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Stochastic Orderings and Ageing Properties of Residual Life Lengths of Live Components in (n-k+1)-Out-Of-n Systems

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  30 January 2018

Narayanaswamy Balakrishnan ,
Ghobad Barmalzan  and
Abedin Haidari
Narayanaswamy Balakrishnan*
Affiliation:
McMaster University
Ghobad Barmalzan*
Affiliation:
Zabol University
Abedin Haidari*
Affiliation:
Zabol University
*
∗ Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada. Email address: bala@mcmaster.ca
∗∗ Postal address: Department of Statistics, Zabol University, Sistan and Baluchestan, Iran.
∗∗ Postal address: Department of Statistics, Zabol University, Sistan and Baluchestan, Iran.
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Abstract

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Suppose that a system consists of n independent and identically distributed components and that the life lengths of the n components are Xi, i = 1, …, n. For k ∈ {1, …, n - 1}, let X(k)1, …, X(k)n-k be the residual life lengths of the live components following the kth failure in the system. In this paper we extend various stochastic ordering results presented in Bairamov and Arnold (2008) on the residual life lengths of the live components in an (n - k + 1)-out-of-n system, and also present a new result concerning the multivariate stochastic ordering of live components in the two-sample situation. Finally, we also characterize exponential distributions under a weaker condition than those introduced in Bairamov and Arnold (2008) and show that some special ageing properties of the original residual life lengths get preserved by residual life lengths.

Keywords

(n-k+1)-out-of-n systemstochastic orderingmultivariate mixturedecreasing hazard ratelive componentorder statistics

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 58 - 68
Copyright
© Applied Probability Trust 

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