Probability risk assessment approach for sequential, prior and trigger-dependent multi-state systems based on DBNs

In industrial engineering, the components of a critical system are capable of being in partial failure modes, except for “perfect state” and “complete failure”, and the failure behavior of those usually manifests as dynamicity and dependence. However, traditional dynamic fault trees (DFTs), which represent an event as a dichotomous variable, and the extended ones in probability risk assessment cannot actually grasp the dynamic properties of some multi-state systems (MSSs). For these issues, this article further extends the classical DFT language for sequential, prior and trigger-dependent MSSs and presents a unified framework of probability risk analysis based on the dynamic Bayesian net (DBN). First, three types of multi-state dynamic gates (MSDGs) for representation of the above-mentioned failure behavior were defined, and the algorithm for mapping MSDGs to DBNs was proposed. Next, this paper employs the classic Markov chain based on the improved approach of Kronecker algebra to verify these models. Finally, combining a specific example of a shield excavation system, we discuss how the MSDGs can be adopted as a compact modeling language and analyze the dynamic probability risk of the system by compiling the model into a DBN.