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An Approximation of the Interval Availability Distribution

Published online by Cambridge University Press:  27 July 2009

Marcel A. J. Smith
Marcel A. J. Smith
Affiliation:
Erasmus University Rotterdam, Econometrics and Operations Research, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
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Abstract

In this paper, we consider the interval availability distribution of a two-state single unit. We fit the interval availability distribution directly to a beta distribution, such that the probability of nil and a 100% availability is correct as well as the expectation and the variance. The method is fast and easy to implement and gives good results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 4 , October 1997 , pp. 451 - 467
Copyright
Copyright © Cambridge University Press 1997

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References

1.Abate, J. & Whitt, W. (1993). Numerical inversion of Laplace transforms of probability distributions. ORSA Journal on Computing (to appear).Google Scholar
2.Aven, T. (1993). On performance measures for multi-state monotone systems. Reliability Engineering & System Safety 41: 259–266.Google Scholar
3.Bain, L.J. & Engelhardt, M. (1987). Introduction to probability and mathematical statistics. Boston: PWS Publishers.Google Scholar
4.Csenki, A. (1995). A new approach to the cumulative operational time for semi-Markov models of repairable systems, (to appear).Google Scholar
5.Davies, B. & Martin, B. (1979). Numerical inversion of the Laplace transform: A survey and comparison of methods. Journal of Computational Physics 33: 1–32.Google Scholar
6.Haukaas, H. & Aven, T. (1996). Formulae for the down time distribution of a system observed in a time interval. Reliability Engineering and System Safety 52: 19–26.CrossRefGoogle Scholar
7.Heijden, M.C. Van der & Schornagel, A. (1988). Interval un-effectiveness distribution for a k out of n multi-state reliability system with repair. European Journal of Operational Research 36: 66–77.CrossRefGoogle Scholar
8.Iseger, P.W. den, Smith, M.A.J., & Dekker, R. (1996). Computing compound distributions faster! Insurance: Mathematics and Economics (to appear).Google Scholar
9.Johnson, M.A. & Taaffe, M.R. (1989). Matching moments to phase type distributions: Mixtures of Erlang distributions of common order. Communications in Statistics—Stochastic Models 5(4): 711–743.CrossRefGoogle Scholar
10.Reibman, A., Smith, R., & Trivedi, K. (1989). Markov and Markov reward model transient analysis: An overview of numerical approaches. European Journal of Operational Research 40: 257–267.Google Scholar
11.van Rijn, C.F.H. & Schornagel, A. (1987). Stamp, a new technique to asses the probability distribution of system effectiveness. Proceedings of the Seventeenth Annual Meeting of the Systems Reliability Service Associate Members, The SRS Quarterly Digest, pp. 50–58.Google Scholar
12.Takács, L. (1957). On certain sojourn time problems in the theory of stochastic processes. Acta Mathematica Academiae Scientiarum Hungaricae 8: 169–191.CrossRefGoogle Scholar
13.Tijms, H.C. (1994). Stochastic models: A computational approach. Chichester: John Wiley & Sons.Google Scholar
14.Wartenhorst, P. (1990). Bounds for the interval availability distribution. Report BS-R9031, CWI, Amsterdam.Google Scholar