Numerical experiments on order statistics method based on Wilks' formula for best-estimate plus uncertainty...

Area of Science:

• Nuclear Engineering
• Reliability Engineering
• Statistical Analysis

Background:

• The best-estimate plus uncertainty method is crucial for nuclear power plant safety analysis.
• Accurate uncertainty propagation, encompassing both epistemic and aleatory uncertainties, is essential for reliable safety assessments.
• Wilks' formula-based order statistics method offers a robust approach for this analysis.

Purpose of the Study:

• To assess the characteristics of the order statistics method based on Wilks' formula for nuclear safety evaluations.
• To verify the distribution-free and order-free properties of the method through numerical experiments.
• To investigate the impact of Wilks' formula order on tolerance limit estimation.

Main Methods:

• Numerical experiments were conducted using 21 trial distributions and random samples.
• The study focused on one-sided tolerance limits, common in safety evaluations.
• Various orders of Wilks' formula were analyzed to determine their effect on results.

Main Results:

• The order statistics method based on Wilks' formula demonstrated clear order-free and distribution-free characteristics.
• The number of simulations required is independent of the number of uncertainty parameters.
• Higher-order Wilks' formulas yielded less conservative and more sensitive tolerance limits.

Conclusions:

• The order statistics method based on Wilks' formula is a reliable and statistically sound tool for nuclear safety analysis.
• Its distribution-free nature ensures applicability across various data distributions.
• Employing higher-order formulas is recommended for optimizing tolerance limit estimation in safety assessments.