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Asymptotic reliability of consecutive k-out-of-n systems

Part of: Combinatorics Special processes

Published online by Cambridge University Press:  14 July 2016

E. R. Canfield  and
W. P. Mccormick
E. R. Canfield*
Affiliation:
University of Georgia
W. P. Mccormick*
Affiliation:
University of Georgia
*
∗ Postal address: Department of Computer Science, The University of Georgia, 415 Graduate Studies Center, Athens, GA 30602, USA.
∗∗ Postal address: Department of Statistics, The University of Georgia, Athens, GA 30602, USA.
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Abstract

By studying the minimum of moving maxima, that is the maxima taken over a sliding window of length k in an i.i.d. sequence, we obtain new results on the reliability of consecutive k-out-of-n systems. In particular, we give the reliability asymptotically with both k and n varying. The underlying method of our approach is to analyze the singularities of a generating function.

Keywords

LIMIT LAWSGENERATING FUNCTIONSI.I.D. SEQUENCESRELIABILITY

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 05A15: Exact enumeration problems, generating functions
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 142 - 155
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported by the National Security Agency.

References

[1]Ahlfors, L. V. (1966) Complex Analysis, 2nd edn. McGraw-Hill, New York.Google Scholar
[2]Chernick, M. R., Hsing, T. and Mccormick, W. P. (1991) Calculating the extremal index for a class of stationary stochastic processes. Adv. Appl. Prob. 23, 835–850.Google Scholar
[3]Chryssaphinou, O. and Papastavridis, S. G. (1990) Limit distribution for a consecutive k-out-of-n:F system. Adv. Appl. Prob. 22, 491–493.Google Scholar
[4]Chryssaphinou, O. and Papastavridis, S. G. (1990) Reliability of a consecutive k-out-of-n system in a random environment. J. Appl. Prob. 27, 452–458.Google Scholar
[5]Dekkers, A. and De Haan, L. (1989) On the estimation of the extreme-value index and large quantile estimation. Ann. Statist. 17, 1795–1832.Google Scholar
[6]Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.Google Scholar
[7]Feller, W. (1968) Probability Theory and its Applications. Wiley, New York.Google Scholar
[8]Goulden, I. P. (1987) Generating functions and reliabilities. Util. Math. 32, 141–147.Google Scholar
[9]Guibas, L. J. and Odlyzko, A. M. (1980) Long repetitive patterns in random sequences. Z. Wahrscheinlichkeitsth. 55, 241–262.Google Scholar
[10]Hwang, F. K. (1986) Simplified reliabilities for consecutive-k-out-of-n systems. SIAM J. Alg. Disc. Meth. 7, 258–264.Google Scholar
[11]Lambiris, M. and Papastavridis, S. (1985) Exact reliability formulas for linear and circular consecutive-k-out-of-n systems. IEEE Trans. Reliability 34, 124–126.Google Scholar
[12]Li, Zhi-Feng (1989) Stability theorems for maxima of m-dependent sequences. Preprint.Google Scholar
[13]Mccormick, W. P. and Reeves, J. H. (1988) Approximating the distribution of an extreme statistic based on estimates from a generating function. Stoch. Proc. Appl. 27, 307–316.Google Scholar
[14]Papastavridis, S. G. (1987) A limit theorem for the reliability of a consecutive k-out-of-n system. Adv. Appl. Prob. 19, 746–748.Google Scholar