Wilks’ formula applied to computational tools: A practical discussion and verification

Abstract Wilks’ non-parametric method for setting tolerance limits using order statistics has recently become popular in the nuclear industry. The method allows analysts to predict a desired tolerance limit with some confidence that the estimate is conservative. The method is popular because it is simple and fits well into established regulatory frameworks. A critical analysis of the underlying statistics is presented in this work, including a derivation, analytical and statistical verification, and a broad discussion. Possible impacts of the underlying assumptions for application to computational tools are discussed. An in-depth discussion of the order statistic rank used in Wilks’ formula is provided, including when it might be necessary to use a higher rank estimate.

[1]  S. S. Wilks.  Statistical Prediction with Special Reference to the Problem of Tolerance Limits , 1942 .

[2]  Sung Won Bae,et al.  ANALYSIS OF UNCERTAINTY QUANTIFICATION METHOD BY COMPARING MONTE-CARLO METHOD AND WILKS’ FORMULA , 2014 .

[3]  R. P. Martin,et al.  AREVA's realistic large break LOCA analysis methodology , 2005 .

[4]  S. S. Wilks.  Determination of Sample Sizes for Setting Tolerance Limits , 1941 .

[5]  W. Whitman,et al.  Heat Transfer for Oils and Water in Pipes1 , 1928 .

[6]  Sigeiti Moriguti,et al.  A MODIFICATION OF SCHWARZ'S INEQUALITY WITH APPLICATIONS TO DISTRIBUTIONS' , 1953 .

[7]  Horst Glaeser,et al.  GRS Method for Uncertainty and Sensitivity Evaluation of Code Results and Applications , 2008 .

[8]  H. O. Hartley,et al.  Universal Bounds for Mean Range and Extreme Observation , 1954 .

[9]  Abraham Wald,et al.  An Extension of Wilks' Method for Setting Tolerance Limits , 1943 .

[10]  S. Moriguti.  Extremal properties of extreme value distributions , 1951 .

[11]  Michael R Chernick,et al.  Bootstrap Methods: A Guide for Practitioners and Researchers , 2007 .

[12]  N. Papadatos.  Maximum variance of order statistics , 1995 .

[13]  E. J. Gumbel,et al.  The Maxima of the Mean Largest Value and of the Range , 1954 .

[14]  N. Balakrishnan.  A simple application of binomial--negative binomial relationship in the derivation of sharp bounds for moments of order statistics based on greatest convex minorants , 1993 .

[15]  H. Robbins.  On the Measure of a Random Set , 1944 .

[16]  Brian J. Williams,et al.  Uncertainty Quantification in a Regulatory Environment , 2015 .

[17]  Attila Guba,et al.  Statistical aspects of best estimate method - I , 2003, Reliab. Eng. Syst. Saf..

[18]  F. Dittus,et al.  Heat transfer in automobile radiators of the tubular type , 1930 .

[19]  W. A. Shewhart,et al.  Statistical method from the viewpoint of quality control , 1939 .

[20]  Bani K. Mallick,et al.  The Method of Manufactured Universes for validating uncertainty quantification methods , 2011, Reliab. Eng. Syst. Saf..

[21]  B. Arnold,et al.  A first course in order statistics , 2008 .

[22]  J. S. Huang.  Sharp bounds for the expected value of order statistics , 1997 .