The Shewhart-type RZ control chart for monitoring the ratio of autocorrelated variables
Bibliographic record
Abstract
In many industrial manufacturing processes, the quality of products can depend on the relative amount between two quality characteristics X and Y. Often, this calls for the on-line monitoring of the ratio Z=X/Y as a quality characteristic itself by means of a control chart. A large number of control charts monitoring the ratio have been investigated in the literature under the assumption of independent normal observations of the two quality characteristics. In practice, due to the high frequency in sensor data collection, both autocorrelation and cross-correlation between consecutive observations can exist for X and Y and should be modelled to protect against the false alarm rate inflation when implementing a control chart for monitoring the ratio Z=X/Y. In this paper, we tackle this problem by investigating the performance of the Phase II Shewhart-type RZ control chart monitoring the ratio of two normal variables whose relationship is captured by a bivariate time series autoregressive model VAR(1), which can also account for the cross-correlation between the two quality characteristics. With the numerical study, we discuss how the design and the statistical performance of the Shewhart-type RZ control chart change with the VAR(1) model's parameters. We also provide an example to illustrate the use of the Shewhart-type RZ control chart with bivariate time series of observations in a furnace process.
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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 | 0.006 | 0.033 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| 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".