Background
Box-Behnken design is a response surface methodology design. It is used to further study the quadratic effect of factors after identifying the signficant factors using screening factorial experiments.

Box-Behnken designs do not contain any points at the vertices of the experimental region. This could be advantageous when the points on the corners of the cube represent factor-level combinations that are prohibitively expensive or impossible to test because of physical process constraints.

Consider a UV-light system that is used to inactivate fungal spores of Aspergillus niger in corn meal.* Fungal contamination of grains during the post-harvest period has been a recurring health hazard.

The response is the log10 reduction of the fungal spores. Therefore, the goal is to maximize the reduction (response).

Three process parameters in the UV-light system will affect the inactivation results. They are: A) treatment time (number of pulses), B) the distance from the UV strobe and C) input voltage for the UV lamp.

A 15 run Box-Behnken design with three center points is conducted. A full quadratic model is fitted to the data. Using this model, the optimal setting that gives the largest reduction of fungal spores was found.

Experiment Design
The experimenters use DOE++ to design a Box-Behnken design. The design-specific settings and the factor properties used are shown next.

The design matrix and the response data are given in the "UV-light Treatment" Folio.

Analysis Part I
Step 1: After performing the experiment according to the design and recording the results, the experimenters enter 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:

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, C, AC and AA are significant. The p value for factor B is 0.1481, which is close to the risk level 0.1. Therefore, the experimenters decide that it will also be included in the final 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: In the Select Effects window, 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.

Conclusions
The optimal solution is found to be A = 100 s, B = 3 cm and C = 3800 v. Under these settings, the expected logarithmic transformation of the reduction is 4.9. Keep in mind that it is necessary to conduct an experiment using these settings to confirm this conclusion.

* S. Jun, J. Irudayaraj, A. Demirci and D. Geiser, "Pulsed UV-light treatment of corn meal for inactivation of Aspergillus niger spores," International Journal of Food Science and Technology, 2003, 38, 883-888.