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On the distribution of time to first system failure

Published online by Cambridge University Press:  14 July 2016

Dalen T. Chiang  and
Shun-Chen Niu
Dalen T. Chiang
Affiliation:
Cleveland State University
Shun-Chen Niu*
Affiliation:
Cleveland State University
*
∗Postal address: The James J. Nance College of Business Administration, Department of Marketing and Quantitative Business Analysis, Cleveland State University, Cleveland OH 44115, U.S.A.
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Abstract

For a maintained reliability system, i.e., components may be repaired upon failures, we prove that the distribution of time to first system failure starting with all components new is NBU under the following conditions: (a) non-repairable components have NBU uptime distributions, (b) repairable components have exponential uptime and DFR downtime distributions. This is a slight generalization of a theorem of Barlow and Proschan (1976). However, our method of proof is different from theirs. We also show that the initial up-period of the system is stochastically larger than any other system up-period. Finally, a method of finding a lower bound for the expected time until first system failure is outlined using our main result.

Keywords

MAINTAINED RELIABILITY SYSTEMSTIME TO FIRST SYSTEM FAILURENEW BETTER THAN USED DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 481 - 489
Copyright
Copyright © Applied Probability Trust 1980 

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