Extended preventive replacement policy for a two-unit system subject to damage shocks
Bibliographic record
Abstract
We consider a system consisting of two units (A and B), which is subject to two types of shocks (I and II) that occur according to a non-homogeneous Poisson process. The probabilities of these two shock types are age-dependent. Each type-I shock causes a minor failure of unit A, which can be corrected by a minimal repair. Meanwhile, this type of shock results in a certain amount of damage to unit B. These damages to unit B are accumulated to trigger a preventive replacement (PM) or a corrective replacement (CM) action. In addition, a minor failure for unit B with the cumulative damage of z will occur with probability at a type-I shock instant. Type-II shock is a major one that causes system replacement. We consider a two-dimensional PM policy, which prescribes that the system is preventively replaced at age T, or at the time when the total damage to unit B exceeds a prespecified level Z (but less than the failure level K where K > Z) or is replaced correctively at first type-II shock or when the total damage to unit B exceeds a failure level K, whichever occurs first. Thus, both PM and CM actions may be performed in our model. To minimise the expected cost per unit time, the optimal policy (, ) is derived analytically and determined numerically. We also show that our model is a generalisation of many previous maintenance models in the literature.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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".