Model Graphs

 

Use the Factors Tool to choose the effect you wish to display. You can view One Factor plots of the main effects of each factor as it moves from its low to high setting.

 

 

An Interaction plot shows whether the effect of moving from a low to a high setting of one factor depends on the setting of a second factor.

 

 

Example: Increasing A: Magnesium Stearate from 3.5 to 14.0 mg/tab decreases Hardness. However, the drop in Hardness due to increasing Magnesium Stearate also depends on the setting of D: Granulation Blend Time. A steeper drop in hardness at high blend time (red line) is seen compared to low Granulation Blend Time (black line). Similarly, at low Magnesium Stearate there is no statistical difference in Hardness using short vs. long Blend Time – 95% least significant difference (LSD) bars overlap – compared with high Magnesium Stearate where there is a statistical difference in hardness – 95% LSD bars for short (black) and long (red) Granulation Blend Time do not overlap.

Independently of Magnesium Stearate and Granulation Blend Time, B: Granulation Paste Type statistically significantly decreases Hardness as the ratio changes from 0.8 to 1.2 eq. Therefore, to increase Hardness we must use low Magnesium Stearate and low Granulation Paste Type and, at low Magnesium Stearate, Hardness is robust or insensitive to changes in Granulation Blend Time.

Choose alternative ways to plot the effects of the factors using the View menu

Cube plot displays the effects of three factors – we see confirmation that the combination of low Magnesium Stearate & low Granulation Paste Type (bottom left-hand cube edge) yields the best results for Hardness. There is little change in Hardness as Granulation Blend Time varies at low Magnesium Stearate
 

Contour plot displays the gradations of effect on Hardness as two factors vary

 

 

3D Surface displays the predicted response as a 3rd dimension and is rotatable using the Rotation tool

 

 

Model Graphs: 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

Optimization: Multiple Results

 

Following the steps above to also analyse the Degradation & Dissolution responses suggests ideal settings for the four factors:

A: Magnesium Stearate low to achieve criteria for Hardness (>20lb) & Dissolution (>95%)
B: Granulation Paste Type low to help meet the targets for Hardness & Dissolution
C: Dibasic Sodium Phosphate at low setting provides a wider operating window for Magnesium Stearate to meet criteria for Degradation (<4.5mg/h), but needs to be set high in order to also meet Dissolution goal
D: only affects Hardness, but at low Magnesium Stearate Hardness is robust to changes in Granulation Blend Time so set it at its most practical/economical setting

Example: Dissolution

 

 

 

Example: Hardness

 

 

 

Once you have arrived at models for all your responses, Design Expert provides optimization tools to help locate settings and ranges to simultaneously meet the Criteria and Goals you set for 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 or 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).

Here the solutions are displayed as a report.
 

Here the solutions are presented as ramps.

 

 

 

Click Graphs to locate the most desirable solution or region and by how much desirability falls off as you deviate from this ideal (c.f. Taguchi loss function).

Choose 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 (c.f. all or nothing loss function).

On this graph and on the Overlay Plot below, 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

Overlay Plot

 

 

 

Point Prediction presents the predicted values of each your responses for specified factor settings together with the reliability surrounding a predicted average result (SE Mean & 95% Confidence Interval), or a predicted individual result (SE Prediction & 95% Prediction Interval).

To choose settings for the parameters on which to base predictions:

• click on the Numerical Solutions, or
• use the Factors Tool to move the slider bars (Guages), or
• enter values on the Sheet

Optimization: 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

Optimization: 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

< previous

return to contents