A comparative study of KooN configurations’ PFH formulas and new generalization

• Published in: International journal of system assurance engineering and management Vol. 16; no. 4; pp. 1398 - 1408
• Main Authors: Omeiri, Hanane, Innal, Fares
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.04.2025; Springer Nature B.V
• Subjects: Comparative studies; Configurations; Engineering; Engineering Economics; Failure; Logistics; Marketing; Markov chains; Organization; Original Article; Quality Control; Reliability; Safety and Risk; Safety barriers; KooN; IEC 61508; Markov models; PFH
• ISSN: 0975-6809; 0976-4348
• DOI: 10.1007/s13198-025-02768-7

Safety instrumented systems (SISs) are considered as paramount safety barriers in nowadays industrial installations. The average probability of dangerous failure on demand ( PFD avg ) and the average failure frequency ( PFH ) are the main performance indicators related to SIS reliability. The aim of this paper is the study of different PFH formulas sets provided in the literature and the development of new formulas generalizations. The PFH formulas are associated with the commonly used KooN (K-out-of-N) configurations, namely: 1oo1, 1oo2, 2oo2, 2oo3 and 1oo3. More specifically, the considered PFH formulas are those given in IEC 61508 standard, PDS handbook, and the formulas newly developed by the authors of this paper based on Markov models. In particular, their underlying assumptions are highlighted and a comparative study between the numerical results they produce is performed and checked against the numerical values derived from Markov models. The examination of the obtained results showed that the IEC 61508 (first edition) formulas (slightly modified) and the newly developed ones provided very similar results that are close to those derived from Markov models. An illustrative example provided in the IEC 61508–6 has been studied through the calculation of its failure frequency using the different PFH formulas.