Building the Design

Having established that four out of the eight factors do not affect the responses (i.e., the process is robust to these factors over the ranges studied), you may delete the four factors from the Design (Actual) layout. To do this right click on the headings of the factors you wish to delete, select Delete Factor and click Yes when asked if you are sure. This has the effect of turning the original 2^8-4 resolution IV fractional factorial screening design in eight factors into a 2⁴ full factorial design in the four important factors; ideal for estimating their main effects and 2-Factor Interactions unambiguously.

A-Hot Bar and B-Dwell Time together with their interaction affect both the average seal strength of the packs as well as their variation. We would choose the settings of these two factors to minimise variation, whilst achieving a target seal strength. C-Pressure and D-Material Temperature affect just the average seal strength, so these can be adjusted to target the average seal strength. We can now augment this design with experiments to model the curvature in these two responses.

Augmenting an existing design creates a second block of runs, unless you stipulated otherwise to Design Expert. With the blocking retained, the analysis removes any block-to-block differences due to equipment, environmental or operational changes.

Augmenting to a Central Composite Design

Assuming you have run a factorial/fractional factorial design to estimate main effects & 2-Factor Interactions and have witnessed significant curvature in your design region, you can augment your design with a second block of runs to make it into a Central Composite Design (CCD). Notice that in the classical layout, the star (or alpha) points are the extreme factor levels and extend beyond the inner factorial points. However, these can be impracticable, so when you define the additional CCD points, you can choose other practical values for alpha. Augmenting the factorial with these star points allows estimation of the individual squared terms, which provide a fit of the curvature.

From the Design Layout screen choose Design Tools and Augment Design… Augment. The most common sequential method for modelling curvature is to select Central Composite. Click OK to get the dialogue for augmenting the pre-existing design with star and centre point runs needed to estimate the curvature terms.

If you retain the default Rotatable Alpha, the new runs will be outside the original design region. If these are impractical, select either Face Centred or Other and enter a more appropriate coded value for alpha in the field provided. Refer to the Optimisation Designs Tipsheet for more help on selecting alpha. Click OK.

Design Expert adds the runs needed to apply response surface methods and build a more predictive model in a second block.

Augmenting to a RSM D-Optimal Design

As with augmenting a factorial design to make a CCD, the Response Surface Model (RSM) D-optimal augmentation enables you to model detected curvature and a suspected optimum. Unlike CCD augmentation, RSM D-optimal also allows you to include additional model points to counter previously failed experiments or missing 2-Factor Interactions, or to drop terms and decrease the number of runs required to estimate the desired model.

At the Design Layout screen choose Design Tools and Augment Design… Augment. Select RSM D-optimal and press OK to arrive at the standard menu for generating RSM D-optimal designs.

Click Edit model and select the model you want to fit from the Order menu (e.g., select a Quadratic model to create a design to model curvature). You can also reduce the model by removing terms you know are unimportant (e.g., remove a quadratic term for a factor that is only likely to have a linear effect). This will reduce the Total Experiments you have to run. Double click on a term to remove the M, signifying that the term has also been removed from the model. Double click on the term again to reinstate it.

In this example Design Expert informs us that the Total Experiments = 8 will be generated and added to the existing design. Press OK to augment the design.

You can also build a RSM design using the central composite augmentation described above and modify the alpha values, or other design settings, in the design layout itself before undertaking to run the experiments.

You can also use the Optimization Designs Tipsheet to set up a CCD from scratch using the Response Surface tab. The CCD screen allows you to enter the factor ranges in terms of the outer axial points as well as the inner factorial points so you can better manage the extremes of your experimental space.

To find out more about how the D-optimal algorithm works for RSM D-Optimal augmentation and how to use it confidently, please also refer to the Optimization Designs Tipsheet.

Running the Experiments and Entering the Data

For each augmented design point, run the experiment and enter the results for each response into the Design (Actual) sheet