Application of Probabilistic Flaw Tolerance Evaluation

Optimizing NDE Inspection Requirements

There have been several industry initiatives to support optimization of examination requirements for various items/components (both Class 1 and Class 2 components) in lieu of the requirements in the ASME Code, Section XI.  The ultimate objective of these initiatives is to optimize the examination requirements (through examination frequency reduction, examination scope reduction, or both) while maintaining safe and reliable plant operation.  There are various examples of examination optimization for both boiling water reactors (BWRs) and pressurized water reactors (PWRs).  Each of these technical bases for examination optimization relies on a combination of items.  The prior technical bases have relied on: (1) operating experience and prior examination results as well as (2) some form of deterministic and/or probabilistic fracture mechanics.   For BWRs, the two main technical bases that are used are BWRVIP-05 and BWRVIP-108.  These technical bases provide the justification for scope reduction for RPV circumferential welds, nozzle-to-shell welds, and nozzle inner radius sections.  For PWRs, the main technical basis for RPV welds is WCAP-16168.  These technical bases are for the RPV welds of BWRs and PWRs which represent just a small subset of the examinations required by the ASME Code, Section XI.  Therefore, the industry is evaluating whether technical bases can be optimized for other components requiring examinations.

Recently, Structural Integrity (SI) and the Electric Power Research Institute (EPRI) worked on developing technical bases for other ASME Code, Section XI components.  The first of these components are PWR main steam and feedwater nozzle-to-shell welds and nozzle inner radius examinations.  These are Section XI Item Nos. C2.21, C2.32, and C2.22.  This technical basis work included a review of the inspection history for these items, selection of representative main steam and feedwater nozzle configurations for evaluation, evaluation of potential degradation mechanisms, and flaw tolerance evaluations consisting of probabilistic and deterministic fracture mechanics analyses.

As with all inspection optimization technical bases, a survey of inspection results was performed.  The survey of results for the three ASME Code items of interest was performed.  These results are contained in EPRI Report No. 3002012965.  Out of a total of 727 examinations identified for the plants that responded, only one examination identified an indication that exceeded the acceptance criteria of the ASME Code, Section XI.  This one examination identified a flaw during a surface examination of the nozzle-to-shell weld.  Since it was a surface examination, the indication was removed by light grinding.  No other issues or indications were identified in the survey results.  As the survey results showed a very limited number of indications that exceeded the acceptance criteria, these items warrant an evaluation of optimized examination requirements.

FIGURE 1. Finite Element Model and Locations of Stress Extraction

To perform the flaw tolerance evaluation, SI developed and performed several stress analyses.  Figure 1 shows a finite element model of the feedwater nozzle and the paths where stresses were extracted.  Figure 2 shows hoop and axial stresses for the various transients and loading conditions analyzed.

FIGURE 2. Through-Wall Stress Results for Evaluation

The stress results were used in a probabilistic fracture mechanics (PFM) evaluation to determine the probability of leakage and failure for the various inspection scenarios.  The goal in the PFM evaluation was to demonstrate that the probability of failure is less than the NRC requirement of 1×10-6 failures per year.  The evaluation used a SI-developed software called “PROMISE (PRobabilistic OptiMization of InSpEction)”.  The software uses a Monte Carlo probabilistic analysis technique with the overall technical approach shown in Figure 3.

FIGURE 3. Technical Approach for PFM Evaluation

The PFM analysis includes many factors that are treated as random variables, such as:

  • Crack distribution (length and depth)
  • Fracture Toughness
  • Inspection Coverage
  • Examinations Performed (PSI and ISI with defined intervals)
  • Probability of Detection for Examinations
  • Applied Stresses (operating loads, transients, and residual)


FIGURE 4. Effect of Inservice Inspection on the Probability of Failure

Sensitivity studies were performed to identify the random variables that have the most impact on the calculated probabilities.  Sensitivity to the probability of rupture, probability of leakage, or both, were evaluated.  The evaluation also varied inputs to demonstrate that this technical basis was applicable to a range of plant designs.

The evaluation looked at various inspection scenarios for the main steam and feedwater nozzles.  The various scenarios looked at the preservice inspection (PSI) for all cases and then various options of 10, 20, and 30-year intervals.  The results of these evaluations are shown in Figure 4.  Based on the results, several various inspection scenarios would meet the safety goal of less than 1×10-6 failures per year.

The full discussion of the work performed for the main steam and feedwater nozzles is contained in EPRI Report No. 3002014590 and is available for download at  The report provides a list of requirements that must be met to be considered bounded by the evaluation.  If bounded, the technical basis can be used by plants to support plant specific relief requests to justify alternative examination strategies for their main steam and feedwater nozzle welds.  For information on this specific topic or the flaw tolerance approach please contact D.J. Shim ( or Chris Lohse (

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