Performance measures for systems under multiple environments

In this paper, the system which operates in multiple environments is studied. The environment process is governed by a Markov process, and the deterioration process is governed by another Markov process given the system in a certain environment. In terms of the above two processes, a new Markov process is constructed to represent the evolution of the system. In terms of Ion-Channel modeling theory, Markov process theory and matrix partition method, some reliability indexes for the system are obtained, i.e., system reliability, environment reliability, system multiple-interval reliability, system availability, environment availability, system multiple-point availability, etc. Finally, a numerical example is given to illustrate the results obtained in the paper.