Efficient reliability analysis of generalized k-out-of-n phased-mission systems

A $k$-out-of-$n$ phased-mission system (PMS) is a PMS where the system structure is $k$-out-of-$n$: G in each phase. This paper investigates $k$-out-of-$n$ PMSs with phase-K-out-of-N requirement, where the entire mission is successful if at least K out of the N phases achieve success. Such system is referred to as a generalized $k$-out-of-$n$ PMS ($k$/$n$-GPMS). The $k$/$n$-GPMSs are prevalent in applications such as satellites, unmanned aerial vehicles (UAVs), wireless sensor networks and so on. In this paper, a novel method based on multi-valued decision diagram (MDD) is proposed to analyze the reliability of $k$/$n$-GPMSs, where the number of available components n, the required number of components k, and the components failure behaviors in different phases may vary. Distinguishing from the traditional phase-by-phase MDD generation method, the proposed method considers the behavior of all phases simultaneously and generates only one MDD model in a top-down manner. To illustrate the application of the proposed method, the reliability and the sensitivity of a four UAVs system which conducts supplies delivery mission is analyzed. The complexity analysis is performed. The correctness and efficiency are verified and demonstrated by several case studies. The proposed method is also compared with Monte Carlo simulation method.