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Some Reliability Fault-Testing Models

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  • Richard Butterworth

    (Naval Postgraduate School, Monterey, California)

Abstract

This paper presents several fault-testing models. Our system is composed of n components that either work or fail. The systems treated are the k -out-of- n type ( k / n ). This system works if and only if k or more of its components work, making the series ( n / n ) and parallel (1/ n ) systems special cases. Components can be individually tested and tests give perfect information. Each test has a time to complete it and testing procedures are judged by the expected cumulative testing time they require. In the first model, the components are assumed to function or fail independently of each other. A feasible test procedure must determine (as) if the system is working or has failed. This is solved for the series and parallel systems and, under a possibly restrictive hypothesis, for the general k / n system. In another model, the components are assumed to be nominally independent conditioned on the system being failed. Here a feasible test procedure must locate all failed components. This problem is solved for the general k / n system.

Suggested Citation

  • Richard Butterworth, 1972. "Some Reliability Fault-Testing Models," Operations Research, INFORMS, vol. 20(2), pages 335-343, April.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:2:p:335-343
    DOI: 10.1287/opre.20.2.335
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    Cited by:

    1. Azaiez, M.N. & Bier, Vicki M., 2007. "Optimal resource allocation for security in reliability systems," European Journal of Operational Research, Elsevier, vol. 181(2), pages 773-786, September.
    2. Wei Chen & Milind Dawande & Ganesh Janakiraman, 2018. "Optimal Procurement Auctions Under Multistage Supplier Qualification," Manufacturing & Service Operations Management, INFORMS, vol. 20(3), pages 566-582, July.
    3. B. De Reyck & Y. Grushka-Cockayne & R. Leus, 2007. "A New Challenge in Project Scheduling. The Incorporation of Activity Failures," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(3), pages 410-435.
    4. Rostami, Salim & Creemers, Stefan & Wei, Wenchao & Leus, Roel, 2019. "Sequential testing of n-out-of-n systems: Precedence theorems and exact methods," European Journal of Operational Research, Elsevier, vol. 274(3), pages 876-885.

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