Modeling Recurrent Failure Processes using Padé Approximants
Bibliographic record
Abstract
The practical goal of modeling the recurrent failure process of a system is to predict the expected number of failure events over time and to estimate various reliability indices (e.g., availability) of the system. Usually, the respective stochastic process is modeled by a sequence of random failure times from lifetime distributions as a function on the ordinal number of a consecutive event. Parameters of these failure time distribution functions are usually evaluated using the maximum likelihood estimation (MLE). This approach becomes more and more challenging as the number of estimated process parameters increases. The proposed approach is based on regression analysis of data obtained from a nonparametric evaluation of recurrent events. In the first step, the asymptotic formula for small failure numbers is obtained using traditional MLE considering only first failures. Then the obtained function is multiplied by the Pade (rational) function, and the regression procedure is applied to the product for the estimation of coefficients of the approximation function. The previously developed (for the case of Pade approximants) advanced method for minimizing the residual sum of squares is used. In contrast to the traditional method, it leads to a system of linear equations and therefore is not limited by the number of estimated parameters. The efficiency of the model is illustrated by several examples. Limitations of the method (which are mostly based on the accuracy of nonparametric analysis) are discussed too.
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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 | 0.001 |
| 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".