Optimal Inspection Interval for a Two-Component System with Failure Dependency
Bibliographic record
Abstract
In this paper, optimization of periodic inspection interval for a twocomponent system with failure dependency is presented. Failure of the first component is soft, namely, it does not cause the system stop, but it increases the system operating costs. The second component’s failure is hard, i.e. as soon as it occurs, the system stops operating. Any failure of the second component increases the first component’s failure rate. Failure of the first component is only detected if inspection is performed. Thus, the first component is periodically inspected and if found failed, it is perfectly repaired and it is restored to as good as new. Failure of the second component is detected as soon as it occurs. Since this failure causes the system stop, it is immediately replaced. It is assumed that the time for replacement or repaired is negligible. We model the first component’s failure as a non-homogeneous Poisson process (NHPP) with increasing failure rate and the second component’s failure as a homogeneous Poisson process (HPP) with constant failure rate. The objective is to find the optimal inspection interval for the first component such that the expected total cost per unit time is minimized. A simplified numerical example along with sensitivity analysis on cost parameters is given.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".