MONOTONICITY PROPERTIES OF RESIDUAL LIFETIMES OF PARALLEL SYSTEMS AND INACTIVITY TIMES OF SERIES SYSTEMS WITH HETEROGENEOUS COMPONENTS
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Bibliographic record
Abstract
Here, we discuss the stochastic comparison of residual lifetimes of parallel systems and inactivity times of series systems by means of the reversed hazard rate order when the components of the systems are independent but not necessarily identically distributed. We also establish some monotonicity properties of such residual lifetimes of parallel systems and inactivity times of series systems. These results extend some of the recent results in this direction due to Zhao, Li, and Balakrishnan [21], Kochar and Xu [12], and Saledi and Asadi [16].
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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)
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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