General conditions for comparing the reliability functions of systems of components sharing a common environment

We present general criteria for analyzing the crossing characteristics of R I , the reliability function of an m-of-n system of components operating within a laboratory (or test-bench) environment, and R O , the reliability function of the same system now operating subject to an external environment. Inside the laboratory the components' lifetimes may be dependently distributed, and the external environment is modeled using the general approach of Lindley and Singpurwalla (1986). Our techniques, which utilize results basic to the theory of order statistics, apply to broad classes of external environment models.