A new sampling strategy for the Shewhart control chart monitoring a process with wandering mean
Why this work is in the frame
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Bibliographic record
Abstract
In many processes, such as in chemical and process industries, the observations of a quality characteristic to be monitored may be correlated, if sampling intervals are short. Correlation can be modelled by considering the process mean as a random variable wandering according to an autoregressive[GRAPHICS]model and the observations from the process modelled as the mean plus a random error due to short-term variability or measurement error. The sensitivity of the Shewhart[GRAPHICS]control chart in the detection of a special cause is negatively affected by presence of correlation among observations. To overcome this problem, a new sampling strategy, denoted as ESSI (Equally Spaced Samples Items), is proposed to implement the Shewhart[GRAPHICS]control chart as opposed to the traditional rational subgrouping approach. The ESSI sampling strategy allows observations belonging to the same sample to be collected from the process at equally spaced time intervals between two successive inspections. A numerical analysis shows that the implementation of the ESSI strategy in presence of a process wandering mean significantly improves the statistical performance of the Shewhart[GRAPHICS]control chart vs. rational subgrouping for different levels of autocorrelation. Furthermore, by implementing the ESSI sampling strategy, the selection of the width of control limits for the control chart is independent of the correlation. An illustrative example shows the implementation of the proposed strategy.
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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 | 0.008 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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