Gamma distribution parameter estimation for field reliability data with missing failure times
Bibliographic record
Abstract
Maximum likelihood estimators have been developed for the gamma distribution when there is missing time-to-failure information. Data sets with missing time-to-failure data can arise from field data collection systems that rely on recorded observations of the system by the operators and maintenance personnel. In many regards, this type of data is highly desirable because it implicitly accounts for all actual usage and environmental stresses. Unfortunately the component times-to-failure are not always recorded for fielded systems because of a lack of elapsed time meters, unsatisfactory data reporting requirements, or incomplete or lost information. When only data of this type is available, it creates a non-standard form of da'ta censoring and it has generally not been possible to fit most common time-to-failure distributions. Reliability practitioners have sometimes made unsubstantiated simplifying assumptions so the data can be used. In this paper, a more rigorous approach is presented. Maximum likelihood estimators are derived and demonstrated for the gamma distribution based on merged data records where the individual failure times have not been recorded. These results are important because the gamma distribution can model diverse time-to-failure behavior. This provides a particularly useful tool for data sets that may otherwise not be satisfactorily analyzed.
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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 | 0.015 | 0.065 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".