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Stat 321 A Taguchi Case Study Experiments to Minimize Variance

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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

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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

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

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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.

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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

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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.

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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.

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

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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

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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.

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