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We study an impact of a random environment on lifetimes of coherent systemswith dependent components. There are two combined sources of this dependence.One results from the dependence of the components of the coherent systemoperating in a deterministic environment and the other is due to dependence ofcomponents of the system sharing the same random environment. We providedifferent sets of sufficient conditions for the corresponding stochasticcomparisons and consider various scenarios, namely, (i) two different coherentsystems operate under the same random environment; (ii) two coherent systemsoperate under two different random environments; (iii) one of the coherentsystems operates under a random environment, whereas the other under adeterministic one. Some examples are given to illustrate the proposedreasoning.

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