Variable Ordering Strategies Of Multiple-valued Decision Diagram For K-out-of-n Phased-mission Systems

Phased-mission systems are systems which perform their missions in multiple consecutive and non-overlapped phases.This paper focuses on the k-out-of-n phased-mission systems of which the system structure for each phase is k-out-of-n.k-out-of-n phased-mission systems widely exist in many fields such as cloud computing,Internet of Things,smart home,wireless sensor networks and other fields.Most systems have high requirements for reliability.At present,the multiplevalued decision diagram(MDD)is a common model to study the reliability of such systems.Before generating an MDD model,it is necessary to order the variables.The order of the variables directly affects the size of the MDD,which in turn affects the reliability modeling and analysis efficiency of the systems.Most of the existing variable ordering strategies are based on fault tree traversal,which are not suitable for analysis methods that directly generate the MDD,and lack of MDD variable ordering strategies specially proposed for k-out-of-n phased-mission systems.In order to improve the efficiency of reliability modeling and analysis for k-out-of-n phasedmission systems,this paper proposes corresponding MDD variable ordering strategies according to the structural characteristics of k-out-of-n phased-mission systems.Firstly,according to the structural characteristics of the k-out-of-n phased-mission systems with no common components in each phase,the corresponding MDD variable ordering strategy is proposed,and the corresponding theoretical analysis is carried out with examples.Secondly,according to the structural characteristics of k-out-of-n phased-mission systems with the same common components in each phase,the corresponding MDD variable ordering strategies are proposed,and the corresponding theoretical analyses are carried out with examples.Finally,experiments are designed for these two types of systems respectively to compare the number of non-sink nodes in the MDD generated by the variable order corresponding to the proposed variable ordering strategies with other variable orders.The results show that the number of non-sink nodes in the MDD obtained by the variable order corresponding to the proposed variable ordering strategies is less than other variable orders,which indicates that the proposed variable ordering strategies can improve the efficiency of MDD reliability analysis of k-out-of-n phased-mission systems.