Parameter estimation for load‐sharing system subject to Wiener degradation process using the expectation‐maximization algorithm
Bibliographic record
Abstract
Abstract In practice, many systems exhibit load‐sharing behavior, where the surviving components share the total load imposed on the system. Different from general systems, the components of load‐sharing systems are interdependent in nature, in such a way that when one component fails, the system load has to be shared by the remaining components, which increases the failure rate or degradation rate of the remaining components. Because of the load‐sharing mechanism among components, parameter estimation and reliability assessment are usually complicated for load‐sharing systems. Although load‐sharing systems with components subject to sudden failures have been intensely studied in literatures with detailed estimation and analysis approaches, those with components subject to degradation are rarely investigated. In this paper, we propose the parameter estimation method for load‐sharing systems subject to continuous degradation with a constant load. Likelihood function based on the degradation data of components is established as a first step. The maximum likelihood estimators for unknown parameters are deduced and obtained via expectation‐maximization (EM) algorithm considering the nonclosed form of the likelihood function. Numerical examples are used to illustrate the effectiveness of the proposed method.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| 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".