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Comparisons in the mean residual life order of coherent systems with identically distributed components
Author(s) -
Navarro Jorge,
Gomis M. Carmen
Publication year - 2015
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2121
Subject(s) - independent and identically distributed random variables , order statistic , stochastic ordering , residual , representation (politics) , reliability (semiconductor) , mathematics , statistics , exponential distribution , component (thermodynamics) , reliability theory , order (exchange) , random variable , computer science , algorithm , failure rate , power (physics) , physics , finance , quantum mechanics , politics , political science , law , economics , thermodynamics
The comparisons of the performance of coherent systems (under different stochastic criteria) is an important task in the reliability theory. Several results have been obtained in the literature for the stochastic, hazard rate and likelihood ratio orders. In this paper, we obtain comparison results for the mean residual life order of coherent systems with identically distributed (ID) component lifetimes. These results can be applied not only to the usual case of systems with independent and identically distributed components but also to the case of systems with exchangeable components and to the more general case of just ID components. The results obtained are based on the representation of the system distribution as a distorted distribution of the common components' distribution. Some specific comparison results are given to illustrate the theoretical results. The comparison results for distorted distributions given here can also be applied to other statistical concepts such as order statistics, generalized order statistics or record values. Copyright © 2015 John Wiley & Sons, Ltd.