Stat 321 A Taguchi Case Study

Experiments to Minimize Variance

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

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

See the design matrix

Note the factorial in V and W factors in each row of

the main design.

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.

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

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.

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.

The Good and Bad of Taguchi

• The Great Debate of 1985-1992

• "The Ten Top Triumphs and Tragedies of Taguchi."

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

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.