Combined Markov and UGF Methods for Multi-State Repairable Phased Mission Systems

The reliability analysis of multi-state phased mission systems (MS-PMS) is a crucial area of study in systems engineering and reliability engineering. An MS-PMS consists of multiple phases where the system can exist in different operational states in each phase. The system transitions from one phase to the next based on the success or failure of the current phase. The reliability of an MS-PMS depends on the reliabilities of each phase and the transition probabilities between system states across phases. By thoroughly analyzing the reliability of each phase and accurately estimating the probabilities of state transitions, the overall system reliability can be determined. Several methods are used for MS-PMS reliability analysis, such as Markov models, Universal Generating Function (UGF) technique, Petri nets, fault trees, etc. This study evaluated the reliability analysis of an MS-PMS with a combination of Markov and UGF techniques. This method is defined as a combined technique in the literature. The Markov modeling approach represents the system as a set of states with transitions between states based on the failure and repair of components. In addition, the UGF technique converts the Markov model into a set of algebraic equations that can be solved to obtain reliability metrics such as system availability, mean time to failure, etc. In this research, a three-phased multi-state repairable system was discussed. Transition diagrams were created based on components for all phases, and the resulting differential equations were solved. Then, the UGF method was applied according to the system structure of the phases, and the reliability metrics of the system were obtained.