Optimizing the Periodic Inspection Interval for a 1‐out‐of‐2 Cold Standby System Using the Delay‐Time Concept
Bibliographic record
Abstract
Abstract In this article, we deal with a 1‐out‐of‐2 system with a cold‐standby component. The failure process of these two components is statistically identical and characterized by the delay‐time concept, which divides the component's life into a two‐stage process with a normal stage from new to a defect initiation point and a following failure delay stage from this point to failure. A fixed interval periodic inspection is carried out to check whether the working component is defective or not. If a defect is identified, the working component is shut down and sent to be repaired. The repair shop capacity is limited for repairing one component only. If the repair shop is occupied by the standby component (under repair) when the working one is failed, the system is shut down. There are five scenarios of the state of the system at an inspection epoch, which are derived analytically. The expected total cost per unit time of the system consists of the expected cost caused by preventive repair, unplanned failure repair, and system downtime. In this article, these three costs are determined and the optimal inspection interval with respect to the minimum of the expected total cost per unit time is found. To incorporate a nonexponential distribution for the normal time, delay stages, and repair time of the components, the elapsed time in the normal time, delay stages, and repair time at inspection is taken into consideration. A stationary distribution of the elapsed time exists, and it is calculated by an iteration method. Copyright © 2012 John Wiley & Sons, Ltd.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 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 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".