Building the Design (Response Surface Tab)

There are three response surface method (RSM) designs you will commonly choose from:

• Central Composite Design (CCD)
• Box-Behnken Design (BBD)
• D-Optimal Design 

1. Central Composite Design (CCD)

 

This is the most popular design for modelling curvature, or an optimum, as it is sequentially created by augmenting a two (±1) level design with centre points and axial points; which are a distance of -alpha & +alpha from the centre of the design in coded units

 

Click the CCD Options button to change the default design points. You can change how far the axial points are extended.

 

 

 
Consider the following options:

• Alpha = Rotatable desirable properties of 5 settings for each factor and equal reliability for predictions the same distance from the centre of your design. If these are too extreme or impractical try…
• Alpha = Face Centred (CCF) extends the axial points to the faces of your factorial (±1) design. There are only 3 settings for each factor, but the axial points are not extended beyond current ranges
• Alpha = Other permits you to control how far the axial points are extended (e.g., alpha < 1 brings the points inside the design creating a 5-level central composite inscribed (CCI) design

Rotatable CCD provides excellent prediction capability across the experimental space; CCF has better capability nearer the centre and CCI only nearest to the centre

CCD is insensitive to missing data or failed experiments

Click Factor Ranges in Terms of Alphas to set the axial points at your practical extremes DX will adjusts the ±1 factorial settings accordingly

Separate factorial & axial points into blocks to manage or to remove systematic bias between experiments

Click Type. If ≥ 5 factors, then DX uses a green fractional factorial core design if you select Full, or a red fractional factorial core if you select Small 

2. Box-Behnken Design (BBD)

 

Box-Behnken Design is design created solely to model curvature, or an optimum. There are only 3 settings for each factor. These are positioned at the midpoints of the edges of the design; emphasising an ideal as well as specific setting for each of your factors. BBD provides strong prediction capability near the centre of your experimental space (where the optimum is presumed to be), but is weaker at the corners of this space.

BBD requires fewer experiments to set up compared to a CCD, but is not recommended if you expect missing data or failed experiments

You can change the number of Centre points, but stick with the default unless resource is an issue, and you can divide the experiments into Blocks for reasons of management or bias

If a CCD or BBD (standard design) is not fit for purpose, practical or flexible then consider using a D-Optimal design.

3. D-Optimal Design

 

The key benefits of D-optimal designs:

• Resource Efficient requiring even fewer experiments compared with both BBD & CCD, and the capacity to further decrease the number of runs using your existing process knowledge
• Augments an existing set of data to improve the predictive power of your model for optimization, design repair, or inclusion of previously performed experiments (c.f. augmenting designs for optimisation)
• Constraints on the experimental space can be imposed by clicking Edit Constraints to exclude undesirable/unnecessary conditions, or to choose from a specific Candidate List of desirable experiments

The standard menu for generating D-Optimal designs allows you to create a model to suit your current state of knowledge (e.g., Quadratic to model curvature) and your pocket!

 

 

• Edit model: Specify the model you want to fit with only the effects of interest based on your experience: reduce a model & therefore the resources needed to estimate it, by removing terms you think are unlikely to be important. Double click on a term to remove it from the Model (M)
• You are then informed of the type of runs needed to fit (Model points) and test your model (lack of fit & Replicates) as well as the Total runs required
• The D-optimal algorithm selects a subset of design points from the list of Candidate points to maximize the information about your specified model

Enter one constraint per row in the spaces provided. In this example, the constraint ensures that settings of spray rate (D) cannot fall below a certain g/min to compensate for increasing batch size. This excludes a particular region of experimental space where you cannot get a response.

 

Click Evaluation and the Graphs button to graph the standard error plot with the constraints and the excluded area visible

 

 

Entering Factors and Responses

 

To enter factors & responses for each of the above three Response Surface designs

• Simply select the number of Numeric and Categoric factors and enter the factor names, units and extreme low and high levels. For a CCD, the distance of the axial points from the centre of the design (i.e., alpha) is automatically determined
• Click Continue to provide Block names (e.g., operators), if you chose to perform the runs in more than one block, or to enter the number, names and units of the responses
  

Running the Experiments and Entering the Data

 

For each experiment run in Run order, enter the results for each response into the Design (Actual) sheet. An alternative Run Sheet view, for carrying out & recording your results offline, is available under the View menu

 

Right click on a column heading to display options relating to that column:

• Std – sort your design into a standard order
• Run – sort into a randomised run order
• Block – display point type e.g., Factorial, Axial etc.
• Factor – edit information e.g., ranges, decimal place
• Response – e.g., simulate results
  

 

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