Generalized Tolerance Limit Evaluation Method to Determine Statistically Meaningful Minimum Code Simulations
Bibliographic record
Abstract
The tolerance limit approach has been internationally adopted for nuclear safety analyses as a way of identifying more realistic safety limits in the Best Estimate Plus Uncertainty (BEPU) methodology. The approach is based on the Wilks’ formula set suggested by the GRS (Gesellschaft fu¨r Anlagen-und Reaktorsicherheit), and consists of two approaches; one-sided approach to obtain a statistical meaning of the maximum output value in the multiple code runs, and two-sided approach for the minimum and maximum values at the same time. The Wilks’ formula set suggested by the GRS has been employed without questioning any ambiguities in its true meaning, especially in the two-sided approach. In this paper, the formula set is derived based on the binomial distribution as a direct vehicle to the formulas for clarification purposes. This approach is distinguished from the present integral form of the original Wilks’ formula in that it is based on the probability density function and the joint probability density function associated with the order statistics. The purposes of this paper are to derive the true meanings of the present Wilks’ formulas, which are applied in the nuclear safety analysis, and to derive a new set of formulas to determine statistically meaningful minimum number of code runs in the BEPU. An improved formula set, which consists of the Generalized Maximum Tolerance Limit (GMTL) and the Generalized Max-Mini Tolerance Limit (GMMTL), is proposed with an emphasis on a new form of the two-sided formula: Centered Two-sided Tolerance Limit (CTTL) formula, which is directly derived from the GMMTL formula. For example, a minimum number of 146 code runs is suggested in lieu of the present 93 code runs to achieve the 95th percentile with 95% confidence in the two-sided approach.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".