XLSTAT: Surface Response Design in Excel

 

Background

Response surface designs are used to analyze problems in which a response is influenced by several variables and for which the objective is to optimize that response.

Note: Screening designs, on the contrary, are used to analyze the factors and not to optimize the response.

 

Dataset for Example

The attached data come from a classic example described in [Louvet, F. et Delplanque L. (2005). Design Of Experiments: The French touch, Les plans d’expériences : une approche pragmatique et illustrée, Alpha Graphic, Olivet, 2005]. An experimental design to analyze a 2-factors response surface is used to graphically represent this surface and analyze it.

We will use this example to find the optimum value of debinding temperature (F1) and debinding time (F2) of an industrial process in order to extract the binder in the field of ceramics. We seek to obtain a maximum percentage of extracted binder.

 

Setting Up

• Open XLSTAT.

• Click on the Design Of Experiments (DoE) menu and select the Surface response designs feature.

• The dialog box pops up.

• In the General tab, select the table of quantitative factors (this table must contain a maximum of two rows, the minimum and the maximum for each of the factors), as well as the number of responses (1).

 

• In the Options tab, select a central composite design as the type of design.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Results of the generation of the experimental design

A table with all the information associated with the factors is displayed.

Next, the design is displayed, and you must fill in the last column with the experimental results (response). The response optimization table below will auto-populate once the responses are entered.

After generating the design, perform the 13 experiments and enter the results in the response column.
Then, in the optimization table, select the option to maximize the response to find the optimal debinding temperature (F1) and time (F2) for maximizing binder extract percentage.

In the tutorial workbook, the results are pre-filled and highlighted in yellow for easy identification.

 

Setting Up

You have two options to analyze the design:

Option 1: Click Run the analysis below the design table to open a pre-configured dialog box for computations.
Option 2: Go to the Design Of Experiments (DOE) menu and select Analysis of a surface response design.

• Click the button to open the dialog box.

• In the General tab, select the experiment results column, the design, and the variable info table. Ensure all design columns are selected for proper analysis.

• In the Options tab, enable response optimization and select the correct table, ensuring the column headers are accurate.

• Click OK to start computations.

• In the next dialog box, select all terms to include the quadratic model.

 

Interpreting the Results

A first table is displayed, providing the results of the responses optimization. This shows us several effective solutions to obtain a maximum percentage of extracted binder. According to this table, it is therefore necessary to have a debinding temperature of around 109°C and a debinding time of around 55 minutes.

Further details include model parameters and equation.
The response surface is then shown via 2D and 3D contour graphs, with the optimal area highlighted in red.

The optimum is around 135 degrees Celsius and 52 minutes. The value of the response variable at this point is greater than 72.4%.