Comparing lifetimes of coherent systems with dependent components operating in random environments. (September 2019)

• Record Type: Journal Article
• Authors: Kamal Hazra, Nil; Finkelstein, Maxim
• Is Part Of: Journal of applied probability. Volume 56:Number 3(2019)
• Page Start: 937
• Page End: 957
• Publication Date: 2019-09
• Subjects: Coherent system, -- distortion/domination function, -- dependent component, -- k-out-of-n system, -- random environment, -- stochastic order; Primary 90B25, -- Secondary 60E15, -- 60K10; 519.2
• DOI: 10.1017/jpr.2019.53
• Languages: English
• ISSNs: 0021-9002

Abstract

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.