Copula-based reliability and safety analysis of safety-critical systems with dependent failures

A safety-critical system (SCS) is a system whose failure could result in a certain serious consequence, such as loss of life and significant damage to property or environment. Examples of SCSs abound in real-world applications, such as medical instruments, emergency shutdown systems, and fire/gas detection systems. An SCS can assume 1 of 3 states: working, safe failure, and dangerous (or unsafe) failure. To analyze reliability and safety of SCSs accurately, we build multi-state models of an SCS and its constituent units. The dependent relationships (nonlinear correlation) of different parts within a safety-critical unit as well as across the units are modeled using the Copula method. Formulas computing reliability and safety indexes of a safety-critical unit and of safety-critical series or parallel systems are derived. Numerical examples are provided to demonstrate the application of the proposed methodology.