Reliability Analysis of Tree-Structured Systems Using Characteristic Function

This paper provides an efficient algorithm for computing the reliability of both tree-structured and hierarchical array systems with k-out-of-n failure criteria. The algorithm utilizes characteristic functions and avoids working directly with probability mass functions. A case study is investigated to illustrate the efficiency of the proposed algorithm. Compared with conventional analysis methods, the proposed algorithm shows superiorities in both efficiency and feasibility. It may significantly help system designers facilitate the reliability analysis and optimization of large-scale tree-structured and hierarchical array systems, especially in model-based systems engineering (MBSE).