Automatic Generation of Markov Models in Safety Instrumented Systems with Non-identical Channels

Existing methods of automatic creation for Markov models were limited to systems with identical channels. This paper focuses on how to automatically generate the Markov models of systems with non-identical channels. Each channel is characterized by its own failure rate. The system state matrix is defined and the failure criterion of the state is given. The automatic creation framework for system with non-identical channels is introduced in flow diagram. A computer program based on the automatic creation framework is developed. Many safety related factors, such as failure modes, restorations, common cause failures, self-diagnostic and repair rates are included in this framework. Finally, an example of 1oo2D system is studied, which shows that the average probability of failure on demand (PFD_avg) of the system is closely related to the diversity of the channel´s failure rate. The results show that the diversity of the channel should not be neglected when building the precise Markov model of the safety system.