Some Ordering Properties of Coherent Systems under Different Random Environments

In reliability engineering, components of the coherent system may be dependent since they operate in a common random environment. This paper uses multivariate distortion function to describe the dependence among lifetimes of components and the structure function of the coherent system. Some sufficient conditions are given to compare two coherent systems under different random environments in the sense of usual stochastic order, failure rate order, reversed failure rate order and likelihood ratio order.