MDD Variables Ordering Strategies for <i>k</i> ‐Out‐of‐ <i>n</i> Phased‐Mission Systems

ABSTRACT The k ‐out‐of‐ n phased‐mission systems (PMSs) widely exist in the areas such as cloud computing, smart grids, industrial manufacturing, and so on. Accurate and efficient reliability analysis methods are required for such systems in critical applications. Multiple‐valued decision diagram (MDD) is a common model for reliability analysis of k ‐out‐of‐ n PMSs. To construct the system MDD, each variable corresponding to a system component is assigned a different order. Different input variable orders can lead to dramatically different sizes of final system MDD, which in turn affects the reliability analysis efficiency for such systems. This paper aims to reduce the nonsink nodes during system MDD generation by investigating optimal MDD variable ordering strategies for the systems. Unlike those variable ordering strategies based on fault tree traversal or PMS‐BDD variable ordering, the proposed strategies take full advantage of the structural characteristics of the k ‐out‐of‐ n PMSs and incorporate all interrelationships among the number of components shared by all phases, and the system structure parameters k and n . The proposed optimal strategies are validated through both theoretical analysis and experimental evaluations.