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ON THE IFR PROPERTY PRESERVATION FOR MARKOV CHAIN IMBEDDABLE SYSTEMS

Published online by Cambridge University Press:  27 February 2007

M. V. Koutras  and
P. E. Maravelakis
M. V. Koutras
Affiliation:
Department of Statistics and Insurance Science, University of Pireaus, Pireaus, Greece, E-mail: mkoutras@unipi.gr
P. E. Maravelakis
Affiliation:
Department of Statistics and Insurance Science, University of Pireaus, Pireaus, Greece, E-mail: mkoutras@unipi.gr
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Abstract

In the present article, we consider a class of reliability structures that can be efficiently described through a finite Markov chain (Markov chain imbeddable systems) and investigate its closeness with respect to the increasing failure rate (IFR) property. More specifically we derive a sufficient condition for the system's lifetime to have increasing failure rate when the identical and independent components comprising it own this property. As an application of the general theory, we establish an alternative proof of the IFR property preservation for the k-out-of-n system and derive some related results for the family of weighted k-out-of-n systems.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 2 , April 2007 , pp. 201 - 216
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing, Silver Spring, MD: To Begin with.
Boutsikas, M.V. & Koutras, M.V. (2000). Reliability approximation for Markov chain imbeddable systems. Methodology and Computing in Applied Probability 2: 393–411.Google Scholar
Chao, M.T. & Fu, J.C. (1989). A limit theorem for certain repairable systems. Annals of the Institute of Statistical Mathematics 41: 809–818.Google Scholar
Chao, M.T. & Fu, J.C. (1991). The reliability of a large series system under Markov structure. Advances in Applied Probability 23: 894–908.Google Scholar
Esary, J.D. & Proschan, F. (1963). Relationship between system failure rate and component failure rates. Technometrics 5: 183–189.Google Scholar
Fu, J.C. (1986). Reliability of consecutive k-out-of-n:F systems with (k − 1) step Markov dependence. IEEE Transactions in Reliability 35: 602–606.Google Scholar
Fu, J.C. & Lou, W.Y. (1991). On reliabilities of certain linearly connected engineering systems. Statistics & Probability Letters 12: 291–296.Google Scholar
Koutras, M.V. (1996). On a Markov chain approach for the study of reliability structures. Journal of Applied Probability 33: 357–367.Google Scholar
Lutkepohl, H. (1997). Handbook of matrices. New York: Wiley.
Ross, S. (2003). Introduction to probability models. San Diego: Academic Press.
Taylor, H.M. & Karlin, S. (1984). An introduction to stochastic modeling. Orlando, FL: Academic Press.
Wu, J.S. & Chen, R.J. (1994). An algorithm for computing the reliability of a weighted-k-out-of-n system. IEEE Transactions in Reliability 45: 327–328.Google Scholar