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Calculation of the Availability of a Two-Unit Parallel System With Cold Standby

An Illustration of the Embedding Technique

Published online by Cambridge University Press:  27 July 2009

Frank A. Van Der Duyn Schouten  and
Tjerk Ronner
Frank A. Van Der Duyn Schouten
Affiliation:
Centre for Mathematics and Computer Science P.O. Box 4079, 1009 AB Amsterdam, The Netherlands Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
Tjerk Ronner
Affiliation:
Department of EconometricsFree University, P.O. Box 7161, 1007 MC Amsterdam, The Netherlands
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Abstract

A two-unit parallel system with cold standby, Markovian degradation of the working unit and one repair facility is considered. The calculation of the availability of this system under a control-limit repair policy is discussed. Iterative schemes for computing the availability in case of Erlangian repair-time distributions are presented along with numerical results.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 3 , July 1989 , pp. 341 - 353
Copyright
Copyright © Cambridge University Press 1989

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References

Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing.New York: Holt, Rinehart and Winston.Google Scholar
Birolini, A. (1985). On the use of stochastic processes in modelling reliability problems. Lecture Notes in Economics and Mathematical Systems, No. 252. Berlin: Springer Verlag.Google Scholar
deKok, A.G. Kok, A.G., Tijms, H.C., & vander Duyn Schouten, F.A. der Duyn Schouten, F.A. (1984). Approximations for the single-product production-inventory problem with compound Poisson demand and service level constraints. Advances Applied Probability 16: 378–401.Google Scholar
Ferguson, T.S. (1967). Mathematical statistics. A decision theoretic approach. New York: Academic Press.Google Scholar
Kawai, H. (1981). An optimal maintenance policy of a two-unit standby system. Transactions of IECE of Japan, Vol. E64, No. 9, pp. 579–582.Google Scholar
Ross, S.M. (1970). Applied probability models with optimization applications. San Francisco, California: Holden Day.Google Scholar
Tijms, H.C. (1986). Stochastic modelling and analysis: a computational approach. Chichester: Wiley.Google Scholar
Tijms, H.C. & vander Duyn Schouten, F.A. der Duyn Schouten, F.A. (1978). Inventory control with two switch-over levels for a class of M/G/1 queueing systems with variable arrival and service rate. Stochastic Processes and Their Applications 6: 213–222.Google Scholar
vander Heijden, M.C. der Heijden, M.C. (1987). Interval availability distribution for a 1-out-of 2 reliability system with repair. Probability in Engineering and Information Sciences 1: 211–224.Google Scholar
Whitt, W. (1980). Uniform conditional stochastic order. Journal of Applied Probability 17: 112–123.Google Scholar