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

Part of: Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  12 July 2019

Bo H. Lindqvist ,
Francisco J. Samaniego  and
Nana Wang
Bo H. Lindqvist*
Affiliation:
Norwegian University of Science and Technology
Francisco J. Samaniego*
Affiliation:
University of California, Davis
Nana Wang*
Affiliation:
University of California, Davis
*
*Postal address: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Email address: [email protected]
**Postal address: Department of Statistics, University of California, Davis, Mathematical Sciences Building, One Shields Avenue, CA 95616, USA. Email address: [email protected]
***Postal address: Biometric Research, Merck Research Laboratories, 770 Sumneytown Pike, West Point, PA 19486, USA. Email address: [email protected]
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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.

Keywords

Coherent systemmixed systemsignaturestochastic orderingmean residual life orderdecreasing failure rateorder statisticsspacings

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 1 , March 2019 , pp. 153 - 173
Copyright
© Applied Probability Trust 2019 

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