Stress-Strength Reliability Model with The Exponentiated Weibull Distribution: Inferences and Applications
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Bibliographic record
Abstract
In this paper, we deal with the estimation of the reliability $R=P(Y<X)$ where $X$, a unit strength, and $Y$, a unit stress, are independent exponentiated Weibull random variables. The maximum likelihood and Bayesian methods are used to make inference about $R$. We obtain the Baysian estimator using Lindely's procedure under squared error loss and LINEX loss functions with gamma prior for the unknown model parameters. The asymptotic and bootstrap confidence intervals are obtained as well as the credible interval for R is constructed in view of the empirical Bayesian procedure. For illustrative purposes, analysis of real data sets is presented. Mont Carlo simulations are carried out to compare the performances of the different estimators.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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.
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