Boolean Algebraic Methods for Phased-mission System Analysis

Most reliability analysis techniques and tools assume that a system is used for a mission consisting of a single phase. However, multiple phases are natural in many missions. The failure rates of components, system con guration, and success (failure) criteria may vary from phase to phase. In addition, the duration of a phase may be deterministic or random. We describe a new technique for phased-mission system reliability analysis based on Boolean algebraic methods. Our technique is computationally e cient and is applicable to a large class of systems for which the failure criterion in each phase can be expressed as a fault tree (or an equivalent representation). Our technique avoids state space explosion that commonly plague Markov chain-based analysis. We develop a phase algebra to account for the e ects of variable con gurations and failure criteria from phase to phase. Our technique yields exact (as opposed to approximate) results. We demonstrate the use our technique by means of an example and present numerical results to show the e ects of mission phases on the system reliability. An early version of this paper appeared in the Proceedings of ACM SIGMETRICS. This research in part was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the authors were in residence at the Institute for ComputerApplications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681.