Systems often operate in phased missions where their reliability structure varies over a set of consecutive time periods, known as phases. The reliability of a phased mission is defined as the probability that all phases in the mission are completed without failure. While the Binary Decision Diagram (BDD) method has been shown to be the most efficient solution for measuring the reliability of phased missions with non-repairable components with mutually exclusive failure modes, the existing BDD based methods are still unable to analyze large systems without considerable computational expense. This paper introduces a new BDD based method that is shown to provide improved efficiency and accuracy in the repeat analysis of this type of phased mission.