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

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  • Jin, Hui
  • Lundteigen, Mary Ann
  • Rausand, Marvin

Abstract

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.

Suggested Citation

  • Jin, Hui & Lundteigen, Mary Ann & Rausand, Marvin, 2013. "New PFH-formulas for k-out-of-n:F-systems," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 112-118.
    • Handle: RePEc:eee:reensy:v:111:y:2013:i:c:p:112-118
    DOI: 10.1016/j.ress.2012.11.007
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    References listed on IDEAS

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    1. Guo, Haitao & Yang, Xianhui, 2007. "A simple reliability block diagram method for safety integrity verification," Reliability Engineering and System Safety, Elsevier, vol. 92(9), pages 1267-1273.
    2. F Innal & Y Dutuit & A Rauzy & J-P Signoret, 2010. "New insight into the average probability of failure on demand and the probability of dangerous failure per hour of safety instrumented systems," Journal of Risk and Reliability, , vol. 224(2), pages 75-86, June.
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    Cited by:

    1. Alizadeh, Siamak & Sriramula, Srinivas, 2018. "Impact of common cause failure on reliability performance of redundant safety related systems subject to process demand," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 129-150.
    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. Hokstad, Per, 2014. "Demand rate and risk reduction for safety instrumented systems," Reliability Engineering and System Safety, Elsevier, vol. 127(C), pages 12-20.
    4. 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.
    5. Mo, Yuchang & Xing, Liudong & Amari, Suprasad V. & Bechta Dugan, Joanne, 2015. "Efficient analysis of multi-state k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 95-105.

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