Journal of Applied Probability

Stochastic orderings and ageing properties of residual life lengths of live components in (n-k+1)-out-of-n systems

Narayanaswamy Balakrishnan, Ghobad Barmalzan, and Abedin Haidari

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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.

Article information

Source
J. Appl. Probab., Volume 51, Number 1 (2014), 58-68.

Dates
First available in Project Euclid: 25 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1395771413

Digital Object Identifier
doi:10.1239/jap/1395771413

Mathematical Reviews number (MathSciNet)
MR3189441

Zentralblatt MATH identifier
1295.60023

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]

Keywords
(n-k+1)-out-of-n system stochastic ordering multivariate mixture decreasing hazard rate live component order statistics

Citation

Balakrishnan, Narayanaswamy; Barmalzan, Ghobad; Haidari, Abedin. Stochastic orderings and ageing properties of residual life lengths of live components in ( n - k +1)-out-of- n systems. J. Appl. Probab. 51 (2014), no. 1, 58--68. doi:10.1239/jap/1395771413. https://projecteuclid.org/euclid.jap/1395771413


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