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Safety Margin Optimisation by Probabilistic Analysis

[+] Author Affiliations
L. Stefanini, F. J. Blom

NRG, Petten, Netherlands

Paper No. PVP2017-65141, pp. V01BT01A061; 7 pages
  • ASME 2017 Pressure Vessels and Piping Conference
  • Volume 1B: Codes and Standards
  • Waikoloa, Hawaii, USA, July 16–20, 2017
  • Conference Sponsors: Pressure Vessels and Piping Division
  • ISBN: 978-0-7918-5791-5
  • Copyright © 2017 by ASME


Deterministic assessment codes can contain large safety factors that give very conservative results. By applying probabilistic analysis to these deterministic assessments, an implicitly accepted probability of failure can be determined. The probability of failure is implicit because it is calculated with the parameter values resulting in a state that is deterministically accepted by the code [2]. When these probabilities are compared for similar deterministic assessments, the excess conservatism can be shown and possibly reduced.

During the present study a probabilistic analysis of the critical crack length initiation was performed. Such analysis led to the formulation of a corrective action proposal to the Master Curve approach given in BS7910:2013 Annex J.

Firstly a deterministic calculation was performed with the Kr-Lr method to define the Critical Length of a through-wall circumferential crack present in a nuclear reactor’s piping. The value of Kmat used in the Kr-Lr method was calculated for a probability of 0.05 and with T0 directly measured (T0 a unique value).

The second step was to pass to probabilistic calculation. Here Kmat was calculated from both T0 directly measured and T0 estimated by Charpy-V tests (T0 as a distribution). The results from these calculations gave the probability of a crack being equal to the Critical Crack Length. Moreover, these results showed that the Tk safety margin introduced in BS7910:2013 Annex J introduce an excess conservatism.

Results from the probabilistic calculations were then compared to the implicitly accepted failure probability Pf (5%) that results from deterministic analysis (T0 considered as a single value) to account for the effects of T0 distribution. An optimized Tk was then found to account for the real uncertainty of the statistical distribution.

Finally, excluding a dependency on the yield stress, the Tk optimization method was generalized. A new correlation for the Tk safety margin is proposed.

Copyright © 2017 by ASME
Topics: Safety , Optimization



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