Generalized analytical expressions for safety instrumented systems' performance measures: PFDavg and PFH

• A set of generalized PFDavg and PFH formulas are developed.
• The proposed analytical expressions are simple and easy to implement.
• Partial stroke tests and common cause failures are considered.
• The validation of the suggested equations is performed at different stages of their development.

Safety Instrumented Systems (SIS) constitute an indispensable element in the process of risk reduction for almost all of nowadays' industrial facilities. The main purpose of this paper is to develop a set of generalized and simplified analytical expressions for two commonly employed metrics to assess the performance of SIS in terms of safety integrity, namely: the Average Probability of Failure on Demand (PFDavg) and the Probability of Dangerous Failure per Hour (PFH). In addition to the capability to treat any K-out-of-N architecture, the proposed formulas can smoothly take into account the contributions of Partial Stroke Testing (PST) and Common Cause Failures (CCF). The validity of the suggested analytical expressions is ensured through various comparisons that are carried out at different stages of their construction.