Methods and Sample Size Effect Evaluation for Wafer Level Statistical Bin Limits Determination with Poisson Distributions
Bibliographic record
Abstract
In a modern semiconductor device manufacturing industry, statistical bin limits on wafer level test bin data are used for minimizing value added to defective product as well as protecting end customers from potential quality and reliability excursion. Most wafer level test bin data show skewed distributions. By Monte Carlo simulation, this paper evaluates methods and sample size effect regarding determination of statistical bin limits. In the simulation, it is assumed that wafer level test bin data follow the Poisson distribution. Hence, typical shapes of the data distribution can be specified in terms of the distribution's parameter. This study examines three different methods; 1) percentile based methodology; 2) data transformation; and 3) Poisson model fitting. The mean square error is adopted as a performance measure for each simulation scenario. Then, a case study is presented. Results show that the percentile and transformation based methods give more stable statistical bin limits associated with the real dataset. However, with highly skewed distributions, the transformation based method should be used with caution in determining statistical bin limits. When the data are well fitted to a certain probability distribution, the model fitting approach can be used in the determination. As for the sample size effect, the mean square error seems to reduce exponentially according to the sample size.
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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 | 0.150 | 0.441 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.009 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.072 | 0.004 |
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".