Example of Analyze Variability

A quality engineer for a building products manufacturer is developing a new insulation product. The engineer designs a 2-level full factorial experiment to study the effects of several factors on the variability in insulation strength. While conducting the strength experiment, the engineer decides to collect extra samples to examine the effects of the factors on the variability in insulation strength. The engineer collects six repeat measurements of strength at each combination of factor settings and calculates the standard deviation of the repeats.

The engineer analyzes the variability in a factorial design to determine how material type, injection pressure, injection temperature, and cooling temperature affect the variability in the strength of the insulation.

  1. Open the sample data, InsulationStrength.MTW.
  2. Complete Example of Pre-Process Responses for Analyze Variability.
  3. Choose Stat > DOE > Factorial > Analyze Variability.
  4. In Response (standard deviations), enter Std.
  5. Click Terms.
  6. In Include terms in the model up through order, choose 2 from the drop-down list. Click OK.
  7. Click Graphs.
  8. Under Effects Plots, select Pareto.
  9. Under Residual Plots, select Three in one.
  10. Click OK in each dialog box.

Interpret the results

In the Analysis of Variance table, the p-value for the main effect for Material and the interaction Material*InjPress are significant at the α-level of 0.05. The engineer can consider reducing the model.

The R2 value shows that the model explains 97.75% of the variance in strength, which indicates that the model fits the data extremely well.

The Pareto plot of the effects allows you to visually identify the important effects and compare the relative magnitude of the various effects. In addition, you can see that the largest effect is Material*InjPress (AB) because it extends the farthest. Material*CoolTemp (AD) is the smallest because it extends the least.

The residual plots do not indicate any problems with the model.

Analysis of Variability: Std versus Material, InjPress, InjTemp, CoolTemp

Method Estimation Least squares
Analysis of Variance for Ln(Std) Source DF Adj SS Adj MS F-Value P-Value Model 10 65.4970 6.5497 21.73 0.002 Linear 4 31.7838 7.9459 26.36 0.001 Material 1 30.0559 30.0559 99.71 0.000 InjPress 1 1.1104 1.1104 3.68 0.113 InjTemp 1 0.1005 0.1005 0.33 0.589 CoolTemp 1 0.5170 0.5170 1.71 0.247 2-Way Interactions 6 33.7132 5.6189 18.64 0.003 Material*InjPress 1 32.0953 32.0953 106.47 0.000 Material*InjTemp 1 1.1466 1.1466 3.80 0.109 Material*CoolTemp 1 0.0010 0.0010 0.00 0.956 InjPress*InjTemp 1 0.2046 0.2046 0.68 0.448 InjPress*CoolTemp 1 0.2642 0.2642 0.88 0.392 InjTemp*CoolTemp 1 0.0014 0.0014 0.00 0.948 Error 5 1.5072 0.3014 Total 15 67.0043
Model Summary for Ln(Std) S R-sq R-sq(adj) R-sq(pred) 0.549040 97.75% 93.25% 76.97%
Coded Coefficients for Ln(Std) Ratio Term Effect Effect Coef SE Coef T-Value P-Value VIF Constant 0.3424 0.0481 7.12 0.001 Material -0.9598 0.3830 -0.4799 0.0481 -9.99 0.000 1.00 InjPress -0.1845 0.8315 -0.0922 0.0481 -1.92 0.113 1.00 InjTemp 0.0555 1.0571 0.0278 0.0481 0.58 0.589 1.00 CoolTemp -0.1259 0.8817 -0.0629 0.0481 -1.31 0.247 1.00 Material*InjPress -0.9918 0.3709 -0.4959 0.0481 -10.32 0.000 1.00 Material*InjTemp 0.1875 1.2062 0.0937 0.0481 1.95 0.109 1.00 Material*CoolTemp 0.0056 1.0056 0.0028 0.0481 0.06 0.956 1.00 InjPress*InjTemp -0.0792 0.9239 -0.0396 0.0481 -0.82 0.448 1.00 InjPress*CoolTemp -0.0900 0.9139 -0.0450 0.0481 -0.94 0.392 1.00 InjTemp*CoolTemp 0.0066 1.0066 0.0033 0.0481 0.07 0.948 1.00
Regression Equation in Uncoded Units Ln(Std) = -1.30 - 0.158 Material + 0.0148 InjPress + 0.0180 InjTemp + 0.0031 CoolTemp - 0.01322 Material*InjPress + 0.01250 Material*InjTemp + 0.00028 Material*CoolTemp - 0.000141 InjPress*InjTemp - 0.000120 InjPress*CoolTemp + 0.000044 InjTemp*CoolTemp
Alias Structure Factor Name A Material B InjPress C InjTemp D CoolTemp
Aliases I A B C D AB AC AD BC BD CD
By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy