Example of Analyze Response Surface Design

A package engineer needs to ensure that the seals on plastic bags that hold a product are strong enough to prevent leaks, yet not so strong that the consumer cannot open the bags. The engineer wants to optimize the seal strength to between 24 and 28 lbs (lower and upper bounds) with a target of 26 lbs. The engineer also wants to minimize the variability of seal strength so that it is 1 or less. The engineer determines that hot bar temperature, dwell time, hot bar pressure, and material temperature are factors that contribute to the strength of the seal. The engineer also determines that hot bar temperature and dwell time are important factors for reducing the variation. The engineer designs a central composite response surface experiment to examine the factors that impact the strength and variability of the seal.

The engineer collects data and analyzes the design to determine which factors impact seal strength.

  1. Open the sample data, SealStrength.MTW.
  2. Choose Stat > DOE > Response Surface > Analyze Response Surface Design.
  3. In Responses, enter Strength.
  4. Click Graphs.
  5. Under Residual Plots, select Four in one.
  6. Click OK in each dialog box.

Interpret the results

In the Analysis of Variance table, the p-values for the HotBarT*HotBarT, DwelTime*DwelTime, and HotBarT*DwelTime are significant. The engineer can consider reducing the model to remove the terms that are not significant. For more information, go to Model reduction.

The R2 value shows that the model explains 78.58% of the variance in strength, which indicates that the model fits the data adequately. The predicted R2 of 0 suggests that this model is overfit, which supports reducing the model.

The Pareto plot of the effects allow 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 HotBarT*DwelTime (AB) because it extends the farthest.

In the residuals plots, the points on the normal probability plot do not follow the straight line. Reducing the model may fix this.

Response Surface Regression: Strength versus HotBarT, DwelTime, HotBarP, ...

Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Model 14 1137.51 81.251 4.19 0.004 Linear 4 218.65 54.662 2.82 0.060 HotBarT 1 68.13 68.129 3.52 0.079 DwelTime 1 70.94 70.939 3.66 0.074 HotBarP 1 52.62 52.616 2.71 0.119 MatTemp 1 26.96 26.963 1.39 0.255 Square 4 372.07 93.018 4.80 0.010 HotBarT*HotBarT 1 202.61 202.611 10.45 0.005 DwelTime*DwelTime 1 175.32 175.318 9.05 0.008 HotBarP*HotBarP 1 50.52 50.522 2.61 0.126 MatTemp*MatTemp 1 37.87 37.866 1.95 0.181 2-Way Interaction 6 546.79 91.132 4.70 0.006 HotBarT*DwelTime 1 540.47 540.470 27.89 0.000 HotBarT*HotBarP 1 0.12 0.121 0.01 0.938 HotBarT*MatTemp 1 0.30 0.305 0.02 0.902 DwelTime*HotBarP 1 4.84 4.840 0.25 0.624 DwelTime*MatTemp 1 0.90 0.899 0.05 0.832 HotBarP*MatTemp 1 0.16 0.160 0.01 0.929 Error 16 310.08 19.380 Lack-of-Fit 10 308.20 30.820 98.51 0.000 Pure Error 6 1.88 0.313 Total 30 1447.60
Model Summary S R-sq R-sq(adj) R-sq(pred) 4.40228 78.58% 59.84% 0.00%
Coded Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 28.44 1.66 17.09 0.000 HotBarT 1.685 0.899 1.87 0.079 1.00 DwelTime -1.719 0.899 -1.91 0.074 1.00 HotBarP 1.481 0.899 1.65 0.119 1.00 MatTemp 1.060 0.899 1.18 0.255 1.00 HotBarT*HotBarT -2.662 0.823 -3.23 0.005 1.03 DwelTime*DwelTime -2.476 0.823 -3.01 0.008 1.03 HotBarP*HotBarP -1.329 0.823 -1.61 0.126 1.03 MatTemp*MatTemp -1.151 0.823 -1.40 0.181 1.03 HotBarT*DwelTime -5.81 1.10 -5.28 0.000 1.00 HotBarT*HotBarP -0.09 1.10 -0.08 0.938 1.00 HotBarT*MatTemp -0.14 1.10 -0.13 0.902 1.00 DwelTime*HotBarP 0.55 1.10 0.50 0.624 1.00 DwelTime*MatTemp 0.24 1.10 0.22 0.832 1.00 HotBarP*MatTemp -0.10 1.10 -0.09 0.929 1.00
Regression Equation in Uncoded Units Strength = -289.3 + 2.287 HotBarT + 206.6 DwelTime + 0.124 HotBarP + 0.594 MatTemp - 0.00426 HotBarT*HotBarT - 39.6 DwelTime*DwelTime - 0.000532 HotBarP*HotBarP - 0.00288 MatTemp*MatTemp - 0.930 HotBarT*DwelTime - 0.000070 HotBarT*HotBarP - 0.00028 HotBarT*MatTemp + 0.0440 DwelTime*HotBarP + 0.047 DwelTime*MatTemp - 0.00010 HotBarP*MatTemp
Fits and Diagnostics for Unusual Observations Std Obs Strength Fit Resid Resid 3 20.69 14.43 6.26 2.20 R 5 27.43 21.72 5.71 2.01 R 9 25.99 20.16 5.83 2.05 R 19 21.38 15.10 6.28 2.21 R R Large residual

Effects Pareto for Strength

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