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Optimum Checking Schedules for Systems Subject to Random Failure

Author

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  • Joseph B. Keller

    (Courant Institute of Mathematical Sciences, New York University)

Abstract

An optimum checking schedule is one that minimizes the expected cost, which is the sum of the cost of checking and the expected loss due to an undetected failure. The problem is made tractable by supposing that checking is so frequent that it can be described by a continuous density n(t) of checks per unit time. The optimum n(t) is found by the methods of the calculus of variations. An explicit result is given when the loss is proportional to the duration of an undetected failure. A minimax solution is also given for the case in which the probability of failure is not known.

Suggested Citation

  • Joseph B. Keller, 1974. "Optimum Checking Schedules for Systems Subject to Random Failure," Management Science, INFORMS, vol. 21(3), pages 256-260, November.
    • Handle: RePEc:inm:ormnsc:v:21:y:1974:i:3:p:256-260
    DOI: 10.1287/mnsc.21.3.256
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    Cited by:

    1. R Jiang & A K S Jardine, 2005. "Two optimization models of the optimum inspection problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1176-1183, October.
    2. Nakagawa, T. & Mizutani, S., 2009. "A summary of maintenance policies for a finite interval," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 89-96.
    3. Ahmadi, Reza & Wu, Shaomin, 2017. "A novel data-driven approach to optimizing replacement policy," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 506-516.
    4. Jonathan E. Helm & Mariel S. Lavieri & Mark P. Van Oyen & Joshua D. Stein & David C. Musch, 2015. "Dynamic Forecasting and Control Algorithms of Glaucoma Progression for Clinician Decision Support," Operations Research, INFORMS, vol. 63(5), pages 979-999, October.
    5. Fakher, Hossein Beheshti & Nourelfath, Mustapha & Gendreau, Michel, 2018. "Integrating production, maintenance and quality: A multi-period multi-product profit-maximization model," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 191-201.
    6. Darghouth, M.N. & Chelbi, Anis & Ait-kadi, Daoud, 2012. "A profit assessment model for equipment inspection and replacement under renewing free replacement warranty policy," International Journal of Production Economics, Elsevier, vol. 135(2), pages 899-906.
    7. Mesak, Hani I. & Zhang, Hongkai & Pullis, Joe M., 2010. "On optimal service capacity allocation policy in an advance selling environment in continuous time," European Journal of Operational Research, Elsevier, vol. 203(2), pages 505-512, June.
    8. B. C. Giri & T Chakraborty, 2007. "Optimal production, maintenance, and warranty strategies for item sold with rebate combination warranty," Journal of Risk and Reliability, , vol. 221(4), pages 257-264, December.
    9. Leung, Francis Kit-nam, 2001. "Inspection schedules when the lifetime distribution of a single-unit system is completely unknown," European Journal of Operational Research, Elsevier, vol. 132(1), pages 106-115, July.

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