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

Charles Wells ()

Annals of Operations Research, 2015, vol. 235, issue 1, 757-769

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

Keywords: Uptime; Bounds; Repairable and nonrepairable failures; Aging (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10479-015-1950-1

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