Graph-based reliability evaluation of a reconfigurable multi-stage system using sequential unconnected path sets

Admitting its potential in flexible manufacturing, the reconfigurable multi-stage system (RMS) is widely used in modern industries while its reliability is of great importance since the failure of any composing stage will lead to the system failure and abortion of the whole mission. In this paper, we present a survival signature-based framework for the reliability of an RMS. The idea of our approach is to convert a conventional probability estimation problem to a graph-based path-searching problem, thus the tedious Monte Carlo sampling is simplified. To this end, an unconnected path graph method is developed to calculate the number of working paths of the equivalent graph model of RMS. Instead of directly enumerating all possible working paths, those paths of interest are identified by searching unconnected nodes via backtracking while the computation cost is reduced. To further address the case of an RMS with shared components, a sequential unconnected path graph (SUPG) method is developed. The proposed method is validated through two numerical cases and an application example. The results show our method can identify the “bottleneck” stage once the system is reconfigured with saved computational cost.