Stochastic comparisons of series-parallel and parallel-series systems with dependence between components and also of subsystems
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Bibliographic record
Abstract
<p style='text-indent:20px;'>In this paper, we consider series-parallel and parallel-series systems comprising dependent components that are drawn from a heterogeneous population consisting of <inline-formula><tex-math id="M1">\begin{document}$ m $\end{document}</tex-math></inline-formula> different subpopulations. The components within each subpopulation are assumed to be dependent, and the subsystems themselves are also dependent, with their joint distribution being modeled by an Archimedean copula. We consider a very general setting in which we assume that the subpopulations have different Archimedean copulas for their dependence. Under such a general setup, we discuss the usual stochastic, hazard rate and reversed hazard rate orders between these systems and present a number of numerical examples to illustrate all the results established here. Finally, some concluding remarks are made. The results established here extend the recent results of Fang et al. (2020) in which they have assumed all the subsystems to be independent.</p>
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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 | 0.000 | 0.000 |
| 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