Confirmation of Wilks’ method applied to TRACE model of boiling water reactor spray cooling experiment

Travis Mui, Tomasz Kozlowski

Research output: Contribution to journalArticlepeer-review


Wilks’ formula has been frequently used to quantify the minimum amount of computational work required to meaningfully assess a model's uncertainty, due to its nonparametric statistical nature that does not require knowledge of the distribution of the qualifying parameters of interest. Additionally, this method allows for any number of input uncertain parameters in the simulation model. This is favorable due to considerable computational expense of typical nuclear safety simulations, providing a quantifiable number of code executions that can statistically verify a desired level of safety. However, there are various existing definitions and uses of Wilks’ theorem in such scenarios, which the present study aims to investigate and quantify for a real thermal-hydraulics experiment used for reactor safety licensing. In this work, the U.S. NRC TRACE thermal-hydraulics code was chosen to simulate the separate-effect spray cooling tests performed by ASEA-ATOM for licensing of BWR SVEA-64 fuel. The computational model was evaluated by performing forward uncertainty quantification (UQ) using Dakota as the analysis tool and code driver on 31 identified sensitive parameters. Using this validated model, the TRACE model was sampled 1000 times with four different input parameter probability distributions to produce four model data sets to assess the applicability of Wilks’ theorem within a realistic nuclear safety analysis scenario. The obtained results compared various Wilks-defined 'sample sizes’ according to one-sided confidence intervals for the 1st, 2nd and 3rd-order statistics, and with the two-sided confidence interval for the 1st-order statistics. The comparison demonstrated that Wilks’ method satisfies the reactor safety modeling requirements at the 95%/95% tolerance/confidence level as determined by the U.S. NRC.

Original languageEnglish (US)
Pages (from-to)53-59
Number of pages7
JournalAnnals of Nuclear Energy
StatePublished - Jul 2018


  • BWR spray cooling
  • Uncertainty quantification
  • Wilks method

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


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