Interpret the key results for Predict Taguchi Results

Complete the following steps to interpret a Taguchi design. Key output includes the fitted values and the factor levels.

In This Topic

Step 1: Examine the predicted values
Step 2: Use the predicted values to determine the best factor settings
Step 3: Perform confirmation runs

Step 1: Examine the predicted values

The predicted values show the fitted values of selected characteristics at the specified factor settings. The fitted values are based on the model that you specified.

If there are minimal interactions between the factors or if the interactions are correctly accounted for by the predictions, the observed results from the follow-up confirmation runs should be similar to the predicted results. On the other hand, if there is substantial disagreement between the predicted and the observed results, then there may be unaccounted for interactions or unforeseen noise effects. This suggests that more investigation is necessary.

In this example, Minitab displays the predicted values for the signal-to-noise ratio, slope, standard deviation, and the natural logarithm of the standard deviation. There are four predicted values for each characteristic, which correspond to the four combinations of factor levels that the experimenters selected. Each row of the predicted values corresponds to a row of factor levels. For example, the first predicted values row corresponds to the first factor level row, and so on.

Predicted values

Prediction

S/N Ratio	Slope	StDev	Ln(StDev)
4.82849	0.65021	0.161827	-1.20846
7.68268	0.99350	0.401050	-0.87014
7.09082	0.87225	0.355527	-0.93760
9.94501	1.21554	0.594751	-0.59928

Settings

Variety	Light	Fertilizer	Water
2	1	2	1
2	1	2	2
2	2	2	1
2	2	2	2

Key Results: S/N Ratio, Slope, StDev, Ln(StDev)

The second row of predicted values shows the predictions for high level (2) of Variety, low level (1) of Light, high level (2) of Fertilizer, and high level (2) of Water:

S/N ratio = 7.68268
Slope = 0.99350
Standard deviation = 0.401050
Natural log of standard deviation = −0.87014

Step 2: Use the predicted values to determine the best factor settings

Use the predicted values to determine which factor settings lead to the best result for your product or process.

The goal of the typical robust parameter design study is to determine the factor settings that will minimize the variability of the response about some ideal target value (or target function in the case of a dynamic response experiment). Taguchi methods accomplish this by a two-step optimization process. The first step is to minimize variability, and the second step is to achieve the target.

First, set all factors that have a substantial effect on the signal-to-noise ratio at the level where the signal-to-noise is maximized.
Then, adjust the level of one or more factors that substantially affect the mean (or slope) but not the signal-to-noise to put the response on target.

An alternative approach is to start by minimizing the standard deviation and then adjust a factor that affects the mean but does not affect the standard deviation.

In this example, the goal is to determine which factor settings increase the slope (basil plant growth rate), without introducing an excessive amount of variability. The experimenters considered the first value in the predicted slope column, 0.65021, to be too low. They considered the other three slopes to be high enough. Next, the experimenters wanted to determine which factor setting offer the best combination of high growth rate and low variability.

When considering signal-to-noise ratios as a measure of variability, higher S/N ratios correspond to lower levels of variability. The fourth combination seems to be best at 9.94501.
When considering standard deviation as a measure of variability, lower standard deviations correspond to lower levels of variability. The second and third combinations (0.401050 and 0.355527) are approximately equivalent and considerably better than the fourth combination (0.594751). There is not much difference in the standard deviation between the second and third configurations, but the slope and S/N are better for the second configuration.

The experimenters narrowed the choices to the second and fourth combinations. Both have Variety 2, Fertilizer 2, and Water 2. The only difference is in the level of Light. The experimenters ultimately chose the second combination because the standard deviation is substantially less for that combination and because lower light levels substantially reduce expenses.

Predicted values

Prediction

S/N Ratio	Slope	StDev	Ln(StDev)
4.82849	0.65021	0.161827	-1.20846
7.68268	0.99350	0.401050	-0.87014
7.09082	0.87225	0.355527	-0.93760
9.94501	1.21554	0.594751	-0.59928

Settings

Variety	Light	Fertilizer	Water
2	1	2	1
2	1	2	2
2	2	2	1
2	2	2	2

Key Results: Predicted Values, Settings

The fourth combination for the S/N seems to be best at 9.94501. There is very little difference in the standard deviation between the second and third configurations, but the slope and S/N are better for the second configuration.

Step 3: Perform confirmation runs

You should perform confirmations runs at the selected levels to confirm that the predicted values are reliable. For the basil data, the selected levels were used in the original experiment, so the experimenters first verified the predictions against the observations from the original experiment. The original results agree quite closely with the predicted values, as shown in the table below.

	Original	Predicted
S/N	7.10	7.68268
Slope	0.926	0.99350
StDev	0.409	0.401050
LnStDev	−0.894	−0.87014