Evaluating the Reliability Function and the Mean Residual Life for Equipment With Unobservable States
Bibliographic record
Abstract
This article proposes a model to calculate the reliability function, and the mean residual (remaining) life of a piece of equipment, when its degradation state is not directly observable. At each observation moment, an indicator of the underlying unobservable degradation state is observed, and the monitoring information is collected. The observation process is due to a condition monitoring system where the obtained information is not perfect. For that reason, the observation process doesn't directly reveal the exact degradation state. To match an indicator's value to the unobservable degradation state, a stochastic relation between them is given by an observation probability matrix. It is assumed that the equipment's unobservable degradation state transition follows a Markov chain, and we model it using a hidden Markov model. The Bayes' rule is used to determine the probability of being in a certain degradation state at each observation moment. Cox's time-dependent proportional hazards model is considered to model the equipment's failure rate. This paper addresses two main problems: the problem of imperfect observations, and the problem of taking into account the whole history of observations. Two numerical examples are presented.
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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 | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".