The Straight Way to a Final Result: Mixture Design of Experiments

Copyright © 2012, SAS Institute Inc. All rights reserv ed.
THE STRAIGHT WAY TO A FINAL
RESULT:
MIXTURE DESIGN OF EXPERIMENTS
Bernd Heinen
Sr. Systems Engineer
bernd.heinen@jmp.com

Running experiments is an essential part of all development, improvement, upscaling and research
activitiy.
Very often, still today, experiments are run following traditional legacy designs.
This goes to the extent that only one factor gets changed over a series of experiments.
Single factor experiments are not possible in mixture designs as all the components have to add up
to the total amount. If the volume of one component goes up others need to go down.
Are you designing each experiment?
Do you exactly know what your design space looks like?
Are you aware of constraints?
Is your experimental design optimized for the design space and the constraints given?
Do you know in advance how many experiments you will need to definitively answer your questions?
Are you making the best use of the data generated?
Are you using your experimental data for interactive what-if scenario analyses?
Let‘s go!

Mixture experiments have the specific side condition that the levels of their factors are not independent
from each other. If the amount of one component is known, there are only limited options for the rest. If
all but one components are known the last one has no options any more.
Frequency distribution of
fractions of three
components used for
twelve experiments
With a fraction of 50%
selected for the first
component there are only
few combinations left for
the other two
The contribution of the last
component is determined
by the others.

The Ternary Plot is a graphical representation of mixtures that allows to represent three factors (three
dimensions) in one graph. Dots mark the combinations at which experiments have been carried out.
Their color is an indicator for the level of the response variable as well. Isometric lines show the
interpolated „landscape“ of a result (or response) variable over the experimental space as it is derived
from the experiments.
Current
mixture setting
of the slider
Expected result for
response variable at
optimal settings

Oil
0
00
1 1
1
To set up a mixture design does not require any statistical knowledge. The single components need to
be listed and it is relevant to state if interactions are expected.
If every component could take any proportion from 0 to 1 (equivalent of 0% to 100%) then the whole
experimental space will be covered as it is spanned by the Ternary Plot. The experiments will be
arranged such that the vertices and the edges will be covered.
List of all pairwise
interactions

Water0
0.25
Vinegar
0.375 0.125
Oil
0.75
0.5
Often components contribute with different
fractions to the mixture. If accordingly specified,
the experimental space is a limited area.
Experimental mixtures then cover the vertices and
the center.

Oil : Vinegar ≥ 3 : 1
Oil : Vinegar ≤ 2 : 1
Constraints that link components among each other further restrict the experimental space.
Again, the test mixtures cover the vertices, the edges and the center.

Factor Profiler and Mixture Profiler
set to center experiment
Factor Profiler and Mixture Profiler
set to maximum response
When the experiments have been run and
the response variable was measured and
captured the result is used to answer the
questions behind the experiment. In this
example „how do we get the maximal
response?“
Linked profilers let you find the desired
optimum and explore the behaviour of the
mixture in the vicinity of the optimal point.
Also the whole experimental space can be
analyzed to gain better understanding of
the system‘s behaviour.

More mixture factors and more response variables don‘t make it more difficult. The whole design process
scales to arbitrary volumes. It‘s just a bit more typing.

Profilers still show the response variables from all aspects,yet the factor profiler (top left) gives the best
overview and access to data and models. Here all profilers are set to center values.

Same dashboard as before, all profilers set to the optimum value, i.e. hardness close to ist target value
of 50 at minimal achievable cost.

Very often a mixture is not used „as is“ but as part of a process.

Responses along with their
goals, factors with their
roles and test ranges and
constraints are defined just
as in the simpler examples
before. Mixture components
and process variables are
specified in the same
manner.

Mixture ComponentsProcess Factors
All factors set to optimal values. Yellow are the most influential ones. Time doesn‘t impact any of
the response variables so it can be set to the shortest time possible to save money.

Know the design space
Place experiments where
exactly they are needed.
Make as few experiments
as possible, but no less
(adapted from Einstein)
Summary 1

THE ULTIMATE
CHALLENGE
COMBINE MIXTURE AND PROCESS FACTORS IN ONE
EXPERIMENT
Mixture
Process
Summary 2

Put all relevant factors into one consistently designed experiment
Get answers in a predictable process
Get Information Get in Touch
www.jmp.com www.jmp.com/trial
Webcast on Demand JMP Offices
JMP DOE Brief JMP Contact
JMP YouTube Channel Bernd Heinen Linkedin
Bernd Heinen Xing
Summary 3

The Straight Way to a Final Result: Mixture Design of Experiments

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The Straight Way to a Final Result: Mixture Design of Experiments