Hierarchical Dependability Modeling with Multi-State Systems

In this paper, we discuss the hierarchical modeling in model-based dependability evaluation. The hierarchical modeling is a modeling approach that combines non-state-space models such as fault trees and state-space models such as Markov chains. It can mitigate the state explosion problem for state-space models. The fundamental idea is that state-space models are used to represent the dynamic behavior for basic events of non-state-space model. This enables us to represent the dynamic behavior of the system. On the computation of dependability indices such as system reliability, we utilize the non-state-space model. This structure reduces the number of states to be evaluated. The existing hierarchical approaches deal with binary-type reliability models, focusing only on the working and failure of the system/components. In this paper, we extend the existing hierarchical approach to handle the computation of dependability indices using the multi-state system instead of a fault tree, thereby accommodating both reliability and certain performance models, rather than being limited to binary-type models. Additionally, we introduce the computation method with MtMDD (multi-terminal multi-valued decision diagram). Numerical results demonstrated that the proposed hierarchical modeling can efficiently describe multi-state systems and effectively obtain desired dependability indices. It outperforms existing approaches such as Kronecker representation.