Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T05:20:33.144Z Has data issue: false hasContentIssue false
  • English
  • Français

A general shock model for a reliability system

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Georgios Skoulakis
Georgios Skoulakis*
Affiliation:
University of North Carolina
*
∗ Postal address: Department of Finance, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, IL 60208-20001, USA. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study a reliability system subject to shocks generated by a renewal point process. When a shock occurs, components fail independently of each other with equal probabilities that are random numbers drawn from a distribution that may differ from shock to shock. We first consider the case of a parallel system and derive closed expressions for the Laplace-Stieltjes transform and the expectation of the time to system failure and for its density in the case that the distribution function of the renewal process possesses a density. We then treat a more general system structure, which has some very important special cases, such as k-out-of-n:F systems, and derive analogous formulae.

Keywords

System reliabilityshock modelsrandom environmentparallel systemgeneral system

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K37: Processes in random environments
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 925 - 935
Copyright
Copyright © by the Applied Probability Trust 2000 

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

[1] Chryssaphinou, O., and Papastavridis, S. (1990). Reliability of a consecutive-k-out-of-n system in a random environment. J. Appl. Prob. 27, 452–458.CrossRefGoogle Scholar
[2] Griffith, W. S. (1986). On consecutive-k-out-of-n:failure systems and their generalizations. In Reliability and Quality Control, ed. Basu, A. P. Elsevier, Amsterdam, pp. 157–165.Google Scholar
[3] Lambiris, M., and Papastavridis, S. (1985). Exact reliability formulas for linear and circular consecutive-k-out-of-n:F systems. IEEE Trans. Rel. 34, 124–126.Google Scholar
[4] Nakagawa, T. (1979). Further results of replacement problem of a parallel system in random environment. J. Appl. Prob. 16, 923–926.CrossRefGoogle Scholar
[5] Petakos, K., and Tsapelas, T. (1997). Reliability analysis for systems in a random environment. J. Appl. Prob. 34, 1021–1031.Google Scholar
[6] Råde, L. (1976). Reliability systems in random environment. J. Appl. Prob. 13, 407–410.Google Scholar
[7] Resnick, S. (1992). Adventures in Stochastic Processes. Birkhäuser, Basel.Google Scholar
[8] Ross, S. M. (1983). Stochastic Processes. John Wiley, New York.Google Scholar
[9] Srinivas, I. (1992). Distribution of the lifetime of consecutive k-within-m-out-of-n:F systems. IEEE Trans. Rel. R41, 448–450.Google Scholar