Trend analysis of the power law process with censored data
Bibliographic record
Abstract
In this paper we assume that the failures of a system follow a non-homogenous Poisson process (NHPP) with a power law intensity function. NHPP is a model commonly used to describe a system with minimal repairs. In many situations, such as hidden failures, failure times of a system are subject to censoring. Current trend analysis methods in the literature for NHPP consider only right censoring and do not address recurrent failure data with left or interval censoring and periodic or non-periodic inspections. We use the likelihood ratio test to check for trend in the failure data. We use the EM algorithm and a recursive method to calculate the likelihood for estimating the parameters of the power law process in the case of null and alternative hypotheses (no trend and trend assumptions). As an example, the proposed method is applied to the failures of a medical infusion pump. It was found that the likelihood ratio test and the proposed recursive method can be applied successfully to censored data, although the method may be computationally intensive for larger datasets. We also compared the likelihood method to an ad-hoc method using the mid points of censoring intervals instead of unknown failure times. The comparison showed that using the midpoints is not reliable and may result in incorrect conclusion about the trend. The proposed method can be applied to other repairable systems used in industry.
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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 | 0.009 | 0.042 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".