Numerical experiment to evaluating two-sided tolerance limit for safety analysis
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Full Text |
Pdf
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Author |
Seola Han and Taewan Kim
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e-ISSN |
1819-6608 |
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On Pages
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2075-2079
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Volume No. |
18
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Issue No. |
18
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Issue Date |
November 30, 2023
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DOI |
https://doi.org/10.59018/0923254
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Keywords |
nonparametric order statistics, wilks’ formula, GRS method, best-estimate plus uncertainty, centered two-sided tolerance limit.
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Abstract
Uncertainty analysis is required to quantify uncertainties in safety evaluation for industrial applications when the
best-estimate methodology is employed. The nonparametric order statics method suggested by the GRS (Gesellschaftfür
Anlagen-und Reaktorsicherheit) is one of the uncertainty evaluation methodologies to obtain the figure of merits with a
probability of 95 % and confidence of 95 %, namely 95/95 value. In this method, the number of repeated calculations with
perturbation to acquire the 95/95 value is decided by a formula suggested by Wilks and is dependent on the number of
uncertainty parameters. Thus, the method is effective when the reference system has a large number of parameters which
bring uncertainty in the analysis. Previous studies indicate that the method can estimate the 95/95 value successfully when
the figure of merit has one-sided tolerance limit where either the upper or lower limit exits. However, when it is necessary
to cut off the tails of 2.5% evenly in both ends, namely the centered two-sided tolerance limit, the suggested formula
results in a lower confidence level. Thus, a modified formula is suggested in this study to account for such characteristics,
and, as a result, the number of repeated calculations required to obtain the 95/95 value is calculated. The validity of the
formula and the number of repeated calculations are examined using numerical experiments for 21 different distributions.
The numerical experiment has been conducted with one to ten million sample sets to estimate the confidence level. The
results of the numerical experiments indicate that the 95/95 value is predicted successfully by the repeated calculations
decided by the modified formula when the figure of merit has characteristics of the centered two-sided distribution, while
the existing formula results in a confidence level of 80%.
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