Example of Analyze Taguchi Design (Static)

An engineer for a golf equipment manufacturer wants to design a new golf ball to maximize ball flight distance. The engineer has identified four control factors (core material, core diameter, number of dimples, and cover thickness) and one noise factor (type of golf club). Each control factor has 2 levels. The noise factor is two types of golf clubs: driver and a 5-iron. The engineer measures flight distance for each club type, and records the data in two noise factor columns in the worksheet.

Because the goal of the experiment is to maximize flight distance, the engineer uses the larger-is-better signal-to-noise ratio (S/N). The engineer also wants to test the interaction between core material and core diameter.

  1. Open the sample data, GolfBall.MTW.
  2. Choose Stat > DOE > Taguchi > Analyze Taguchi Design.
  3. In Response data are in, enter Driver and Iron.
  4. Click Analysis.
  5. Under Fit linear model for, check Signal to Noise ratios and Means. Click OK.
  6. Click Terms.
  7. Move terms A: Material, B: Diameter, C: Dimples, D: Thickness, and AB from Available Terms to Selected Terms. Click OK.
  8. Click Options.
  9. Under Signal to Noise Ratio, select Larger is better. Click OK.
  10. Click Analysis Graphs, then select Four in one.
  11. Click OK in each dialog box.

Interpret the results

Minitab provides an estimated regression coefficients table for each response characteristic that you select. In this example, the engineer chose two response characteristics — the signal-to-noise ratio (S/N) and the means. Use the p-values to determine which factors are statistically significant and use the coefficients to determine each factor's relative importance in the model.

In this example, for S/N ratios, all the factors have a p-value less than 0.05 and are statistically significant at a significance level of 0.05. Frequently, a significance level of 0.10 is used for evaluating terms in a model. The interaction is statistically significant at a significance level of 0.10. For means, core material (p = 0.045) and core diameter (p = 0.024) are statistically significant at a significance level of 0.05, and the interaction of material with diameter (p = 0.06) is statistically significant at a significance level of 0.10. However, because both factors are involved in the interaction, you need to understand the interaction before you can consider the effect of each factor individually.

The absolute value of the coefficient indicates the relative strength of each factor. The factor with the largest coefficient has the largest impact on a given response characteristic. In Taguchi designs, the magnitude of the factor coefficient usually mirrors the factor ranks in the response tables.

The response tables show the average of each response characteristic for each level of each factor. The tables include ranks based on Delta statistics, which compare the relative magnitude of effects. The Delta statistic is the highest minus the lowest average for each factor. Minitab assigns ranks based on Delta values; rank 1 to the highest Delta value, rank 2 to the second highest, and so on. Use the level averages in the response tables to determine which level of each factor provides the best result.

In Taguchi experiments, you always want to maximize the S/N ratio. In this example, the ranks indicate that core diameter (B) has the most influence on both the S/N ratio and the mean. For S/N ratio, cover thickness (D) has the next largest influence, followed by core material (A) and dimples (C). For means, core material (A) has the next largest influence, followed by dimples (C) and cover thickness (D).

For this example, because the goal is to increase ball flight distance, the engineer wants the factor levels that produce the highest mean. The levels averages in the response tables show that the S/N ratios and the means are maximized at the Level 1 value for each factor, which corresponds with the following factor settings:
  • Liquid core (A)
  • Core diameter (B) = 118
  • Dimples (C) = 392
  • Cover thickness (D) = 0.06
The main effects plots and the interaction plots confirm these results. The interaction plots show that, with the liquid core, the flight distance is maximized when the core diameter is 118.

To continue this analysis, the engineer can use Predict Taguchi Results to determine the predicted S/N ratios and means at these factor settings. For more information, go to Example of Predict Taguchi Results

Linear Model Analysis: SN ratios versus Material, Diameter, Dimples, Thickness

Estimated Model Coefficients for SN ratios Term Coef SE Coef T P Constant 38.181 0.4523 84.418 0.000 Material Liquid 3.436 0.4523 7.596 0.017 Diameter 118 3.967 0.4523 8.772 0.013 Dimples 392 2.982 0.4523 6.593 0.022 Thicknes 0.03 -3.479 0.4523 -7.692 0.016 Material*Diameter Liquid 118 1.640 0.4523 3.625 0.068
Model Summary S R-Sq R-Sq(adj) 1.2793 99.21% 97.23%
Analysis of Variance for SN ratios Source DF Seq SS Adj SS Adj MS F P Material 1 94.427 94.427 94.427 57.70 0.017 Diameter 1 125.917 125.917 125.917 76.94 0.013 Dimples 1 71.133 71.133 71.133 43.47 0.022 Thickness 1 96.828 96.828 96.828 59.17 0.016 Material*Diameter 1 21.504 21.504 21.504 13.14 0.068 Residual Error 2 3.273 3.273 1.637 Total 7 413.083

Linear Model Analysis: Means versus Material, Diameter, Dimples, Thickness

Estimated Model Coefficients for Means Term Coef SE Coef T P Constant 110.40 8.098 13.634 0.005 Material Liquid 36.86 8.098 4.552 0.045 Diameter 118 51.30 8.098 6.335 0.024 Dimples 392 23.25 8.098 2.871 0.103 Thicknes 0.03 -22.84 8.098 -2.820 0.106 Material*Diameter Liquid 118 31.61 8.098 3.904 0.060
Model Summary S R-Sq R-Sq(adj) 22.9035 97.88% 92.58%
Analysis of Variance for Means Source DF Seq SS Adj SS Adj MS F P Material 1 10871 10871 10870.8 20.72 0.045 Diameter 1 21054 21054 21053.5 40.13 0.024 Dimples 1 4325 4325 4324.5 8.24 0.103 Thickness 1 4172 4172 4172.4 7.95 0.106 Material*Diameter 1 7995 7995 7994.8 15.24 0.060 Residual Error 2 1049 1049 524.6 Total 7 49465
Response Table for Signal to Noise Ratios Larger is better Level Material Diameter Dimples Thickness 1 41.62 42.15 41.16 34.70 2 34.75 34.21 35.20 41.66 Delta 6.87 7.93 5.96 6.96 Rank 3 1 4 2
Response Table for Means Level Material Diameter Dimples Thickness 1 147.26 161.70 133.65 87.56 2 73.54 59.10 87.15 133.24 Delta 73.73 102.60 46.50 45.68 Rank 2 1 3 4
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