Comparing Lifetimes of Coherent Systems with Dependent Components Operating in Random Environments

TL;DR

This paper analyzes how random environments influence the lifetimes of coherent systems with dependent components, providing conditions for stochastic comparisons across various environmental scenarios.

Contribution

It introduces new sufficient conditions for stochastic comparisons of coherent systems operating in dependent and random environments, considering multiple operational scenarios.

Findings

Derived conditions for stochastic dominance in different environmental settings

Analyzed dependence effects on system lifetime distributions

Provided illustrative examples for the theoretical results

Abstract

We study an 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 coherent systems operate under the same random environment; (ii) two coherent systems operate under two different random environments; (iii) one of the coherent systems operates under a random environment, whereas the other under a deterministic one. Some examples are given to illustrate the proposed reasoning.