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Preservation of the mean residual life order for coherent and mixed systems

Lindqvist, Bo Henry; Samaniego, Francisco J.; Wang, Nana
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2632706
Date
2019
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  • Institutt for matematiske fag [2676]
  • Publikasjoner fra CRIStin - NTNU [41890]
Original version
Journal of Applied Probability. 2019, 56 (1), 153-173.   10.1017/jpr.2019.11
Abstract
The signature of a coherent system has been studied extensively in the recent literature. Signatures are particularly useful in the comparison of coherent or mixed systems under a variety of stochastic orderings. Also, certain signature-based closure and preservation theorems have been established. For example, it is now well known that certain stochastic orderings are preserved from signatures to system lifetimes when components have independent and identical distributions. This applies to the likelihood ratio order, the hazard rate order, and the stochastic order. The point of departure of the present paper is the question of whether or not a similar preservation result will hold for the mean residual life order. A counterexample is provided which shows that the answer is negative. Classes of distributions for the component lifetimes for which the latter implication holds are then derived. Connections to the theory of order statistics are also considered.
Publisher
Cambridge University Press
Journal
Journal of Applied Probability

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