James J. Filliben
Statistical Engineering Division, ITL
Green Tweed Corporation
Mansfield attended SED's experiment design for industry 5-day course: Improving Product and Process Quality Using Experiment Design given by Eric Lagergren, Lisa Gill, and James Filliben on December 1 5, 1997 at NIST. Green-Tweed Corporation is a semiconductor-related company in Pennsylvania. The goal of Mansfield's project was to develop stronger bond strengths in certain semiconductor components. Mansfield had 8 factors under investigation: 1. cleaning agent; 2. surface roughness; 3. pre-heat time; 4. blast-to-glue time; 5. glue dilution; 6. glue-to-mold time; 7. molding condition; and 8. protection coat.
Based on the course, and the in-class consultation that was part of the course, Corinne had constructed an 8-factor, 16-run, 2-level fractional factorial design which is an excellent, efficient design for her problem. Because of certain complexities in the 8-factor design that was actually run (she chose the non-Yates order design on page 402 of Box, Hunter, & Hunter: Statistics for Experimenters), Corinne was a bit unsure as to the validity and completeness of the conclusions from her analysis.
After making adjustments for the non-Yates confounding structure of her design, we ran a routine re-analysis of her experiment. Her conclusions were reaffirmed in some cases and augmented in others. With respect to the desired increase in bond strength, the important factors were ferreted out, best settings which will yield consistently higher bond strengths were identified, and an empirical model involving the dominant factors and interactions was constructed.
The attached graphic illustates one of the more important
analysis techniques for 2-level factorial designs: an
interactions effect matrix. To protect the proprietary nature of
this industrial experiment, we have scrambled the 8 factors
and coded them on the plot.
Figure 21: This interaction effects plot matrix shows main effects along the diagonal and 2-term interactions off-diagonal. Among the main effects, note the relative importance of factor 6. Among the 2-term interactions, note the intrinsic confounding structure for this 2**(8-4) as revealed by equivalent off-diagonal plots (e.g., the 1-2, 3-7, 5-6, and 4-8 interactions, and the probable reality of the 5-6 interaction.
Date created: 7/20/2001