Differential Smoothing in the Bivariate Exponentially Weighted Moving Average Chart
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Bibliographic record
Abstract
The multivariate exponentially weighted moving average (MEWMA) control chart proposed by Lowry et al. (1992) has become one of the most widely used charts to monitor multivariate processes. Its simplicity, combined with its high sensitivity to small and moderate process mean jumps, is at the core of its appeal. Lowry et al. (1992) advocated equal smoothing of each quality variable unless there is an a priori reason to weight quality characteristics differently. However, one may have situations where differential smoothing may be justified. For instance: (a) departures in process mean may be different across quality variables, (b) some variables may evolve over time at a much different pace than other variables, and (c) the level of correlation between variables could vary substantially. Here, we assess the performance of the differentially smoothed MEWMA chart. The case of two quality variables (BEWMA) is discussed in detail. A bivariate Markov-chain method that uses conditional distributions is developed for average run-length (ARL) calculations. The proposed chart is shown to perform at least as well as Lowry et al. (1992)'s chart and noticeably better in many mean-jump directions. Comparisons with the recently introduced double-smoothed BEWMA chart and the use of univariate charts for the independent case show that the proposed differentially smoothed BEWMA chart has superior performance.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it