2019-01-30

## How can I generate a surface response design and how to do the corresponding analysis of the results?

The family of surface response design is used for modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response.

Remark: In contrast to this, screening designs aim to study the input factors, not the response value.

In this example we search the optimal levels of the debinding temperature (f1) and the debinding time (f2) of an industrial process to extract the binder in the domain of ceramics, which should lead to a maximum percentage of extracted binder.

## Dataset for generating a surface response design

An Excel sheet with both the data and the results can be downloaded by clicking on the button below:

Data are based on the example described in [Louvet, F. and Delplanque L. (2005). Design Of Experiments: The French touch, Les plans d’expériences : une approche pragmatique et illustrée, Alpha Graphic, Olivet, 2005] on page III.2 – 1 ff. An experimental design to study the surface response of 2 factors is used to display graphically the surface response and analyze it.

## Setting up a surface response design with XLSTAT

### 1. Step: Generate an experimental design

After opening XLSTAT, click the DOE button in the ribbon and select Surface response designs (see below).

The Surface response designs dialog box appears. Select the data on the Excel sheet.
Enter the model Name (ceram), select the number of factors (2 in this example) and the number of responses.

In the Factors tab, select the corresponding columns in the Excel sheet named Sheet1 as shown in the screenshot in order to enter the information about the factors:

In the Responses tab enter the information about the response variable.

Once you have clicked on the OK button, the computations start.
A table with information about the factors of the experimental design and the design table itself are displayed in the Excel sheet named ceram.

### 2. Step: Carrying out the experiments.

Now the 13 experiments are carried out and the resulting distance has been entered in the corresponding cells of the generated experimental design.
The results are on a yellow background in the file to find them easier.

### 3. Step: Analysis of the experiments

Click the DOE button in the XLSTAT ribbon and select Analysis of a surface response design (see below).

Once you've clicked on the button, a new dialog box appears.
Select the name of the model by selecting the cell B23 in the Excel sheet of the experimental design (ceram!\$B\$22). By the help of this selection XLSTAT can find information about the chosen experimental planning in the hidden Excel sheet and will use this information during the analysis. Select the result column as shown in the screenshot below.

In the Output tab, activate only the most important information for this tutorial. You can redo the analysis and select more options in order to have additional information in the report.

Once you have clicked on the OK button, the computations start.
The first results are the goodness of fit coefficients. Important indicators are R2 and Q2. A value close to 1 indicates that the model has a good fitting to the data. This ANOVA and its model describe the data very well, because R2 = 0,996.

Further details about the model are available in the two following sections with the model parameters and the model equation.
Then the surface response area is displayed graphically. This is done by an 2d and an 3d contour plot. It can be seen easily that the optimal area is situated in the red area:

The optimum can be located around 135 degree Celsius and 53 minutes and has a value of more than 72,4 %.
Finally, in the two following diagrams the traces of each factor with respect to the answer variable are displayed.

#### Contact our technical support team: support@xlstat.com

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