Okay, so welcome.
I'm Phil Kay, and I'm joined by Hadley Myers.
We're going to talk about O MARS Designs,
this new family of design of experiments
and an ad d-in that gives you a gateway into that world.
I'll start with an introduction,
and I'm going to give you a motivating case study.
I'm going to talk about how these OMARS Designs
bridged the gap between our small, efficient,
Definitive Screening Designs that we're all familiar with,
and the larger, high- powered, more traditional r esponse surface designs
that you might know of.
Then I'll pass over to Hadley
and he'll talk about how you, as a JMP user, can create and evaluate
different OMARS Designs with an add-in that he's been working on.
These O MAR Designs,
they come from a paper by Jose Nunez Ares and Peter Goos.
I'll just show you that briefly.
They've worked through the enumeration of thousands of such designs,
and we'll introduce you to what these designs look like.
I've got a motivating case study to begin.
This is from a published case study.
This was published in the Journal of Clinical Chemistry.
It's a response surface design.
It's about optimizing clinical chemical methods,
so an assay, in this case.
The objective was to optimize an assay method,
maximizing the response,
which is called Elevated Serum 30 degrees C.
They had six factors, each of which was a quantity
of a different reagent,
and they took a traditional approach.
This was done quite some time ago.
They generated a Central Composite Design,
which is a very traditional response surface design for optimization
with 48-runs, which includes four center points.
I've used this to motivate the use of O MARS Designs.
As an alternative to this 48- run design,
I generated a 17- run Definitive Screening Designs for those six factors.
I also generated an alternative 31- run O MARS Design.
I took the model from the original 48-run experiment.
So use that data, fit a model, and use that to simulate the responses
that we might expect for the Definitive Screening Design and fully OMARS Design.
We added an appropriate amount of noise
to that to give us a realistic response simulation.
What you're going to see through this example
is that the Definitive Screening Design is effective at what it should do,
which is finding the most important factors.
The O MARS Design enables us to optimize the process by identifying and estimating
all of the important effects from the response surface model.
In this way, we are saying that these O MARS Designs,
you can think of them as bridging the gap between Definitive Screening Designs
and the traditional response surface method designs,
like the Central Composite Design.
Here is that Central Composite Design.
Here are our six factors, and this is our response of interest.
These are some of the models that we fit, and we're comparing.
It's a traditional face- centered, Central Composite Design.
This is just three of the factors visualized.
You can see we've got our axial points here
on the face of the cube that's described by the factor ranges.
Those kind of designs are very good.
They've got lots of nice properties
in terms of the correlations between effects.
You can see lots of white space here, which means zero correlations,
They're not so great with the quadratic effects.
There's fairly strong correlations between all of our quadratic effects
on one another, which does reduce the power of our ability to estimate
these quadratic effects.
Nevertheless, we can fit a good model to that.
This is the model fit to that original data.
We identified that there really are four critical factors out of the six
and there are various higher order terms as well that are important.
Really the pH, this P 5P OG, and MDH are very important.
The L-a spartic acid and this Tris buffer are much less important.
We can build a good model using that design.
It's quite a big expensive design, though, 48-runs.
What would our alternatives be?
Well, Definitive Screen Designs are obviously very good
for screening these kind of situations, screening for the important factors.
I've generated using the same factors, same factor ranges,
a 17-run Definitive Screening Design for those six factors.
A gain, I've simulated the response data there based on the model
from the published data from the big experiment there.
The definitive screen design does what it's supposed to do.
It finds that we've got these four important factors,
the pH, P5 P, OG, MDH.
It's identified those and it's been able
to identify some of the higher order effects that are important.
Now at this stage, what you could do is augment.
Screening design is all about screening for the important factors
and then in the next step of the sequence, experimental sequence,
we can augment to learn more about the higher order effects,
the higher order terms for the response surface model.
What I'm going to show you here, though, is an alternative approach
we could have taken.
Here is an experimental design with 31 runs.
Again, same six factors, the same factor ranges.
You'll notice that it is a three- level design.
For each factor, we've got settings at three levels.
It's a response surface design.
If we compare it using the compare designs platform,
then we can compare those two designs.
The Definitive Screening Design here in blue,
we're looking at the powers versus the 31 run OMARS Design.
Well, it's not a surprise that the 31-run design has higher power.
Generally, we've got more runs, so we would expect that.
We can see significantly higher power for these quadratic effects, though.
Another thing to look at that might be of interest
is the color map on correlations.
Here's our 17-run Definitive Screening Design,
and you might recognize that color map,
if you know anything about Definitive Screening Designs then.
This color map is really a key.
It demonstrates a key property of Definitive Screening Designs,
which is that all of our main effects are orthogonal to one another,
and the main effects are also orthogonal to the second order effects,
the quadratics and the two-factor interactions.
That's what all that white space there means.
Then within the higher order terms,
there is some degree of correlation, but no complete correlation, no aliasing.
We are always able to estimate some of these higher order terms,
and those higher order terms are, at least, orthogonal,
completely separately estimated from the main effects factors,
the fact ors main effects rather.
Now if we look at this 31-run O MARS Design,
you can see its got similar properties.
Again, we've got orthogonal main effects,
and those main effects are orthogonal to the second order effects.
You can see we've got lower correlation between the quadratic effects,
Overall with the two- factor interactions as well,
there are lower correlations.
Why are these things called OMARS?
Well, OMARS stands for Orthogonal Minimally Aliased R esponse Surface
Again, we've got orthogonal main effects,
and we've got minimal aliasing between our second order effects as well,
and it's a response surface design.
In fact, both of these,
both the Definitive Screening Design and the 31- run design are OMARS.
They are both Orthogonal Minimally Aliased Response Surface Designs,
so DSDs are a subset of OMARS.
How well does this perform?
What I've done is I fitted a model to that simulated data.
Again, I simulated the response data for our 31- run O MARS Design,
and I've compared that model against the 17-run Definitive Screening Design.
17-run Definitive Screening Design is doing a reasonable job
of predicting the actual data.
Here, we're comparing how well our two models
from the Definitive Screening Design and the OMARS Design,
how well they fit against the actual data from the 48-run published example.
You can see a much improved model
with the 31- run O MARS Design, as we might expect.
In fact, the 31- run O MARS Design
has identified correctly the higher order terms that are important,
as well as identifying the important factor effects,
which was pretty much
all the Definitive Screening Design was able to do.
Again, just to reiterate, what we're showing here
is that these OMARS Designs
are really an extension of Definitive Screening Designs,
and they are a bridge between that small, efficient Definitive Screening Design
and the larger traditional response surface designs.
At this point, I'll hand you over to Hadley,
who's going to show you more about an add-in that he's created
that will enable you to actually explore this new class of designs for yourself.
All right. Thank you very much, Phil.
Hello to everyone watching this online, wherever you are.
Thank you very much for clicking on this talk.
Before I take you through the add-in to show you how you can use it
to generate these designs and select the best one for you,
I'd like to say that the add-in itself includes 7,886 files,
each one containing a design,
where the main effects are orthogonal to each other into the higher order terms.
The add-in not only gives you access to these 7,886 new designs,
but it also gives you access to all of these designs
with an added center point.
How can we select from among these
almost 16,000 designs the best one for us in our situation,
while the add-in provides us an interface to allow us to do that?
I'll show you how that works.
Right now, the add-in is called OMARS Explorer.
What it will allow us to do
is first indicate the number of factors that we have,
and the add-in at this moment has the ability to generate designs
for five, six, or seven continuous factors.
We can write the maximum number of runs that we can afford,
or that we'd like to do,
as well as whether we'd like a design for which we can estimate
all main effects or all the main effects,
as well as all the two-factor interactions or the full response surface model.
We have the option of generating parallel plots,
something we can use to help us select the right design.
I'll show you how that works. So I'll press okay,
I can put in the names of my factors as well as the high and low settings,
but I'm just going to leave it the way it is for now.
I've been given this table with 2,027 designs that satisfy our requirements.
Each one has five factors less than or equal to 35 runs,
and we can fit a full response surface model.
So how can we now select the best one?
Well, one thing we could use is the local data filter,
where we can select runs of a certain design of a certain run length
with or without center points, as well as our efficiencies.
The average or max variance of prediction and the powers for the intercept,
the main effects, and then the minimum and average powers
for the two-factor interactions in the square terms.
If we have a full response surface model.
Because we generated the parallel plots,
we also have the parallel plot here.
We can use all of this to then zero in
on designs that are the best among all the ones that we've chosen.
If the minimum power of the square terms
was something that was important to us, and I can narrow my search to 10 designs
rather than from among the 2,000 designs that were possible,
once I've done that, I can press this,
Get Summary Results script on the table, and then generate this table here
with the names of the designs, whether the design includes
a center point or not, the number of runs, as well as all of the metrics.
Let's see, I think I'll go ahead and just choose this one here.
I can press make design, and now I've been given this design a JMP.
One thing I'll add is that if you choose a design with the center point,
it adds a -0 at the end to indicate
that the center point has been added to that design.
I can now go ahead and add my response column,
save the table, and I'm ready to start conducting my experiment.
As Phil mentioned before,
Definitive Screening Designs are a subset of OMARS Designs.
Of course, there are many other
Orthogonal Minimally Aliased Designs that are not Definitive Screening Designs.
I'll show you an example here that uses six factors and a maximum of 20 runs.
In this case, we only have eight designs that meet this criteria.
I'm just going to go ahead and select all of them and press Get Summary Results.
Now, this 13- run design here with the center point
is actually the Definitive Screening Design for six factors.
You can see that this design is in every way
except for the power for the intercept, better than this 15- run O MARS Design,
which is not a Definitive Screening Design.
But I'm going to go ahead and select both of these
so that I can compare the designs.
When I do that, it'll open both tables as well as this compare designs platform.
Scrolling down to the color map on correlations,
I can see that the Definitive Screening Design,
which is this one here, looks as I would expect it to.
Of course, the O MARS Design is also orthogonal for the main effects.
That's what defines it as an O MAR Design.
But you'll also notice that
this one happens to be orthogonal
for many of the higher order effects as well.
If I were to try to fit the full response surface model
to add those terms to this model,
of course, I won't be able to add all of them,
but I'm able to add one additional term or to fit one additional term.
Using my O MARS Design,
then I would be using the 13- run Definitive Screening Design.
If I tried to do that ,
so now you'll notice that the powers for the intercept, the main effects,
and the quadratics are all higher for the O MARS Design.
They are lower than the Definitive Screening Design
for the interaction terms.
Looking at the fraction of the design space plot,
you'll see that the OMARS Design has a higher maximum prediction variance,
but is lower than the Definitive Screening Design over
more than 80 percent of the design space.
Interestingly, the Definitive Screening Design platform
doesn't have the ability to generate 15- run six factor designs.
We can generate 13 or 17runs.
If we can't afford 17-runs, but can afford 15,
this provides us perhaps an option that may be suited to us
that we'd like to consider or explore further.
Once again, thank you all for your attention.
At this point, I'd like to turn things back over to Phil.
Just to summarize what you've seen there, what we've shown you,
hopefully, you've seen how these Orthogonal Minimally Aliased
Response Surface designs
can bridge that gap between the small, efficient Definitive Screening Designs
and large high- powered traditional response surface method designs.
You've seen how there's more flexibility.
There are Orthogonal Minimally Aliased Designs with three levels
for different numbers of runs now.
If a Definitive Screen Design doesn't meet your needs
or a traditional Response Surface Method design doesn't meet your needs,
you should now be able to explore these OMARS Designs.
Exploring those designs is now made easier to use as a JMP user
with the add-in that Hadley has created for you.
We'll obviously post links to all of these things in the article
in the community,
and that's a great place to let us know if you've got any questions as well.
Thanks very much for your attention.