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Quasi-stationary distribution of a two-unit warm-standby redundant system

Published online by Cambridge University Press:  14 July 2016

S. Kalpakam  and
M. A. Shahul Hameed
S. Kalpakam*
Affiliation:
Indian Institute of Technology, Madras
M. A. Shahul Hameed*
Affiliation:
Indian Institute of Technology, Madras
*
∗ Postal address: Department of Mathematics, Indian Institute of Technology, Madras 600 036, India.
∗ Postal address: Department of Mathematics, Indian Institute of Technology, Madras 600 036, India.
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Abstract

This paper establishes the existence of the limit as t → ∞ of the distribution of the residual lifetime at time t of a two-unit warm-standby reliability system supported by a single repair facility, conditioned on the event that the system has not been down at any time in (0, t). The conditioned limit distribution is proved to be exponential irrespective of the distributions of the lifetimes and repair times of the individual units, provided that their Laplace transforms are rational functions of their arguments.

Keywords

QUASI-STATIONARY DISTRIBUTIONWARM STANDBYREDUNDANT SYSTEMs-IDENTICAL UNITSONLINE FAILURERESIDUAL LIFETIMERELIABILITY FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 429 - 435
Copyright
Copyright © Applied Probability Trust 1983 

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