Inference for Two-Parameter Birnbaum–Saunders Distribution Based on Type-II Censored Data with Application to the Fatigue Life of Aluminum Coupon Cuts
Bibliographic record
Abstract
This study addresses the problem of parameter estimation and prediction for type-II censored data from the two-parameter Birnbaum–Saunders (BS) distribution. The BS distribution is commonly used in reliability analysis, particularly in modeling fatigue life. Accurate estimation and prediction are crucial in many fields where censored data frequently appear, such as material science, medical studies and industrial applications. This paper presents both frequentist and Bayesian approaches to estimate the shape and scale parameters of the BS distribution, along with the prediction of unobserved failure times. Random data are generated from the BS distribution under type-II censoring, where a pre-specified number of failures (m) is observed. The generated data are used to calculate the Maximum Likelihood Estimation (MLE) and Bayesian inference and evaluate their performances. The Bayesian method employs Markov Chain Monte Carlo (MCMC) sampling for point predictions and credible intervals. We apply the methods to both datasets generated under type-II censoring and real-world data on the fatigue life of 6061-T6 aluminum coupons. Although the results show that the two methods yield similar parameter estimates, the Bayesian approach offers more flexible and reliable prediction intervals. Extensive R codes are used to explain the practical application of these methods. Our findings confirm the advantages of Bayesian inference in handling censored data, especially when prior information is available for estimation. This work not only supports the theoretical understanding of the BS distribution under type-II censoring but also provides practical tools for analyzing real data in reliability and survival studies. Future research will discuss extensions of these methods to the multi-sample progressive censoring model with larger datasets and the integration of degradation models commonly encountered in industrial applications.
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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 | 0.014 | 0.051 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 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".