Interpret your Results (Model Graphs)

Focus on displaying the factors with the most influence on the response(s) – the factors with the greatest significant effects in the ANOVA. To help you decide which factors and views to plot, consider selecting Perturbation from the View menu

The Perturbation graph uses the model terms to display the effect of changing each factor from the reference point (default centre), whilst holding the other factors constant

In this way the plot can be used to decide which factors have the greatest effect on the response as well as locating ideal settings (or a direction) for each factor to improve the response

In this example clearly B-Liquid Volume has the greatest (curve-linear) affect on Hardness; with this response reaching a maximum of approx 12kp at when Liquid Volume = 0.36 coded units (40%w/w). The other 3 factors have very little effect in relation to factor B.

A plot of the One Factor Liquid Volume using the slider bars on the Factors Tool box for the other factors seems to be an obvious choice of plot to describe the effects of the factors on Hardness.

When the ANOVA and Perturbation plot suggest two or more factors are important, consider the Interaction, Contour and 3D Surface plots under the View menu. For example, the strongest effects on the response Compressibility are those of C-Inlet Air Temperature and D-Spray Rate together with their interaction. B-Liquid Volume also has a small positive effect according to the Perturbation plot.

Choose the Contour plot under the View menu to easily determine that to improve or minimise Compressibility (its goal), both Inlet Air Temperature and Spray Rate need to be increased, while Liquid Volume needs to be reduced using its slide bar on the Factors Tool box.

View: 3D Surface displays the predicted compressibility response as a 3rd  dimension versus the two factors Inlet Air Temperature and Spray Rate. The 3D surface is rotatable in any direction using the Rotation tool
To change the factors you are plotting on any axis of any plot, simply right click on the appropriate factor in the Factors Tool box and select the axis of choice

You can change graph properties by right clicking on a graph and select Graph Preferences.  Alter axis scales, the number of contours and their values, font settings etc. Alternatively, add contours or flags (prediction values) to contour plots by right clicking over the graph and selecting the appropriate option; click and drag a contour; or double click on a contour to enter a desired response

Interpret your Results (Optimization: Multiple Responses)

Once you have modelled all your responses and interpret their model graphs in turn, Design Expert provides optimization tools to help locate settings and ranges to simultaneously meet the Criteria and Goals you set for the multiple responses and also for the factors

For Numerical Optimization, set the Criteria: Goal, Lower &/or Upper Limits for the factors and responses. Use Weights & Importance to respectively give more or less emphasis to an individual goal relative to others. Design Expert searches for and lists Solutions (settings for the factors) to match your criteria: from the most to the least desirable – desirability ranges from zero (at least one goal was unachievable) to one (all goals were easily met).

Solutions displayed as a report

Solutions visually presented as ramps

Click Graphs to visually locate the most desirable solution, indicated by a flag, or region and by how much desirability falls off as you deviate from this ideal. In this case, the Numerical optimization Solutions and Graphs suggest the most forcing conditions, or highest settings of B-Liquid Volume, C-Inlet Air Temperature and D-Spray Rate produce the most desirable results in terms of meeting the goals for all the responses. A-Batch Size can vary across its entire range without altering or affecting the desirable region (i.e., the responses are robust to batch size in this region)

For Graphical Optimization, set the Criteria: Lower &/or Upper Limits for the responses to establish a yellow feasible region which meets all the criteria. A limitation of this plot is that it leads to the perception that all results within the yellow region are good, while all results outside are bad (i.e., all or nothing). On either of the two graphs above, click and hold the left mouse button to drag a box over a desirable, or potentially robust, region of conformance in order to zoom-in on that region

Point Prediction presents the predicted values of each your responses together with the reliability surrounding a predicted average result (SE Mean & 95% Confidence Interval), or a predicted individual result (SE Pred & 95% Prediction Interval). You can display the predictions for the desirable Numerical Solutions or for specified factor settings using the Factors Tool – move the slider bars (Gauges) or enter values on the Sheet

If no numerical or graphical solutions are found, you may need to loosen your criteria and try again. You may also wish to consider extrapolated predicted solutions outside of your current ranges. To view these on a graph, right click on the graph; select Graph Preferences; and expand the X1 and X2 Axes. You should verify these extrapolated predictions

In addition to the flag posted when a numerical solution is selected, you can add a flag at any location on an optimization graph by right clicking and selecting Graph Preferences