Optimal Preventive Replacement Under Minimal Repair and Random Repair Cost
Why this work is in the frame
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Bibliographic record
Abstract
A repair/replacement problem for a single unit system with random repair cost is considered. When the unit fails, the repair cost is observed and a decision is made whether to replace the unit or repair it. We assume that the repair is minimal, i.e., the unit is restored to its functioning condition just prior to failure, without changing its age. The unit can be preventively replaced at any time. The problem is formulated as a continuous time decision problem and reduced to an optimal stopping problem in discrete time by applying results from the thoery of jump processes. The existence of the optimal policy is proved and its structure is found using semimartingale decomposition and λ-maximization technique. It is shown that the optimal policy is an age replacement, repair-cost-limit policy, and the optimal preventive replacement time and the repair cost limits can be obtained by solving a system of ordinary differential equations with boundary conditions.
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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 | 0.001 | 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) | 0.001 | 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