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March 2014 Stochastic orderings and ageing properties of residual life lengths of live components in (n-k+1)-out-of-n systems
Narayanaswamy Balakrishnan, Ghobad Barmalzan, Abedin Haidari
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J. Appl. Probab. 51(1): 58-68 (March 2014). DOI: 10.1239/jap/1395771413

Abstract

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.

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Narayanaswamy Balakrishnan. Ghobad Barmalzan. Abedin Haidari. "Stochastic orderings and ageing properties of residual life lengths of live components in (n-k+1)-out-of-n systems." J. Appl. Probab. 51 (1) 58 - 68, March 2014. https://doi.org/10.1239/jap/1395771413

Information

Published: March 2014
First available in Project Euclid: 25 March 2014

zbMATH: 1295.60023
MathSciNet: MR3189441
Digital Object Identifier: 10.1239/jap/1395771413

Subjects:
Primary: 60E15
Secondary: 90B25

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 1 • March 2014
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