Reliability estimation in a Weibull lifetime distribution with zero‐failure field data
Bibliographic record
Abstract
Abstract The estimation of product reliability has attracted worldwide attention during the past several decades. The estimation procedure usually begins with parameter estimation based on test data. When there is no failure occurring in tests, traditional approaches like Maximum Likelihood Estimation (MLE) cannot be applied to estimate parameters. When product lifetime follows a Weibull distribution, to cope with this problem, we propose the modified MLE (MMLE) for estimating the parameters, based on the zero‐failure data. In this paper, we also consider the prior reliability estimate from a similar product and make use of it by incorporating it with the MMLE to construct the shrinkage preliminary test estimator (SPTE). We present the calculation method of the shrinkage factor in the SPTE, by referring to the comparison of critical quality characteristics related to product reliability, between the current batch of products and the similar (or earlier version) batch of products. Restrictions for the shrinkage factor to ensure the performance of SPTE are also discussed. The example demonstrates that the proposed SPTE of the product reliability is an effective methodology to estimate the product reliability and improve the estimation performance of the MMLE, when only zero‐failure data are available. Copyright © 2010 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 | 0.007 | 0.022 |
| 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 | 0.000 | 0.001 |
| 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".