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Coherent structures and unimodality

Part of: Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

S. V. Sabnis  and
Mini R. Nair
S. V. Sabnis*
Affiliation:
Indian Institute of Technology
Mini R. Nair*
Affiliation:
Indian Institute of Technology
*
∗Postal address: Department of Mathematics, Indian Institute of Technology, Bombay, India.
∗Postal address: Department of Mathematics, Indian Institute of Technology, Bombay, India.
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Abstract

This paper is concerned with the preservation of unimodality under coherent structures of independent components having a common life distribution function. This result in a way generalizes a result of Alam [1], as Alam's result indirectly also deals with preservation of unimodality for (n – i + 1)-out-of-n systems of independent and identically distributed components. The usefulness of this property of coherent systems in obtaining sharper upper bounds on the reliability of the concerned system has been illustrated below for a bridge structure with components having a gamma life distribution function.

Keywords

UNIMODALITYRELIABILITY

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60E05: Distributions
Type
Short Communications
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 812 - 817
Copyright
Copyright © Applied Probability Trust 1997 

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References

[1] Alam, K. (1972) Unimodality of the distribution of an order statistic. Ann. Math. Statist. 43, 2041–2044.CrossRefGoogle Scholar
[2] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
[3] Chaudhuri, G., Deshpande, J. V., Dharmadhikari, A. D. (1991) Some bounds on the reliability of coherent systems of IFRA components. J. Appl. Prob. 28, 709–714.Google Scholar
[4] Dharmadhikari, S. and Joag-Dev, K. (1988) Unimodality, Convexity, and Applications. Academic Press, New York.Google Scholar