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

  • Bo H. Lindqvist (a1), Francisco J. Samaniego (a2) and Nana Wang (a2)

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.

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Corresponding author

*Postal address: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Email address: bo.lindqvist@ntnu.no
**Postal address: Department of Statistics, University of California, Davis, Mathematical Sciences Building, One Shields Avenue, CA 95616, USA. Email address: fjsamaniego@ucdavis.edu
***Postal address: Biometric Research, Merck Research Laboratories, 770 Sumneytown Pike, West Point, PA 19486, USA. Email address: nnwang0401@gmail.com

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