New PFH-formulas for k-out-of-n:F-systems

Simplified formulas are popular for reliability analysis of safety instrumented systems (SISs). Both the IEC 61508 standard and the PDS-method provide such formulas for calculation of the average frequency of dangerous failures per hour (PFH). These formulas give reasonably accurate values for the PFH, but both of them also have significant weaknesses. The IEC-formulas can only be applied to systems with up to three elements while the PDS-formulas do not properly account for dangerous detected failures and are not able to include the effects of non-perfect proof-testing. This article presents new PFH-formulas for general k-out-of-n-systems, that take into account both dangerous detected and dangerous undetected failures and also allow for non-perfect proof-testing. The proposed PFH-formulas are compared with the IEC-formulas and the PDS-formulas for some selected systems in a case study, which shows that the new formulas represent an improvement compared to the IEC- and PDS-formulas.