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Extension of ISA TR84.00.02 PFD equations to KooN architectures

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  • Oliveira, Luiz Fernando
  • Abramovitch, Rafael Nelson

Abstract

Simplified equations for PFD evaluation of the most used architectures are given in ISA TR84.00.02-2002 document. This paper introduces a generalization of those equations for applications to any KooN architecture. The meaning of each individual term in the derived equations is explained. To strengthen their validity, several comparisons are made between their results and those of a numerical integration model for PFD assessment. The results show that the values obtained with the generalized equations are very close to those of the numerical model, even for highly redundant configurations. Comparisons are also made with the analytical equations given in IEC 61508. It is argued that the ISA equations are conceptually more consistent than those of IEC 61508 even though the numerical differences between the results are not significant in most practical cases. Overall, the results indicate that the generalized KooN PFD equations derived here may be applied to systems with higher redundancy, thus partly contradicting suggestions made in the above ISA reference that such equations should only be used for the simplest configurations. Some specific practical situations to which they cannot be applied are also pointed out.

Suggested Citation

  • Oliveira, Luiz Fernando & Abramovitch, Rafael Nelson, 2010. "Extension of ISA TR84.00.02 PFD equations to KooN architectures," Reliability Engineering and System Safety, Elsevier, vol. 95(7), pages 707-715.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:7:p:707-715
    DOI: 10.1016/j.ress.2010.01.006
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    1. Dutuit, Y. & Innal, F. & Rauzy, A. & Signoret, J.-P., 2008. "Probabilistic assessments in relationship with safety integrity levels by using Fault Trees," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1867-1876.
    2. Torres-Echeverría, A.C. & Martorell, S. & Thompson, H.A., 2009. "Modelling and optimization of proof testing policies for safety instrumented systems," Reliability Engineering and System Safety, Elsevier, vol. 94(4), pages 838-854.
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    Cited by:

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    2. Mechri, Walid & Simon, Christophe & BenOthman, Kamel, 2015. "Switching Markov chains for a holistic modeling of SIS unavailability," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 212-222.
    3. Xu, Ming & Chen, Tao & Yang, Xianhui, 2012. "The effect of parameter uncertainty on achieved safety integrity of safety system," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 15-23.
    4. Cui, Lin & Shu, Yidan & Wang, Zhaohui & Zhao, Jinsong & Qiu, Tong & Sun, Wenyong & Wei, Zhenqiang, 2012. "HASILT: An intelligent software platform for HAZOP, LOPA, SRS and SIL verification," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 56-64.
    5. Tang, Zhang-Chun & Zuo, Ming J. & Xiao, Ningcong, 2016. "An efficient method for evaluating the effect of input parameters on the integrity of safety systems," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 111-123.
    6. Azizpour, Hooshyar & Lundteigen, Mary Ann, 2019. "Analysis of simplification in Markov-based models for performance assessment of Safety Instrumented System," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 252-260.
    7. Vaurio, Jussi K., 2011. "Unavailability equations for k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 96(2), pages 350-352.
    8. Innal, Fares & Dutuit, Yves & Chebila, Mourad, 2015. "Safety and operational integrity evaluation and design optimization of safety instrumented systems," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 32-50.
    9. Eisinger, S. & Oliveira, L.F., 2021. "Evaluating the safety integrity of safety systems for all values of the demand rate," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    10. Gabriel, Angelito & Ozansoy, Cagil & Shi, Juan, 2018. "Developments in SIL determination and calculation," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 148-161.
    11. Ding, Long & Wang, Hong & Kang, Kai & Wang, Kai, 2014. "A novel method for SIL verification based on system degradation using reliability block diagram," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 36-45.
    12. Torres-Echeverría, A.C. & Martorell, S. & Thompson, H.A., 2011. "Modeling safety instrumented systems with MooN voting architectures addressing system reconfiguration for testing," Reliability Engineering and System Safety, Elsevier, vol. 96(5), pages 545-563.
    13. Meng, Huixing & Kloul, Leïla & Rauzy, Antoine, 2018. "Modeling patterns for reliability assessment of safety instrumented systems," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 111-123.
    14. Innal, Fares & Lundteigen, Mary Ann & Liu, Yiliu & Barros, Anne, 2016. "PFDavg generalized formulas for SIS subject to partial and full periodic tests based on multi-phase Markov models," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 160-170.

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