Phase reduction for efficient reliability analysis of dynamic k-out-of-n phased mission systems

•Dynamic k-out-of-n phased mission systems are modeled.•Phase combination theory is proposed to improve model construction efficiency.•Proposed combination theory is incorporated into decision diagram-based methods.•A case study of an unmanned aerial vehicle system is provided. Many technological and computing systems deployed for critical missions, like unmanned aerial vehicles (UAVs) and wireless sensor networks, are often designed with redundancies to meet the reliability requirement and conduct their mission task through multiple, consecutive phases of operations. Moreover, the number of available components n and the number of working components required for the correct system function k may change from phase to phase. These systems are referred to as dynamic k-out-of-n phased-mission systems (PMSs). This paper makes contribution by exploring the special structure of k-out-of-n PMSs and proposing novel phase combination theory. Under the proposed combination theory, multiple phases meeting certain conditions are merged into one, leading to a reduced number of mission phases and thus greatly improving the efficiency in the PMS reliability analysis. The proposed phase combination theory is demonstrated through both binary and multi-valued decision diagram-based methods for efficient reliability analysis of k-out-of-n PMSs. Detailed case studies of a multi-UAV system performing a three-phase rescue mission are provided to prove the correctness and efficiency of the proposed phase reduction method.