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A method for computing total downtime distributions in repairable systems

Part of: Limit theorems Special processes Stochastic processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Suyono  and
J. A. M. van der Weide
Suyono
Affiliation:
Universitas Negeri Jakarta
J. A. M. van der Weide*
Affiliation:
Delft University of Technology
*
∗∗ Postal address: Delft University of Technology, HB 06.130, Mekelweg 4, 2628 CD Delft, The Netherlands. Email address: j.a.m.vanderweide@its.tudelft.nl
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Abstract

In this paper we derive the distribution of the total downtime of a repairable system during a given time interval. We allow dependence of the failure time and the repair time. The results are presented in the form of Laplace transforms which can be inverted numerically. We also discuss asymptotic properties of the total downtime.

Keywords

DowntimeLaplace transformLaplace–Stieltjes transformpoint process

MSC classification

Primary: 60E10: Characteristic functions; other transforms
Secondary: 60G55: Point processes 60F05: Central limit and other weak theorems 60K05: Renewal theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 643 - 653
Copyright
Copyright © Applied Probability Trust 2003 

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References

Barlow, R. E., and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Embrechts, P., Klüpelberg, C., and Mikosch, T. (1999). Modelling Extremal Events for Insurance and Finance. Springer, Berlin.Google Scholar
Funaki, K., and Yoshimoto, K. (1994). Distribution of total uptime during a given time interval. IEEE Trans. Reliab. 43, 489–492.CrossRefGoogle Scholar
Grandell, J. (1943). Doubly Stochastic Poisson Processes. Springer, Berlin.Google Scholar
Muth, E. J. (1968). A method for predicting system downtime. IEEE Trans. Reliab. 17, 97–102.CrossRefGoogle Scholar
Rényi, A. (1957). On the asymptotic distribution of the sum of a random number of independent random variables. Acta Math. Acad. Sci. Hungar. 8, 193–199.CrossRefGoogle Scholar
Resnick, S. I. (1987). Extreme Values, Regular Variation, and Point Processes. Springer, New York.CrossRefGoogle Scholar
Srinivasan, S. K., Subramanian, R., and Ramesh, K. S. (1971). Mixing of two renewal processes and its applications to reliability theory. IEEE Trans. Reliab. 20, 51–55.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
Widder, D. V. (1946). The Laplace Transform. Princeton University Press.Google Scholar