To illustrate
the use of
response surface
methods (SigmaXL
> Design of
Experiments >
Response Surface
), we will
use a layer cake
baking
experiment. The
response
variable is
Taste Score (on
a scale of 1-7
where 1 is
"awful" and 7 is
"delicious").
Average scores
for a panel of
tasters have
been recorded.
The X Factors
are A: Bake Time
(20 to 40
minutes) and B:
Oven Temperature
(350 to 400 F).
The experiment
goal is to find
the settings
that maximize
taste score.
Other factors
such as pan size
need to be taken
into
consideration.
In this
experiment,
these are held
constant.
Click SigmaXL
> Design of
Experiments >
Response Surface
> Response
Surface Designs.
First we create
a design. The
Number of X
Factors can be 2
to 5. Select
Number of
Factors = 2.
The available
designs are
sorted by number
of runs.
Increasing the
number of runs
allows for
uniform
precision or
blocking, but we
will select the
design with
fewest runs, the
10-Run,
Central
Composite Design
(2 Ctr Pts).
It is a good
practice to
replicate an
experiment if
affordable to do
so. Here we
will select
Number of
Replicates =
2 and check
Block on
Replicates.
Blocking on
replicates
allows us to
perform the
experiment over
a two week
period, with
each block
corresponding to
week number.
Change the
Alpha Axial
Value option
to Face
Centered (Alpha
= 1.0).
This simplifies
the design to a
3 level design,
rather than a 5
level design
with alpha =
1.414. (The
trade-off is
that we lose the
desirable
statistical
property of
rotatability for
prediction).
Tip: This
alpha is the
distance from
the center point
to the end of
the axial (star)
point. Do not
confuse this
with Alpha
for Pareto Chart
which is the
p-value used to
determine
statistical
significance.
Unfortunately
the term “alpha”
has been chosen
by statisticians
to define two
completely
different
things.
Enter
Factor Names
and Level
Settings and
Response Name
as shown:
The
following
worksheet is
created:
The response
taste scores are
entered as
shown:
Open the file
RSM Example –
Cake Bake
(installed with
SigmaXL) to
obtain response
values.
Click SigmaXL
> Design of
Experiments >
Response Surface
> Analyze
Response Surface
Design.
We will use the
default analyze
settings (all
terms in the
model, including
the block term)
to start. Click
OK. The
resulting
Analysis report
is shown:
The model looks
very good with
an R-Square
value of 99.09%
The standard
deviation
(experimental
error) is only
0.19 on a 1 to 7
taste scale.
All of the model
terms are
statistically
significant (P <
.05), but the
Block term is
not, so it
should be
removed from the
model. Note
that AA and BB
denote the
quadratic model
terms.
Click Recall
Last Dialog
(or press F3).
Uncheck
Include Blocks
as shown:
Click OK.
The revised
report is shown
below:
To create a
contour and
surface plot,
click SigmaXL
> Design of
Experiments >
Response Surface
>
Contour/Surface
Plots.
Click OK.
The following
Contour and
Surface Plots
are displayed
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