Differential Smoothing in the Bivariate Exponentially Weighted Moving Average Chart
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.
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 | 0.006 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".