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Comparing lifetimes of coherent systems with dependent components operating in random environments

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

Published online by Cambridge University Press:  01 October 2019

Nil Kamal Hazra  and
Maxim Finkelstein
Nil Kamal Hazra*
Affiliation:
Indian Institute of Technology Jodhpur
Maxim Finkelstein*
Affiliation:
University of the Free State
*
*Postal address: Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar 342037, India.
*Postal address: Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar 342037, India.
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Abstract

We study the impact of a random environment on lifetimes of coherent systems with dependent components. There are two combined sources of this dependence. One results from the dependence of the components of the coherent system operating in a deterministic environment and the other is due to dependence of components of the system sharing the same random environment. We provide different sets of sufficient conditions for the corresponding stochastic comparisons and consider various scenarios, namely, (i) two different (as a specific case, identical) coherent systems operate in the same random environment; (ii) two coherent systems operate in two different random environments; (iii) one of the coherent systems operates in a random environment and the other in a deterministic environment. Some examples are given to illustrate the proposed reasoning.

Keywords

Coherent systemdistortion/domination functiondependent componentk-out-of-n systemrandom environmentstochastic order

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 3 , September 2019 , pp. 937 - 957
Copyright
© Applied Probability Trust 2019 

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