Time-Variant Reliability for Systems with Non-monotonic Limit-State Functions
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Bibliographic record
Abstract
Most engineering time-variant reliability problems are the result of component degradation and stochastic loading. The resultant failure modes, and their resultant limit-state functions, produce limit-state surfaces with unpredictable temporal trajectories that may exhibit a combination of increasing and decreasing failure probabilities. In many cases the trajectories are monotonic so that failure increases predictably: in other cases, this is not so. In this paper we present the discrete-time set theory derivation for non-monotonic situations wherein the limit-state surface may recede to provide, what only appears to be, ever decreasing failure probability. The presence of both monotonic and non-monotonic limit-state functions can be easily detected by a parametric polar plot of the most-likely failure points in standard normal space. The polar plot reveals the temporal limit-state surfaces that need to be retained to represent the system limit-state surfaces at any time instant. The minimum set herein is called the extreme limit-state surface. The impact of the work is that the cumulative distribution function (cdf) can be provided with a minimum of failure and safe events. This in turn gives rise to several solution options such as the multi-normal integral method or a special Monte Carlo simulation that obviates the tedious marching-out routine. A series system and a parallel system show the efficacy of the theory.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.011 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it