Semi-markov process-based integrated importance measure for multi-state systems

Importance measures in reliability engineering are used to identify weak components of a system and signify the roles of components in contributing to proper functioning of the system. Recently, an integrated importance measure (IIM) has been proposed to evaluate how the transition of component states affects the system performance based on the probability distributions and transition rates of component states. In the system operation phase, the bathtub curve presents the change of the transition rate of component states with time, which can be described by three different Weibull distributions. The behavior of a system under such distributions can be modeled by the semi-Markov process. So, based on the reported IIM equations of component states, this paper studies how the transition of component states affects system performance under the semi-Markov process. This measure can provide useful information for preventive actions (such as monitoring enhancement, construction improvement, etc.), and provide support to improve system performance. Finally, a simple numerical example is presented to illustrate the utilization of the proposed method.