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<< Click to Display Table of Contents >> Navigation: Analysis Output > Statistical Analysis > Analysis Comparison & Assumptions |
3DCS supports Monte Carlo (Simulation), and Contributor Analysis (HLM or High, Low, Median). Each analysis method has its own Pro's and Con's. Please see the Linearity section for more information.
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Pros
•Supports both Linear and Non Linear Models
•Extensive Tolerance Distribution Support
•Extensive Statistical Outputs
•Generally Know and Accepted in Industry
Cons
•Simulation must be re-run for model tolerance updates
•Possibly longer run times than Contributor Analysis or GeoFactor Equation-Based
Prior versions of 3DCS assumed Normal distributions for all input circular tolerances (this includes the Position GD&T and Circular Tolerance primarily, but also any GD&T with a Diametrical Zone) in Geofactor Analysis. If a model had non normal distributions, the GeoFactor results may be larger than previously reported because the actual distribution variation is used in the Geofactor Analysis. The new results are an improved prediction of performance and should more closely match any comparison to common practices used in 1D stacks to simulate non-normal distributions.
Pros
•Implicit Linear Model Assumption. Comparative results for non linear models
•Provides contribution to variance for each toleranced point or feature
Cons
•Contributor Analysis must be re-run for model tolerance updates
•Tolerance Distribution is assumed normal along a vector
1.A measurement is a Linear function of the tolerances in the model. The next three assumptions are implied by this one.
2.The measurement has an active direction vector.
3.There is no conditional logic or iterative logic in the model which affects the measurement.
4.There is no interaction between tolerances which affects the measurement.
5.The value of any input is independent of all other inputs.
6.No distributions are truncated.
7.Tolerances are small compared to the dimensions of the parts.
It can be shown that the variance of any Measure Mj is
1. Var(Mj ) = σM2 = GF1 σ12 + GF2 σ22+ GF3 σ32 + ….+ GFn σn2
2. α*σ(Mj) = α*( GF1 σ12 + GF2 σ22+ GF3 σ32 + ….+ GFn σn2 )0.5
where σi are the standard deviation of the relevant input tolerances.
These equations are true regardless of the distribution of the input variables (tolerances).
3DCS calculates the variance of each output using the assigned distribution of each input tolerance using equation 1.
A linear combination of random variables converges to a Normal distribution by the Central Limit Theorem.
The output of Geofactor analysis is assumed to be normal (given the Central Limit Theorem). Therefore the range of the Geofactor Output is
6*σ(Mj) = 6*( GF1 σ12 + GF2 σ22+ GF3 σ32 + ….+ GFn σn2 )0.5
And is predicted to include 99.73% of the population. Note: This can be customized to a different σ level if desired (i.e. ±2σ or ±4σ).
The contribution of a circular tolerance is the sum of its local x and y component contributions, independent of the orientation of the local (x, y) system. With these assumptions it is unnecessary to evaluate the measures with the tolerances set to any values other than the high and low in each of the x and y directions.
Both the HLM and GeoFactor analyses include calculations to capture the effects of size tolerance. Size tolerance ranges are included in the calculations for circular tolerance set to MMC, Feature Position tolerances set to MMC, GD&T callouts set to MMC, and hole-pin floating contributions.
In both HLM and GeoFactor analysis, when a tolerance is in Group mode, it is analyzed as a single contributor. When a tolerance is in Independent mode, each point or feature or CAD-point (the intersection of the mesh) in the tolerance is analyzed as a separate contributor, depending on the preferences.