Phased mission system reliability analysis based on Markov regenerative process

Reliability analysis of phased mission systems (PMS) is important. For the sake of a cost-effective analytical solution, several methods proposed in the literature necessarily need to introduce simplifying assumptions, such as deterministic phase durations and homogeneous Markov intraphase process. To attack the weak points of the state-of-the-art, this paper shows how to analyze reliability of general PMS with random phases duration and Markov regenerative intraphase processes. Thanks to the representative power of Markov regenerative processes (MRGP), the intraphase process of these general PMS may include exponential, deterministic, as well as general transitions. Firstly, these general PMS are modeled under a simple and practical 5-tupIe framework. Then by exploiting the techniques available in the literature for the analysis of the MRGP, we show how to compute conditional transient occupation probability matrix for each phase. Then under assumption that memory is lostable at phase boundaries we propose a divide-and-conquer reliability analysis methodology to avoid building a large MRGP for the whole PMS and it has two steps: solve each intraphase process separately and then calculate the reliability of the system by matrix multiplication. With the proposed method, the reliability of general PMS can be efficiently analyzed.