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The reliability of a large series system under Markov structure

Published online by Cambridge University Press:  01 July 2016

M. T. Chao  and
James C. Fu
M. T. Chao*
Affiliation:
Academia Sinica
James C. Fu*
Affiliation:
University of Manitoba
*
∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, ROC.
∗∗Postal address: Department of Statistics, The University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2.
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Abstract

Let Y1, · ··, Yn be a finite Markov chain and let f be a binary value function defined over the state space of the Y's. We study the reliability of general series system having the structure function φ (Y) = min {f(Y1), · ··, f(Yn)} and show that, under certain regularity conditions, the reliability of the system tends to a constant c (1 ≥ c ≥ 0), where c often has the form c = exp {–λ}.

Keywords

GENERAL SERIES SYSTEMCONSECUTIVE-k-OUT-OF-n: F SYSTEMMARKOV CHAINTRANSITION PROBABILITY MATRIX
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 894 - 908
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Research partially supported by the National Science Council of the Republic of China.

Research partially supported under the National Science Council Visiting Professorship Grant of the Republic of China.

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