To attack the weak points of the state-of-the-art, this paper shows how to analyze mission reliability of the generalized PMS with random phases duration and Markov regenerative intraphase processes. These generalized PMS are modeled under a simple and practical 5-tuple analysis model. This paper proves that the underlying intraphase processes are Markov regenerative processes and shows how to compute the conditional transient occupation probability matrix for each phase. Then it shows how to use these matrices to compute mission reliability of the generalized PMS. Using Laplace transformation can simplify the whole analysis process. Equipped with the analysis model, reliability of the generalized PMS can be efficiently analyzed.