
    DOI: 10.1016/j.ejor.2018.10.036
    as

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    Cited by:

    1. Fatemeh Rezaei & Amir Abbas Najafi & Erik Demeulemeester & Reza Ramezanian, 2024. "A stochastic bi-objective project scheduling model under failure of activities," Annals of Operations Research, Springer, vol. 338(1), pages 453-476, July.
    2. Agnetis, Alessandro & Hermans, Ben & Leus, Roel & Rostami, Salim, 2022. "Time-critical testing and search problems," European Journal of Operational Research, Elsevier, vol. 296(2), pages 440-452.

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