Lichten Award Paper: Variational Tolerance Analysis (VTA) - Design and Manufacturing Optimization Using Statistical Simulation
Bibliographic record
Abstract
Appropriate consideration of tolerances is critical to the design and manufacture of products that meet customer requirements and defined cost targets. Tolerance analysis is most commonly conducted at the individual part or sub-assembly level utilizing basic stack-up methods (worst-case analysis) to ensure the producibility of the assembled product. A worst-case analysis assumes that each dimension in the stack-up will be manufactured on the extreme end or limit of its assigned tolerance (max or min) in such a way that all tolerances become additive. This usually results in tighter than required drawing tolerances being assigned to guarantee the product can be assembled. Modern day manufacturing processes focus on targeting the nominal dimensional value, so it is safe to assume that a higher number of parts will be produced closer to the nominal value than parts produced at the extreme end of the tolerance range. When evaluating the tolerance stack-up of a larger assembly with many parts additional tolerance analysis methods apply (Root Sum Squared, RSS), and a worst-case analysis becomes more costly and less meaningful. The RSS method of tolerance analysis takes into consideration manufacturing targets and applies normal distribution methods to assess more likely tolerance results, allowing relaxed drawing tolerances to be assigned while still maintaining a high level of confidence in a successful assembly. For analysis of complex systems or installations, tolerance studies using more sophisticated approaches to deal with variation such as Monte Carlo statistical analysis is required. Variational Tolerance Analysis (VTA) tools available today allow a typical Monte Carlo tolerance simulation to be visualized by the designer through 3-dimensional real time manufacturing simulations and sensitivity analysis. This in turn simplifies the development process and allows better identification of tolerance drivers within a large system installation; analysis of the geometric effect of tolerances within the installation; and the ability to quickly iterate the analysis to optimize designs for producibility and lower cost. In this paper, the use of VTA is assessed and quantified to form a business case for further investment by Lockheed Martin. In the course of this work, VTA has been evaluated both before and after final designs were released to manufacturing.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.026 | 0.008 |
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".