Orderings for series and parallel systems comprising heterogeneous exponentiated Weibull-geometric components
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Bibliographic record
Abstract
Let X1, …, Xn be independent random variables with Xi ∼ EWG(α, β, λi, pi), i = 1, …, n, and Y1, …, Yn be another set of independent random variables with Yi ∼ EWG(α, β, γi, qi), i = 1, …, n. The results established here are developed in two directions. First, under conditions p1 = ⋅⋅⋅ = pn = q1 = ⋅⋅⋅ = qn = p, and based on the majorization and p-larger orders between the vectors of scale parameters, we establish the usual stochastic and reversed hazard rate orders between the series and parallel systems. Next, for the case λ1 = ⋅⋅⋅ = λn = γ1 = ⋅⋅⋅ = γn = λ, we obtain some results concerning the reversed hazard rate and hazard rate orders between series and parallel systems based on the weak submajorization between the vectors of (p1, …, pn) and (q1, …, qn). The results established here can be used to find various bounds for some important aging characteristics of these systems, and moreover extend some well-known results in the literature.
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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 | 0.002 | 0.003 |
| 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 | 0.000 | 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.
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