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Taguchi Innovations

Genichi Taguchi is a noted champion of reducing variation through DOE. Some of his innovations are the testing of "noise" arrays and the use of "signal to noise" ratios to determine optimum settings for robustness.

For example, a Taguchi approach to the experiment described in Table 1 might have extended it to include an "inner array" of the controllable factors tested and an "outer array" of uncontrollable ("noise") factors such as board size and number of layers. Assuming a high and low value was determined for each of these factors and including the results of Table 1 as a nominal setting for these factors, we might obtain the results shown in Table 2.

Table 2
 Controllable Variations Uncontrolled Variations Size: Layers: Test Temp. Length L/T ratio N L H L H N L L H H 1 N N N 1.5 2.9 1.9 2.4 2.6 2 L L L 3.2 9.0 1.8 1.6 7.8 3 H L L 3.1 2.6 2.0 2.3 4.8 4 L H L 1.9 2.4 1.6 1.5 2.9 5 H H L 2.4 2.2 1.5 1.7 1.9 6 L L H 1.6 2.4 1.6 1.5 2.9 7 H L H 1.6 1.9 1.7 1.7 1.8 8 L H H 3.3 3.3 1.6 1.6 3.3 9 H H H 2.2 2.6 1.8 1.6 1.9

The optimum solution shown in Table 1 does not appear bestinTable2. The settings of the controllable factors for other tests (e.g., 5, 6 and 7) give better results across the spectrum of the uncontrolled variations (i.e., more robustness).

Another Taguchi technique is to measure the experiment results in terms which consider both the measured values and their variations. These are called "signal to noise" ratios and stem from another Taguchi invention, called "loss functions." There are loss functions for "smaller is better" (e.g., defects), "nominal is better" (e.g., dimensions of a mechanical part), and "larger is better" (e.g., tensile strength). Each assumes that loss increases with the square of the distance a parameter is from its target value. For the example we have been using, the signal to noise ratio based on the "smaller is better" loss function is:

Combining the experimental results shown in Table 2 into signal to noise ratios, yields Table 3, which indicates that the settings of test number 7 create the most robust design.

Not all statisticians endorse Taguchi's procedures, but they are widely used. Taguchi is affiliated with the American Suppliers Institute (ASI), Allen Park MI, which has registered the term "Taguchi Methods" as a trademark. Taguchi's book, Introduction to Quality Engineering: Designing Quality into Products and Processes, is available from ASI.

Table 3
Test Temp Length L/T Ratio S/N
1 N N N -3.54
2 L L L -6.70
3 H L L -4.71
4 L H L -3.61
5 H H L -2.45
6 L L H -2.83
7 H L H -2.41
8 L H H -4.18
9 H H H -3.05

Other references are:

1. Taguchi Techniques for Quality Engineering, by P.J. Ross, published in 1988 by McGraw-Hill.
2. Quality Engineering Using Robust Design, by M. S. Phadke, 1989, Prentice Hall.
3. Taguchi Methods, A Hands-on Approach, by G. S. Peace, 1993, Addison-Wesley.