Optimal Parameter Selection for Electronic Packaging Using Sequential Computer Simulations

[+] Author and Article Information
Abhishek Gupta

Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104

Yu Ding

Department of Industrial and Systems Engineering, Texas A&M University, 3131 TAMU, College Station, TX 77843-3131

Leon Xu, Tommi Reinikainen

 Nokia Inc., 6000 Connection Drive, Irving, TX 75039

J. Manuf. Sci. Eng 128(3), 705-715 (Aug 28, 2005) (11 pages) doi:10.1115/1.2193551 History: Received December 19, 2004; Revised August 28, 2005

Optimal parameter selection is a crucial step in improving the quality of electronic packaging processes. Traditional approaches usually start with a set of physical experiments and then employ Design of Experiment (DOE) based response surface methodology (RSM) to find the parameter settings that will optimize a desired system response. Nowadays deterministic computer simulations such as Finite Element Analysis (FEA) are often used to replace physical experiments when evaluating a system response, e.g., the stress level in an electronic packaging. However, FEA simulations are usually computationally expensive due to their inherent complexity. In order to find the optimal parameters, it is not practical to use FEA simulations to calculate system responses over a large number of parameter combinations. Nor will it be effective to blindly use DOE-based response surface methodology to analyze the deterministic FEA outputs. In this paper, we will utilize a spatial statistical method (i.e., the Kriging model) for analyzing deterministic FEA outputs from an electronic packaging process. We suggest a sequential method when using the Kriging model to search for the optimal parameter values that minimize the stress level in the electronic packaging. Compared with the traditional RSM, our sequential parameter selection method entertains several advantages: it can remarkably reduce the total number of FEA simulations required for optimization, it makes the optimal solution insensitive to the choice of the initial simulation setting, and it can also depict the response surface and the associated uncertainty over the entire parameter space.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Bending process map

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Figure 2

The CSP-PWB model

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Figure 3

Difference between (a) physical and (b) computer experiments

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Figure 4

An illustration of a complicated response surface

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Figure 5

An illustration of the sequential strategy

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Figure 6

Contour plots of the response (a) and its MSE value (b)

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Figure 7

MSE plots for pairwise design variables

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Figure 8

MSE plots for pairwise design variables after the second stage

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Figure 9

Pairwise interaction plots from the second stage model

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Figure 10

Contour plots: (a) response surface, (b) MSE value for the third stage model

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Figure 11

Traditional response surface methodology for electronic packaging problem



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