Fuzzy Reliability Assessment of Safety Instrumented Systems Accounting for Common Cause Failure

Abstract

Reliability of safety instrumented systems (SISs) is a critical measure to ensure production safety of many industries. This paper focus on low-demand SISs. The reliability of these SISs is quantified by evaluating their probability of failure on demand (PFD). However, due to lack of knowledge, and/or vague judgments from experts, epistemic uncertainty associated with the parameters of components' degradation models is inevitable. Meanwhile, common cause failure (CCF) of two or more components caused by shared environments, often exists in SISs, reliability assessment for a SIS, therefore, becomes a challenging task. In this paper, fuzzy reliability assessment for SISs is conducted by taking account of the CCF among components of a SIS. The fuzzy Markov model is utilized to characterize the degradation process of components under fuzzy environment. The fuzzy state probability distribution of components is, then, calculated by formulating a set of constrained optimization models. Based on the fault tree of a SIS, the fuzzy PFD of the entire SIS with CCFs is formulated by using the $\beta $ -factor to quantify the CCFs. The fuzzy PFD at any $\alpha $ -cut level is, therefore, computed by a constrained optimization model. According to the optimization of parameters of SIS, the lower bound and upper bound of fuzzy PFD of SIS can be determined. Finally, we can quantify the effectiveness of CCF event for assessing the fuzzy PFD of SIS.