Background
Central composite design is the most commonly used response surface methodology (RSM) design. RSM design is usually used to study the quadratic effects of factors.

A chemical engineer is interested in determining the operating conditions that maximize the yield of a process.* Two controllable variables influence process yield: reaction time and reaction temperature.

A central composite design with five center points and alpha = 1.414 is used to conduct the experiment. A full quadratic model is fitted to the data.

Experiment Design
The engineer uses DOE++ to design a central composite design. The design-specific settings, the factor properties and the response properties used are shown next.

The design matrix and the response data are given in the "Central Composite Design" Folio.

Analysis Part I
Step 1: After performing the experiment according to the design and recording the results, the engineer enters the data set into the Standard Folio, as shown next.

Step 2: All effects (i.e. full quadradtics) are selected for inclusion in the analysis, as shown next.

Step 3: The data set is analyzed with the default risk (significance) level of 0.1, using individual terms. The ANOVA table from the Analysis tab is shown next.

This table shows that effects A, B, AA and BB are significant.

Step 4: A Pareto chart is created, as shown next.

From these results, only effects A, B and AA and BB would be included in the reduced model. In fact, term AB could also be included in the model, as it is only slightly below the critical value, as shown in the ANOVA table and Pareto chart. The inclusion or exclusion of AB is a personal decision that should be made based on the knowledge of the experiment and the statistical results. For this example, the engineer decides that only A, B, AA and BB will be included in the model.

Analysis Part II
The results for the reduced model and the optimization are given in the "Reduced Model" Folio.

Step 1: The design Folio is duplicated and the copy is named "Reduced Model."

Step 2: Only the significant effects are selected to calculate the new model, as shown next.

Step 3: The reduced model is calculated. The coefficients for the parameters in the reduced model are:

This model can be used as the final model to conduct optimization.

Step 4: Optimization is performed using the settings shown next.

The optimal solution is shown next.

Step 5: The contour and surface plot can also be used to visually identify the optimal settings for factors A and B, as shown next.

Conclusions
The contour and surface plots show that the maximum yield occurs at Time = 86.8 and Temperature = 176.3°F, which is the same as the result from the optimization. The predicted maximum yield is 80.1861. Keep in mind that it is necessary to conduct an experiment using these settings to confirm this conclusion.

* Montgomery, D. C. Design and Analysis of Experiments, 5th edition, John Wiley & Sons, New York, 2001.