Reliability modelling of redundant safety systems without automatic diagnostics incorporating common cause failures and process demand

Redundant safety systems are commonly used in the process industry to respond to hazardous events. In redundant systems composed of identical units, Common Cause Failures (CCFs) can significantly influence system performance with regards to reliability and safety. However, their impact has been overlooked due to the inherent complexity of modelling common cause induced failures. This article develops a reliability model for a redundant safety system using Markov analysis approach. The proposed model incorporates process demands in conjunction with CCF for the first time and evaluates their impacts on the reliability quantification of safety systems without automatic diagnostics. The reliability of the Markov model is quantified by considering the Probability of Failure on Demand (PFD) as a measure for low demand systems. The safety performance of the model is analysed using Hazardous Event Frequency (HEF) to evaluate the frequency of entering a hazardous state that will lead to an accident if the situation is not controlled. The utilisation of Markov model for a simple case study of a pressure protection system is demonstrated and it is shown that the proposed approach gives a sufficiently accurate result for all demand rates, durations, component failure rates and corresponding repair rates for low demand mode of operation. The Markov model proposed in this paper assumes the absence of automatic diagnostics, along with multiple stage repair strategy for CCFs and restoration of the system from hazardous state to the "as good as new" state.