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A Closed Form Solution for Nonlinear Tolerance Analysis

Geoff Carlson, Brigham Young University
Presented June 15, 2000 at the ADCATS 2000 Conference

Predicting production yields for critical assembly features is computationally intensive when skewed distributions or nonlinear assemblies are present. Current methods require iterative solutions for nonlinear implicit assembly functions. Monte Carlo Simulation (MCS) requires an iterative solution for each simulated assembly. Method of System Moments (MSM) only analyzes a single assembly, but still requires an iterative solution for each dimension in the assembly function.

The Direct 2nd Order Method is a new technique that eliminates the requirement for iterative solutions by providing the second order sensitivities in closed form. By extending the analogy between variation and kinematics, the second order sensitivities can be obtained by performing a kinematic acceleration analysis of a vector loop assembly model. Combining various terms of the acceleration analysis will yield the second order sensitivities in closed form, without iteration.

The second order sensitivities can be used in conjunction with the Method of System Moments (MSM) to calculate the statistical moments of the critical assembly features. By neglecting the components that contribute very little, the number of terms in the MSM raw moment equations can be greatly reduced. These simplified expressions provide accurate estimates of the assembly mean, variance and skewness.

Applications of the Direct 2nd Order Method and the simplified MSM raw moment equations are presented to illustrate how these tools can be used to perform nonlinear variation analysis more efficiently.

Bio:
Geoff Carlson is currently pursuing a MSME degree at Brigham Young University. He is conducting his research under Dr. Kenneth Chase in the field of Statistical Tolerance Analysis. Upon completing his degree in August 2000, Geoff will begin his engineering career working for Lexmark International in Lexington, Kentucky
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