title: Generalizing PFD formulas of IEC 61508 for KooN configurations.
abstract: 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.
authors.affiliation: Siemens, Energy Sector, 160 Herring Road, Macquarie Park, 2113 NSW, Australia. Electronic address: hamid.jahanian@siemens.com.
authors.forename: Hamid
authors.initials: H
authors.lastname: Jahanian
keywords: IEC 61508; Probability of failure on demand; Reliability; SIS; k-out-of-n Configuration