Phase combination for reliability analysis of dynamic k-out-of-n Phase-AND mission systems

Dynamic k-out-of-n phase-AND mission systems (k/n-PAMSs) are systems that the mission conducted involves multiple consecutive phases and the entire mission succeeds when the mission in any one of the phases succeeds. The system structure in each phase is k-out-of-n: G, that is, the mission succeeds in a phase when at least k components out of the n components do not fail in this phase. Furthermore, the number of available components n and the required number of working components k for proper system function may vary from one phase to another. In this paper, the unique structure of k/n-PAMSs is investigated and the phase combination theory is proposed. The proposed theory facilitates the merging of multiple phases, subject to specific conditions, into a single phase. Consequently, the number of mission phases is reduced, significantly enhancing the efficiency of k/n-PAMSs reliability analysis. An improved binary decision diagram-based method and an improved multi-valued decision diagram-based method are proposed for reliability analysis of k/n-PAMSs by the integration of this theory. The performance of the proposed methods is analyzed through several case studies. This paper also applies the proposed methods to the reliability analysis of k/n-PAMSs with repeated phases, demonstrating the effectiveness and efficiency of the methods.