Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-24T13:25:25.704Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arias, E. and Lehtonen, T. (1978) Approximating many server queues by means of single server queues. Math. Operat. Res. 3, 205–223.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1976) Theory of maintained systems: distribution of time to first system failure. Math. Operat. Res. 1, 32–42.CrossRefGoogle Scholar
Brown, M. (1975) The first passage time distribution for a parallel exponential system with repair. In Reliability and Fault Tree Analysis, ed. Barlow, R. E. et al., SIAM, Philadelphia, PA.Google Scholar
Chiang, D. T. and Niu, S. C. (1979) Comparing maintained reliability systems. Working Paper Series No. 79–1, James J. Nance College of Business Administration, The Cleveland State University.Google Scholar
O'brien, G. L. (1975) The comparison method for stochastic processes. Ann. Prob. 3, 80–88.CrossRefGoogle Scholar
Ross, S. M. (1975) On the calculation of asymptotic system reliability characteristics. In Reliability and Fault Tree Analysis, ed. Barlow, R. E. et al., SIAM, Philadelphia, PA.Google Scholar
Ross, S. M. (1976) On time to first failure in multicomponent exponential reliability systems. Stoch. Proc. Appl. 4, 167–173.CrossRefGoogle Scholar
Ross, S. M. and Schechtman, J. (1979) On the first time a separately maintained parallel system has been down for a fixed time. Naval Res. Logist. Quart. 26, 285–290.CrossRefGoogle Scholar
Sonderman, D. (1980) Comparing uniformizable semi-Markov processes. Math. Operat. Res. 5, 110–119.CrossRefGoogle Scholar