Minimizing Cost of Multiple Response Systems by Probabilistic Robust Design
Bibliographic record
Abstract
In the design of products and processes, a methodology that helps adjust the means and tolerances of the design variables to both improve conformance and lower costs is a valuable tool. In this paper, the cost of a product at the manufacturing stage is the sum of the production cost, which includes known costs for tolerances, inspection, and so forth, plus any cost for scrapping or reworking products that do not conform to specifications. We call this added cost the so-called loss-of-quality cost and evaluate it as the probability of nonconformance (of the responses) times established scrap or rework costs. Accurate probability estimates are obtained using full distributions, limit-state functions, and first-order reliability methods (FORM). Probabilities are adjusted through probabilistic robust design. The production costs and the loss-of-quality cost are competing costs and thus their sum provides a single objective function in terms of the means and tolerances of the design variables. The need to satisfy the equations in both the product model and the workings of FORM introduce nonlinear equality constraints. The minimum of the objective function, hence the minimum cost, is obtained by solving a nonlinear, constrained, optimization problem. The design of a mechanism for controlling a grating diffraction spectroscope serves as a case study using the presented method. A minimum cost, the probability of conformance, and the respective parameter settings are found for both complete and zero inspection strategies.
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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 | 0.007 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.002 | 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".