5.5.14 DOE:Response Surface Design

Response-Surface-Design

Summary

Origin’s Design of Experiments app can design an experiment, fit a model to collected data, and find the best factor settings that optimize responses. In this sample, we will optimize responses under a Box-Behnken design.

A company is developing a new facial cream designed to meet two objectives: maximize hydration and target a neutral pH of 7. During the product development phase, the formulation team identified three key variables that influence hydration and pH level:

1. Type of oil used
2. Choice of emulsifier
3. Selected fragrance

All three are measured as a percentage of the ingredients that make up the facial cream.

A response surface design can be used to model the relationship between the response variables (hydration and pH level), and the three factors of interest (oil, emulsifier, and fragrance). The objective is to identify the optimal combination of these three factors that maximize hydration while keeping the pH level at 7. The company has two concerns:

1. They believe that the formula’s consistency will not be maintained at extreme points
2. There is a limited budget for testing the new formula

Given these limitations, an ideal design choice is a Box-Behnken design. Under a Box-Behnken design, experimental runs are restricted to the center area: two factors can vary while the third factor is held at the center level. A Box-Behnken design requires fewer experimental runs and is a good choice when there are limited resources on hand.

Minimum Origin Version Required: OriginPro 2025b SR0

Steps

Create Response Surface Design

1. Select and click on the Design of Experiments app on in the Stats in the Apps Gallery
   
2. Click on Create Design and select Response Surface Design in the pop-up list.
   
3. In the Factorial Design dialog, select Box-Behnken as Response Surface Design. Click Display Available Designs button. The pop-up table shows the number of experimental runs that are required. Along the top are the number of continuous factors. The last row is for the Box-Behnken design. An experiment with three factors will require 15 runs, which includes 3 Center Points and 12 experimental points.
   
4. Under the Factors tab, the Number of Continuous Factors is 3. And then enter 3 factors (oil, emulsifier and fragrance) with Low and High value in the table as following image:
   
5. Go to Setting tab. Keep default setting, and make sure the number of Total Runs is 15. (A total of 15 experimental runs are required.)
   
6. Go to Miscellaneous tab and turn off the Randomize Design option. (The option to Randomize the Design should be used for a real-life example but for the purpose of this tutorial.)
   
7. Click OK to generate the DesignSummary, CodedDesign and DesignTable worksheets. In the DesignTable worksheet, you will find since we chose not to Randomize the Design, the Run Order is the same as the Standard Order. Under Point Type, zero are the three Center Points. Notice that the levels of each factor are maintained so that two factors are allowed to vary while the third factor is kept at the center level.
   

Collect Data and Fit the Model

1. Enter Hydration and pH data in columns H and I of DesignTable worksheet.
   
2. Select and click on the Design of Experiments app again, and then click on Analyze Design.
   
3. In the Model tab, select Hydration under Response drop-down list. Click the + button and select Full Quadratic as Model Type.
   
4. Go to Stepwise tab, set Stepwise as Method and leave the default settings as is.
   
5. Go to Quantities tab and select Coefficients Type as Uncoded.
   
6. Go to Plots tab, add the Fitted Plot option to Plots list. Click OK.
   
7. In the result sheet DOEAnalysis, you can find the stepwise approach was used to remove insignificant terms from the model. Only the main effects – oil, emulsifier, and fragrance – were retained. The p-values for all three terms are less than 0.05.
   An adjusted R-squared of 0.874 demonstrates that the model is effective at capturing variation present in the data. The predictive R-square of 0.794 demonstrates that the model can generalize new data, not just fit the data on hand.
   
   
   The Residual plots show no patterns. The Effects plot shows significance for all three main effects, oil, fragrance, and emulsifier. This is also reflected in the Main Effects plot. All three lines have steep slopes.
   
8. Click on the DOEFindYfromX result sheet. Enter values for oil=9.69, emulsifier=4, and fragrance=0.2, then calculate the value of Hydration using the fitted model. The fitted value of Hydration is 81.4%.
   

Fit the Model for the second response variable, pH

1. Select and click on the Design of Experiments app again, and then click on Analyze Design.
   
2. In the Model tab, select pH under Response drop-down list. Click the + button to make sure the Linear set as Model Type.
   
3. Go to Stepwise tab, make sure Method is None.
   
4. Go to Quantities tab and select Coefficients Type as Uncoded.
   
5. Go to Plots tab, add the Fitted Plot option to Plots list. Click OK.
   
6. In the result sheet DOEAnalysis1, you will find that only one main effect, Oil, is significant.
   

Optimize Response

1. To optimize the response for both Hydration and pH, click on Optimize Response of this app.
   
2. Under Hydration, select Maximize as the Goal. Under pH, select Target, and enter 7 for the Target. Click on Set Lower/Upper Limits to generate system values. Then click OK.
   
3. In the DOEOptimization result sheet, the Solution table displays the combination of values for oil, emulsifier, and fragrance where the response variable Hydration is maximized and pH is 7. The Prediction table shows the fitted values for Hydration and pH at these values.
   
4. Double Click on the Optimization plot to open the interactive window. Move the red lines over the range of values for oil, emulsifier, and fragrance to obtain different Desirability scores.