Time-Variant Reliability for Systems with Non-monotonic Limit-State Functions
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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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".