Multivalued Decision Diagram Modeling Optimization and Evaluation for K ‐Out‐of‐ N Phased‐Mission Systems

ABSTRACT

To address the challenges of state space explosion and low modeling efficiency in the reliability analysis of k ‐out‐of‐ n phased‐mission systems, this paper proposes an efficient modeling and evaluation method based on multivalued decision diagram (MDD). First, a purely topological evaluation framework for MDD state‐space reduction is introduced to optimize variable ordering, eliminating the reliance on prior failure probabilities. By evaluating the mathematical tradeoff among the available components per phase (), fault tolerance demand (), and component state span cost (), the framework quantifies the “pruning cost‐efficiency” of each component. This enables the direct derivation of an optimal variable sequence that minimizes the initial state dimension prior to graph construction. Subsequently, nodes are recursively generated top‐down based on this sequence. Path expansion adheres to rapid local state convergence, utilizing node merging and isomorphic subtree reduction to compress the model and precisely evaluate system reliability. Experiments on a complex unmanned aerial vehicle (UAV) mission system demonstrate that the calculated reliability highly aligns with Monte Carlo simulations. Compared to traditional static structural importance ordering, the proposed framework effectively mitigates concurrent state explosion, reducing same‐layer node merges and isomorphic subtree merges by up to 50% and 35%, respectively, thereby multiplying construction efficiency. Furthermore, extended tests under extreme redundancy constraints validate the method's robustness and “initial dimension reduction” capability. Without the prerequisite of probability priors, the proposed method significantly enhances MDD construction efficiency, exhibiting robust universality and strong engineering scalability.