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A modified repair strategy for two-component systems with revealed and unrevealed faults

Published online by Cambridge University Press:  14 July 2016

Norman L. Johnson  and
Samuel Kotz
Norman L. Johnson*
Affiliation:
University of North Carolina
Samuel Kotz*
Affiliation:
University of Maryland
*
∗Postal address: Department of Statistics, The University of North Carolina at Chapel Hill, 315 Phillips Hall 039 A, Chapel Hill, NC 27514, USA.
∗∗Postal address: Department of Management and Statistics, University of Maryland, College Park, MD 20742, USA.
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Abstract

Some consequences of a modified repair system for Phillips' (1981a, b) model for a two-component system are discussed. In the original model, both components are repaired whenever a revealed fault occurs; in the modified model only faulty components are repaired. Specifically (i) the distribution of time from the initial state up to discovery of an unrevealed fault, (ii) the expected proportion of time during which there exists an unrepaired fault, and (iii) the distribution of number of revealed faults up to and including the one which leads to a discovery of an unrevealed fault, are obtained. The theory is illustrated by examples, based on specific distributions for the times between repairs and occurrences of the two types of faults. A characterization of the exponential distribution is indicated.

Keywords

EXPONENTIAL DISTRIBUTIONEXPONENTIAL INTEGRALGAMMA DISTRIBUTIONSGEOMETRIC DISTRIBUTIONREGENERATION POINTREVEALED FAULTSUNREVEALED FAULTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 178 - 185
Copyright
Copyright © Applied Probability Trust 1987 

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