Integrated importance of multi-state fault tree based on multi-state multi-valued decision diagram

Integrated importance measures have been developed to study the effect of component state probabilities and state transition rates on the multi-state system performance, identifying the weakest component to facilitate the system maintenance and optimization activities. This article proposes an analytical method based on multi-state multi-valued decision diagram for computing the integrated importance measure values. Following a discussion of decomposition and physical meaning of integrated importance measures, the modeling method of multi-state multi-valued decision diagram based on multi-state fault tree analysis is introduced. A five-step integrated importance measure analysis approach based on multi-state multi-valued decision diagram is then proposed. Two case studies are implemented to demonstrate the presented methods. Complexity analysis shows that the multi-state multi-valued decision diagram-based method is more computationally efficient than the existing method using Markov-Bayesian networks.