Reliability evaluation of a Semi-Markov repairable system under alternative environments

To accurately describe the performance of repairable systems operating under alternative environments, for example, mild/harsh, working/idling, maximum/minimum level demand etc., a Semi-Markov process with a finite state space and two different Semi-Markov kernels is introduced. The state set of the system which is regarded as acceptable might depend on the environments. Two important reliability indices, the availability and time to the first system failure, are obtained via Markov renewal theory, transform and matrix methods. The results and numerical examples are also provided for two special cases: (1) when sojourn times under alternative environments are constants and (2) when sojourn times under environments have exponential distributions.