Hi,

I want to create a d-optimal design with the following characteristics:

factor A - numeric 2 levels
factor B - numeric 3 levels
factor C - numeric 2 levels
factor D - categorical 2 levels

Combinations of A, B, C exist for only one of the two levels of factor D.
How do construct the constraint (Multiple Linear Constraint) to describe this?

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If you can tell us more, that may be helpful.

If you can tell us more, that may be helpful.

I want to understand effects (main effects and interactions) of ingredient
level , processing temperature, manufacturing plant and storage time on
product quality.

 The product is a fruit beverage; formulated with 3 levels on concentrate
(factor A), using two processing temperatures (factor C), stored  at three
temperatures (factor B),  at two different plant locations (factor D).  One
plant has process at both temperatures while the other plant can only process
at one temperature.  A trained panel of tasters will taste and evaluate
samples.

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Message posted via MathKB.comhttp://www.mathkb.com/Uwe/Forums.aspx/math-statistics/200807/1

On Jul 11, 10:48 pm, "jiana via MathKB.com" <u44208 at (no spam) uwe> wrote:

If you can tell us more, that may be helpful.

I want to understand effects (main effects and interactions) of ingredient
level , processing temperature, manufacturing plant and storage time on
product quality.

The product is a fruit beverage; formulated with 3 levels on concentrate
(factor A), using two processing temperatures (factor C), stored at three
temperatures (factor B), at two different plant locations (factor D). One
plant has process at both temperatures while the other plant can only process
at one temperature. A trained panel of tasters will taste and evaluate
samples.

--
Message posted via MathKB.comhttp://www.mathkb.com/Uwe/Forums.aspx/math-statistics/200807/1

1) Create the full factorial in all of the factors regardless of the
constraints using any appropriate software.
2) Edit the factorial experiment and delete all runs that do not meet
the constraints specified about.
3) Use the resultant basis set as the set of allowable runs.
4) Use any piece of d-optimal generating software that will allow one
to generate a design from a basis set of allowable runs (Design Expert
does this very well).
5) Evaluate the resultant design very carefully to make sure it meets
your needs. Evaluate the state of multicollinearity in particular by
examining the variance inflation factor (VIF) values and also the
condition number of the design matrix (the ratio of the largest to
smallest eigenvalue).

Disclaimer - I am not affiliated with Stat Ease, the makers of Design
Expert. This just a good piece of software that can execute the above
algorithm.

I see no need for searching for the D-optimal subset of all feasible
trials in this instance. IMHO, all feasible trials should be run... and
probably need to be replicated. He's running low on experimental combinations
already.

I was considering a D-Optimal approach hoping to minimize the number of
samples because the full factorial requires more samples than the panel of
tasters can evaluate each time interval. The panel is well calibrated and
the ratings are done in triplicate.

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Message posted via MathKB.comhttp://www.mathkb.com/Uwe/Forums.aspx/math-statistics/200807/1

On Jul 12, 4:01 pm, "jiana via MathKB.com" <u44208 at (no spam) uwe> wrote:

I see no need for searching for the D-optimal subset of all feasible
trials in this instance. IMHO, all feasible trials should be run... and
probably need to be replicated. He's running low on experimental combinations
already.

I was considering a D-Optimal approach hoping to minimize the number of
samples because the full factorial requires more samples than the panel of
tasters can evaluate each time interval. The panel is well calibrated and
the ratings are done in triplicate.

--
Message posted via MathKB.comhttp://www.mathkb.com/Uwe/Forums.aspx/math-statistics/200807/1

I'm happy to hear that you have a trained taste panel. I assume they
do their work "blind".

Concerning the number of samples...
For one case of "D" there are 2 x 3 x 2 or 12 "experiments" and hence
I imagine 12 samples.

It's not clear to be how you will set A, B, and C for the other case
of "D".
Select one setting of A and of B and of C... perhaps?

I'm concerned that, if you try to reduce those to a subset of them,
you will not be able
to detect the effects you are looking for. There are at least two
concerns here. One is
"the power of the test". The other is if you do not run some of those
18 then you will
most likely not be able to detect and measure interactions among A, B,
and C... if such
interactions are present. Now it is true that you could reduce A, B,
and C to a 2 x 2 x 2
... a classic two level factorial in just 8 experiments... a reduction
from 12 to 8.
And then run a "center-point" with B at its intermediate level in that
layout. That's
nine experiments... a "savings" of three experiments. But if
curvature is actually present
in B you'll have a feeble estimate of that curvature... and may
ultimately need to add
two more experiments to resolve it... a "savings" of just one
experiment. Worse, that would
lead to a sequential set of experiments... starting with nine and then
asking permission to
run two more. This is why I said "he's running low on experimental
combinations."

If you go with a D-optimal and a subset of less than the full
factorial, how many experimental
combinations will you propose to run? Run too few and you will lose
the ability to detect
and measure interactions. As the other commenter suggested, be sure
to check to see whether
the proposed D-optimal plan will actually allow you to estimate
interactions before you start
experimenting. Otherwise, the
data may not be analyzable. OMU

4) Use any piece of d-optimal generating software that will allow one
to generate a design from a basis set of allowable runs (Design Expert
does this very well).

I see no need for searching for the D-optimal subset of all feasible
trials in this instance. IMHO, all feasible trials should be run... and
probably need to be replicated. He's running low on experimental combinations
already.

I see no need for searching for the D-optimal subset of all feasible
trials in this instance. IMHO, all feasible trials should be run... and
[quoted text clipped - 55 lines]
experimenting. Otherwise, the
data may not be analyzable. OMU

Correction...

Not: The other is if you do not run some of those
18 then you will

But: The other is if you do not run some of those
12 then you will OMU