Rubber Tire Study: Taguchi Experiments for Wear Resistance Optimization
This case study explores Taguchi experiments to minimize variance in a rubber tire study. Learn how factors like filler type, rubber quality, and pre-treatment method affect wear resistance. Understand the significance of each factor and how to optimize both mean response and variance. Discover Taguchi's contributions, weaknesses, and the debate surrounding his methods.
Rubber Tire Study: Taguchi Experiments for Wear Resistance Optimization
E N D
Presentation Transcript
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.
