A multi‐state <i>k</i>‐out‐of‐<i>n</i>:F balanced system with a rebalancing mechanism
Bibliographic record
Abstract
Abstract Balanced systems have extensive applications in engineering fields such as new energy storage and aeronautics. The reliability analysis of such systems has been reported in literature. However, most existing studies focus on the binary‐state situation, and research on multi‐state cases and the relevant rebalancing mechanism is still limited. To fill this gap, a multi‐state k ‐out‐of‐ n :F balanced system with a rebalancing mechanism is studied in this paper. Both components and the system have multiple states, and all the components are required to be working in similar states to ensure that the system operates in a balanced condition. It means that the difference between the maximum and minimum component states should not exceed a threshold. Otherwise, the system is out of balance and should be rebalanced by identifying the components whose states are too high and adjusting them into lower states. A continuous‐time Markov process is used to describe the component operation process and relevant reliability indices are derived accordingly. An age maintenance strategy is also proposed and an optimization model is constructed to obtain the optimal results. Finally, numerical examples based on a product line balancing problem are presented to demonstrate the application of the proposed model.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".