Stress-strength reliability under partially accelerated life testing using Weibull model
Bibliographic record
Abstract
The reliability of a system is the probability that its strength exceeds its stress. This reliability is called as the stress-strength reliability. The inferences of the stress-strength reliability R=P(X>Y), when: (1) the strength (X) and stress (Y) are independent random variables follow one-parameter exponential distributions; and (2) the strength variable is subjected to the step-stress partially accelerated life test (SSPALT) are discussed recently. Exponential distribution has limitation to describe the strength and stress due to its constant failure rate. In this paper, we consider the estimate of R, when: (1) X and Y are independent random variables that follow two-parameter Weibull distributions; and (2) the strength variable X is subjected to the SSPALT. The maximum likelihood estimator of R and its asymptotic distribution are not obtained analytically and therefore the asymptotic confidence interval of R is discussed. A real data set is analyzed using the proposed model for illustrative and comparison purposes. Based on the numerical results, we would conclude that the exponential distribution is rejected to fit the strength and stress, at any significant level that is greater than or equal to 2.58%, against the Weibull model.
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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 | 0.002 | 0.007 |
| 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".