A new trigonometric modification of the Weibull distribution: Control chart and applications in quality control
Bibliographic record
Abstract
In the most recent era, the extensions of the probability models via trigonometry methods have received great attention. This paper also offers a novel trigonometric version of the Weibull model called a type-I cosine exponentiated Weibull (for short "TICE-Weibull") distribution. The identifiability properties for all three parameters of the TICE-Weibull model are derived. The estimators of the TICE-Weibull model are derived by implementing the maximum likelihood approach. To demonstrate the effectiveness of the TICE-Weibull model, two applications from real-world phenomena are analyzed. In addition, the proposed statistical model is established for an attribute control chart based on a time-truncated life test. The advantage of the developed charts is examined based on the average run length (ARL). The necessary tables of shift sizes and various sample sizes are offered for numerous values of the distribution parameters, as well as specified ARL and shift constants. Some numerical examples are discussed for various scheme parameters to study the performance of the new TICE-Weibull attribute control charts. According to our search and a brief study of the statistical literature, there is no published work on the development of a control chart using new probability models that are introduced using the cosine function. This is the key motivation of this work, which fills this amazing and interesting research gap.
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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 | 0.004 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".