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A general formula for the downtime distribution of a parallel system

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Harald Haukås  and
Terje Aven
Harald Haukås*
Affiliation:
Rogaland University Centre and University of Oslo
Terje Aven*
Affiliation:
Rogaland University Centre and University of Oslo
*
∗Postal address for both authors: Rogaland University Centre, Ullandhaug, 4004 Stavanger, Norway.
∗Postal address for both authors: Rogaland University Centre, Ullandhaug, 4004 Stavanger, Norway.
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Abstract

In this paper we study the problem of computing the downtime distribution of a parallel system comprising stochastically identical components. It is assumed that the components are independent, with an exponential life-time distribution and an arbitrary repair time distribution. An exact formula is established for the distribution of the system downtime given a specific type of system failure scenario. It is shown by performing a Monte Carlo simulation that the portion of the system failures that occur as described by this scenario is close to one when we consider a system with quite available components, the most common situation in practice. Thus we can use the established formula as an approximation of the downtime distribution given system failure. The formula is compared with standard Markov expressions. Some possible extensions of the formula are presented.

Keywords

DOWNTIME DISTRIBUTIONPARALLEL SYSTEMSYSTEM FAILURE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 772 - 785
Copyright
Copyright © Applied Probability Trust 1996 

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