Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

Area of Science:

• Reliability Engineering
• System Dynamics
• Probabilistic Modeling

Background:

• Quantitative reliability analysis is crucial for complex multi-state systems.
• Existing models often struggle to incorporate diverse repair strategies and maintenance schedules.
• Accurate prediction of system state probabilities under various conditions is challenging.

Purpose of the Study:

• To develop a novel quantitative reliability modeling and analysis method for multi-state elements.
• To integrate perfect repair, imperfect repair, and condition-based maintenance (CBM) into a unified framework.
• To demonstrate the method's applicability using a control unit failure model.

Main Methods:

• Combines the Markov process with dynamic Bayesian networks (DBNs).
• Establishes Markov models for elements under different repair and CBM scenarios.
• Introduces an absorbing set for repairable element reliability and builds DBNs from state-transition relations.

Main Results:

• The method successfully calculates state probabilities for elements and systems under no repair, perfect repair, imperfect repair, and CBM.
• An absorbing set, plotted by differential equations, verifies the reliability of repairable elements.
• Reliability values for a control unit were determined across different failure modes.

Conclusions:

• The proposed Markov process and DBN combination provides a robust method for multi-state system reliability analysis.
• The model effectively accounts for various repair types and condition-based maintenance.
• Identified weak nodes in the control unit highlight areas for potential reliability improvement.