Reliability of safety-instrumented systems subject to partial testing and common-cause failures

Partial testing is sometimes used as a supplement to proof testing to improve the reliability of safety‐instrumented systems (SISs) in low‐demand mode of operation. This paper studies the effect of partial testing on SIS reliability. Simplified formulas are developed to include both partial and proof testing in the calculation of the average probability of failure on demand (PFDavg). The proposed formulas can handle situations where partial testing is performed periodically and non‐periodically. Common‐cause failures (CCFs) are treated by using the beta‐factor model, and different $\beta$ ‐factors can be included for different failure modes. The proposed formulas are compared with existing results for partial verification. A case study is presented to demonstrate the applicability. The proposed formulas can serve as a valuable tool for selecting a cost‐effective strategy for partial testing.