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A characterization of the negative exponential distribution with application to reliability theory

Published online by Cambridge University Press:  14 July 2016

M. J. Phillips
M. J. Phillips*
Affiliation:
University of Leicester
*
∗Postal address: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, U.K.
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Abstract

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

Keywords

CHARACTERIZATION THEOREMNEGATIVE EXPONENTIAL DISTRIBUTIONRELIABILITYREVEALED AND UNREVEALED FAULTSALTERNATING RENEWAL PROCESSTWO-STATE SEMI-MARKOV PROCESSSYSTEM AVAILABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 652 - 659
Copyright
Copyright © Applied Probability Trust 

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