Generalizing PFD formulas of IEC 61508 for KooN configurations

Detailed formulas are given in IEC 61508 for calculating Probability of Failure on Demand for 1oo1, 1oo2, 2oo2, 2oo3 and 1oo3 systems. Simplified PFD formulas are also derived for general k-out-of-n combinations, without incorporating all the elements utilized in IEC 61508 formulas. While there have been other studies on IEC 61508 formulas and the simplified k-out-of-n equations, none have proposed an inclusive generalized form of IEC 61508 formulas to replicate all the specific combinations covered by the standard. This paper uses a detailed analysis to derive a generalized PFD formula based on IEC 61508.6-2011 that can be applied to all k-out-of-n combinations. The proposed formula is verified against both IEC 61508 and the simplified formulas, and its application is demonstrated by a real life example.