1. Stat 321 A Taguchi Case Study Experiments to Minimize Variance

2. Rubber Tire Study with Inner and Outer Arrays Include environmental variables as noise factors in the replicates - the outer array Include our usual control factors as the inner array

3. 8-trial, full factorial Factor A - Type of filler Factor B - Quality of Rubber Factor C - Method of pre-treatment Outer Array Factor V - Air pressure Outer Array Factor W - Ambient temperature Response is wear resistance

4. See the design matrix Note the factorial in V and W factors in each row of the main design.

5. Analysis of responses Y-bar= ave of 4 results per trial (row) Y-bar is analyzed to optimize the mean response log s= natural log of row standard deviation Log s is analyzed to minimize the variance.

6. Analysis of significant factors for variance Factor C is significant for standard deviation, as is the BxC interaction (demonstrated by the normal plot). High level of Rubber (B) with low level of Pre-Treatment (C) gives the best standard deviation

7. Analysis of significant factors for mean response Filler Type (A) and Rubber Quality (B) have significant effect on wear resistance, by F-tests (not clear on normal plot). These F-tests are conservative - less likely to see effects as significant. Why? Wear resistance is maximized with low Filler Type and high Rubber Quality.

8. Conclusions from experiment Settings at low for Filler Type (A), high for Rubber Quality (B), and low for Pre- Treatment (C) maximize wear resistance and minimize variability. When settings to optimize mean response and variance conflict, trade- offs must be made.

9. The Good and Bad of Taguchi The Great Debate of 1985-1992 "The Ten Top Triumphs and Tragedies of Taguchi."

10. Taguchi’s contributions The quality loss function - poor quality is a cost to society Focus on minimizing variance (outer array method) Robustness designed in to counteract environmental and component variation Rebirth of factorial experimentation - from agriculture to engineering

11. Taguchi’s weaknesses Signal-to-noise ratios don't separate the signal and the noise. 3-level factors as a default waste experiment trials. Interactions are assumed to be known ahead of experimentation. Pick-the-winner analysis ignores statistical significance.