Impact of proof test interval and coverage on probability of failure of safety instrumented function

Highlights: • Introduction of proof test coverage makes the calculation of the probability of failure for SIF more accurate. • The probability of failure undetected by proof test is independently defined as P_TIF and calculated. • P_TIF is quantified using reliability block diagram and simple formula of PFD_avg. • Improving proof test coverage and adopting reasonable test period can reduce the probability of failure for SIF. - Abstract: Imperfection of proof test can result in the safety function failure of safety instrumented system (SIS) at any time in its life period. IEC61508 and other references ignored or only elementarily analyzed the imperfection of proof test. In order to further study the impact of the imperfection of proof test on the probability of failure for safety instrumented function (SIF), the necessity of proof test and influence of its imperfection on system performance was first analyzed theoretically. The probability of failure for safety instrumented function resulted from the imperfection of proof test was defined as probability of test independent failures (P_TIF), and P_TIF was separately calculated by introducing proof test coverage and adopting reliability block diagram, with reference to the simplified calculation formula of average probability of failure on demand (PFD_avg). Research results show that: the shorter proof test period and the higher proof test coverage indicate the smaller probability of failure for safety instrumented function. The probability of failure for safety instrumented function which is calculated by introducing proof test coverage will be more accurate.