Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-06T08:31:14.904Z Has data issue: false hasContentIssue false
  • English
  • Français

Interval Availability Distribution for A 1-out-of-2 Reliability System with Repair

Published online by Cambridge University Press:  27 July 2009

M. C. van der Heijden
M. C. van der Heijden
Affiliation:
Department of Actuarial Sciences and EconometricsThe Free University Amsterdam, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper deals with a two-unit reliability model having one operating unit and one cold standby unit and with ample repair facilities. An approximate method is given for the calculation of the probability distribution of the proportion of time that the system is available in a given time period. The approximate method first computes the mean-time-to-failure and the meantime-to-repair and next approximates the up-and-down process of the two-unit reliability system by an alternating renewal process having exponentially distributed on and off periods. Numerical investigations show a satisfactory performance of the approximation. Also, a sensitivity analysis is given.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 2 , April 1987 , pp. 211 - 223
Copyright
Copyright © Cambridge University Press 1987

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

Barlow, R. E. and Proshan, F. (1975). Statistical Theory of Reliability and Life Testing, Holt, Rinehart and Winston, New York.Google Scholar
Birolini, A. (1985). On the Use of Stochastic Processes in Modelling Reliability Problems, Lecture Notes in Economics and Mathematical Systems No. 252, Springer Verlag, Berlin.Google Scholar
Brouwers, J.J.H. (1986). Probabilistic descriptions of irregular system downtime. Reliability Engineering 16: (to appear).Google Scholar
Gertsbakh, I. (1984). Asymptotic methods in reliability: A review. Adv. Appl. Prob. 16: 147–175.CrossRefGoogle Scholar
Gnedenko, B. V., Belyayev, Y. K., and Solovyev, A. D. (1969). Mathematical Methods of Reliability Theory, Academic Press, New York.Google Scholar
Jagerman, D. (1985). Calculation of Laplace Transforms, Research Report, Bell Laboratories, Holmdel.Google Scholar
Keilson, J. (1979). Markov Chain Models: Rarity and Exponentiality, Springer Verlag Berlin.CrossRefGoogle Scholar
Takács, L. (1957). On certain sojourn time problems in the theory of stochastic processes. Acta Math. Acad. Sci. Hungar 8: 169–191.CrossRefGoogle Scholar
Tijms, H.C. (1986). Stochastic Modelling andAnalysis: A Computational Approach, Wiley, New York.Google Scholar
Van, Hoorn M.H. (1984). Algorithms and Approximations for Queueing Systems, CWI Tract No. 8, Center for Mathematics and Computer Science, Amsterdam.Google Scholar
Whitt, W. (1982). Approximating a point process by a renewal process I: Two basic methods. Operations Research 30: 125–147.CrossRefGoogle Scholar