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Stochastic Comparisons of Residual Lifetimes and Inactivity Times of Coherent Systems

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  30 January 2018

Nitin Gupta
Nitin Gupta*
Affiliation:
Jaypee University of Information Technology and Indian Institute of Technology Kharagpur
*
∗ Postal address: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India. Email address: nitin.gupta@maths.iitkgp.ernet.in
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Abstract

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Under the assumption of independent and identically distributed (i.i.d.) components, the problem of the stochastic comparison of a coherent system having used components and a used coherent system has been considered. Necessary and sufficient conditions on structure functions have been provided for the stochastic comparison of a coherent system having used/inactive i.i.d. components and a used/inactive coherent system. As a consequence, for r-out-of-n systems, it has been shown that systems having used i.i.d. components stochastically dominate used systems in the likelihood ratio ordering.

Keywords

Likelihood ratio ordercoherent systemresidual lifeinactivity time

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 3 , September 2013 , pp. 848 - 860
Copyright
© Applied Probability Trust 

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