Example of Analyze Taguchi Design (Dynamic)

An agricultural engineer studies the effect of five factors on the growth of basil plants. The engineer designs a 2-level Taguchi experiment to determine which factor settings increase the plant's rate of growth without increasing the variability in growth. The engineer also manipulates two noise factors to determine which settings for the five factors increase plant growth across the true range of temperature and humidity conditions.

The engineer creates a dynamic design with a signal factor, Time, which is the amount of growth time at 4 levels (3, 5, 7, and 9). The engineer collects and records the data into four columns of the worksheet.

  1. Open the sample data, BasilGrowth.MTW.
  2. Choose Stat > DOE > Taguchi > Analyze Taguchi Design.
  3. In Response data are in, enter T1H1, T1H2, T2H1, and T2H2.
  4. Click Graphs, then under Generate plots of main effects and interactions in the model for select Standard deviations. Click OK.
  5. Click Analysis.
  6. Under Display response tables for, check all options. Under Fit linear model for, check all options. Click OK.
  7. Click Terms.
  8. Move terms A: Variety, B: Light, C: Fertilizer, D: Water, E: Spraying, and AC from Available Terms to Selected Terms. Click OK.
  9. Click Options.
  10. Under Dynamic signal-to-noise ratio, select Fit all lines through a fixed reference point.
  11. Click OK in each dialog box.

Interpret the results

Minitab provides an estimated regression coefficients table for each response characteristic that you select. 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, Fertilizer has a p-value less than 0.05 (p = 0.033) and is statistically significant at a significance level of 0.05. Variety is statistically significant at a significance level of 0.10 (p = 0.064). For the slopes, none of the factors are statistically significant at a significance level of 0.05 or 0.10. For the standard deviations, the p-values indicate that Variety (p = 0.050) is statistically significant at the 0.05 significance level. Fertilizer (p = 0.054), Water (p = 0.057), and Light (p = 0.070) are statistically significant at the 0.10 significance level. Spraying (p = 0.300) and the interaction, Fertilizer*Variety (p = 0.169) are not statistically significant.

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 dynamic Taguchi experiments, you always want to maximize the S/N ratio. In this example, the ranks indicate that Fertilizer has the most influence on both the S/N ratio and the slope. For S/N ratio, Variety has the next largest influence, followed by Water, Light, and Spraying. For slopes, Water has the next largest influence, followed by Light, Variety, and Spraying. For the standard deviations, the ranks are Variety, Fertilizer, Water, Light, and Spraying.

For this example, the engineer wants the factor levels that minimize the standard deviation and maximize the S/N ratio and the slope. The level averages in the response tables show that the S/N ratios and the slopes were maximized using these levels:
  • Variety, Level 2
  • Fertilizer, Level 2
  • Spraying, Level 2
  • There is not a consensus on the best levels for Light and Water, because S/N and slopes are maximized at level 2, but standard deviations are minimized at level 1.
    Note

    For more information on how the engineer resolved the Light and Water settings, go to Example of Predict Taguchi Results

The main effects plots and the interaction plots confirm these results.

Linear Model Analysis: SN ratios versus Variety, Light, Fertilizer, Water, ...

Estimated Model Coefficients for SN ratios Term Coef SE Coef T P Constant 0.4401 0.2384 1.846 0.316 Variety 1 -2.3667 0.2384 -9.926 0.064 Light 1 -1.1312 0.2384 -4.744 0.132 Fertiliz 1 -4.5800 0.2384 -19.209 0.033 Water 1 -1.4271 0.2384 -5.985 0.105 Spraying 1 -0.2127 0.2384 -0.892 0.536 Variety*Fertiliz 1 1 -0.6041 0.2384 -2.534 0.239
Model Summary S R-Sq R-Sq(adj) 0.6744 99.81% 98.69%
Analysis of Variance for SN ratios Source DF Seq SS Adj SS Adj MS F P Variety 1 44.809 44.809 44.809 98.52 0.064 Light 1 10.236 10.236 10.236 22.51 0.132 Fertilizer 1 167.811 167.811 167.811 368.97 0.033 Water 1 16.293 16.293 16.293 35.82 0.105 Spraying 1 0.362 0.362 0.362 0.80 0.536 Variety*Fertilizer 1 2.920 2.920 2.920 6.42 0.239 Residual Error 1 0.455 0.455 0.455 Total 7 242.886

Linear Model Analysis: Slopes versus Variety, Light, Fertilizer, Water, ...

Estimated Model Coefficients for Slopes Term Coef SE Coef T P Constant 0.715353 0.03796 18.846 0.034 Variety 1 -0.028617 0.03796 -0.754 0.589 Light 1 -0.111020 0.03796 -2.925 0.210 Fertiliz 1 -0.188904 0.03796 -4.977 0.126 Water 1 -0.171643 0.03796 -4.522 0.139 Spraying 1 -0.008684 0.03796 -0.229 0.857 Variety*Fertiliz 1 1 -0.020446 0.03796 -0.539 0.685
Model Summary S R-Sq R-Sq(adj) 0.1074 98.20% 87.43%
Analysis of Variance for Slopes Source DF Seq SS Adj SS Adj MS F P Variety 1 0.006551 0.006551 0.006551 0.57 0.589 Light 1 0.098603 0.098603 0.098603 8.55 0.210 Fertilizer 1 0.285477 0.285477 0.285477 24.77 0.126 Water 1 0.235690 0.235690 0.235690 20.45 0.139 Spraying 1 0.000603 0.000603 0.000603 0.05 0.857 Variety*Fertilizer 1 0.003344 0.003344 0.003344 0.29 0.685 Residual Error 1 0.011527 0.011527 0.011527 Total 7 0.641795

Linear Model Analysis: StDevs versus Variety, Light, Fertilizer, Water, ...

Estimated Model Coefficients for StDevs Term Coef SE Coef T P Constant 0.64182 0.01075 59.697 0.011 Variety 1 0.13761 0.01075 12.799 0.050 Light 1 -0.09685 0.01075 -9.008 0.070 Fertiliz 1 0.12592 0.01075 11.712 0.054 Water 1 -0.11961 0.01075 -11.125 0.057 Spraying 1 -0.02108 0.01075 -1.961 0.300 Variety*Fertiliz 1 1 0.03966 0.01075 3.689 0.169
Model Summary S R-Sq R-Sq(adj) 0.0304 99.81% 98.67%
Analysis of Variance for StDevs Source DF Seq SS Adj SS Adj MS F P Variety 1 0.151490 0.151490 0.151490 163.82 0.050 Light 1 0.075040 0.075040 0.075040 81.15 0.070 Fertilizer 1 0.126845 0.126845 0.126845 137.17 0.054 Water 1 0.114456 0.114456 0.114456 123.77 0.057 Spraying 1 0.003556 0.003556 0.003556 3.85 0.300 Variety*Fertilizer 1 0.012581 0.012581 0.012581 13.61 0.169 Residual Error 1 0.000925 0.000925 0.000925 Total 7 0.484893
Response Table for Signal to Noise Ratios Dynamic Response Level Variety Light Fertilizer Water Spraying 1 -1.9266 -0.6911 -4.1399 -0.9870 0.2274 2 2.8068 1.5712 5.0201 1.8672 0.6527 Delta 4.7333 2.2623 9.1600 2.8542 0.4253 Rank 2 4 1 3 5
Response Table for Slopes Level Variety Light Fertilizer Water Spraying 1 0.6867 0.6043 0.5264 0.5437 0.7067 2 0.7440 0.8264 0.9043 0.8870 0.7240 Delta 0.0572 0.2220 0.3778 0.3433 0.0174 Rank 4 3 1 2 5
Response Table for Standard Deviations Level Variety Light Fertilizer Water Spraying 1 0.7794 0.5450 0.7677 0.5222 0.6207 2 0.5042 0.7387 0.5159 0.7614 0.6629 Delta 0.2752 0.1937 0.2518 0.2392 0.0422 Rank 1 4 2 3 5
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