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Bounds on uptime distribution based on aging for systems with finite lifetimes

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  • Charles Wells

Abstract

Consider a system which is subject to occasional failures over its lifetime. Under general stochastic assumptions concerning the occurrence of these failures, the duration of the repair times, and the length of the system’s lifetime, the distribution of the total uptime the system accumulates over its lifetime may be determined. While the distribution is unfortunately complicated except in certain circumstances, it is possible to derive useful bounds based on the aging characteristics of the distributions of interfailure times, repair times, and system life. Bounds are developed for the cases where the system lifetime follows (1) a degenerate distribution (or constant mission duration), (2) an exponential distribution, and (3) a general distribution. These bounds may be interpreted as extensions of well-known bounds based on aging notions from renewal theory. Conditions are identified for when the bounds are sharp, and examples are used to show the computational tractability and usefulness of the results. Copyright Springer Science+Business Media New York 2015

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  • Charles Wells, 2015. "Bounds on uptime distribution based on aging for systems with finite lifetimes," Annals of Operations Research, Springer, vol. 235(1), pages 757-769, December.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:757-769:10.1007/s10479-015-1950-1
    DOI: 10.1007/s10479-015-1950-1
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    References listed on IDEAS

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    1. Charles E. Wells & John L. Bryant, 1985. "On the Replenishment of Repair Kit Inventories for Systems with Life Distributions of Phase Type," Management Science, INFORMS, vol. 31(11), pages 1440-1450, November.
    2. John L. Bryant & Richard A. Murphy, 1983. "Stocking Repair Kits for Systems with Limited Life," Management Science, INFORMS, vol. 29(5), pages 546-558, May.
    3. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2009. "Balancing burn-in and mission times in environments with catastrophic and repairable failures," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1314-1321.
    4. Jiang, R., 2009. "An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1245-1250.
    5. Wells, Charles E., 2014. "Reliability analysis of a single warm-standby system subject to repairable and nonrepairable failures," European Journal of Operational Research, Elsevier, vol. 235(1), pages 180-186.
    6. 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.
    7. Mark Brown, 2013. "Sharp bounds for NBUE distributions," Annals of Operations Research, Springer, vol. 208(1), pages 245-250, September.
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    Cited by:

    1. M. S. Patel & A. A. Khalifa & M. S. Liew & Zahiraniza Mustaffa & Andrew Whyte, 2022. "Downtime cost analysis of offloading operations due to influence of partially standing waves in Malaysian waters and development of graphical user interface," Annals of Operations Research, Springer, vol. 315(2), pages 1263-1289, August.

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