Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-15T01:31:28.627Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Special processes Combinatorics

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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