  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.
