In this section, we start looking outside our cube plot.
What happens when we leave that range from minus one to plus one that we've been so
focused on?
We're going to add a new tool to our toolkit that we used to analyze the data.
The concept called Response Surface Methods (RSM).
Now, in the next video, we will consider in depth the case of a single factor.
Most practical systems, though, have two or more factors that affect the outcome.
But if you understand the idea for
one factor, then the subsequent videos will make more sense.
I'll explain what Response Surface Methods are in this video and
why you would want to use them.
And in the remainder of the videos, we'll see them in action.
When I use data to improve a process or a system, in my experience,
I find that I'm inevitably trying to achieve one of these five objectives.
Trying to learn more or increase my knowledge of the system.
Maybe I'm troubleshooting the process.
Or perhaps, I'm using the data to make some form of prediction.
Or maybe I'm trying to optimize the system in some way.
Or finally, I might just be monitoring the process based on the data to make sure
that I'm retaining all those performance gains I've made in the past.
Those of you taking the course and working in a company, you will find that any
project or task you do likely falls into one of these five categories.
Think back about the past few projects you've been working on.
The biggest problem I often encounter is that people don't have
their objectives clearly in mind.
Once you've figured out your objective, picking the simplest approach, and
using the appropriate tools to solve that problem becomes apparent.
In the prior four modules of this course,
we have focused really only on the first three objectives listed there.
We've hinted a little bit at that fourth one,
trying to optimize the process in some way.
For that first objective, we've seen how we can learn
which factors are important and illuminate which are not.
This improves our overall understanding of the system.
To quote George Box:
"discovering the unexpected is more important than confirming the unknown".
Really think about your experimental results and interpret them every time.
The concepts learnt in this course can also be used to troubleshoot a problem.
If your boss comes to you with a problem, you can brainstorm a list of five, six, or
more factors that are potentially the cause.
Use fractional factorial ideas from module four, and
you can quickly identify which factors are actually related to the issue.
And right since video 2A, we've been making predictions based on
our experimental results, so you're very comfortable with that idea.
In this section, we're going to be optimizing our process.
Let's go back to a familiar process, making popcorn.
And it was perfect timing, that there was a great forum posting about that.
It seems many of you love this snack.
Let's say you were simply investigating two factors.
Cooking time as factor A, and the type of oil as factor B.
And I'm going to use the number of unburned popcorn as the outcome variable.
You'll see why I chose this.
Unburned popcorn are those that have popped but not burned, the white popcorn.
We want to maximize this outcome variable, that's the objective of my experiments.
And here are the results on a cube plot.
You're experts at this now, so you can quickly see that factor B,
the type of oil, has almost no effect on the outcome.
Notice that the first objective was used here.
We have learned in our system that the type of oil over this range of
cooking times seems to have little impact on the outcome.
We've learned something new about our process.
It doesn't mean that oil type is totally irrelevant.
It simply says that over the range of A that we've used here,
cooking time seems to have little effect.
Visually, this means we can collapse our square down to
a single line as shown here.
Let's go apply objective three now and build a predictive model for the system.
Y = 90 + 15 x_A
Note that we don't have to include factor B or
the AB interaction in our model because we've determined that B is not useful.
Here is the R code.
And you will get the exact same result with any statistical software.
Just a brief recap on the interpretation of the 15 x_A term in the model.
That says, when we increase the cooking time from -1 to 0, or
from 0 to +1 in coded units, in other words, a one unit increase, then
the number of popped but unburned popcorn increases on average by a value of 15.
Now response surface methods, or response surface optimization,
uses the idea that this model can tell us where to move to next.
We're going to build on our existing experiments over here
to figure out what happens over there.
We've figured out already that factor B does not play an important role in
this system.
So response surface methods are used after you've already completed your
screening experiments.
That's an important point.
Don't include factors in the optimization that have little or
no effect on the outcome.
Then once we build a model based on they important factors,
we can now go use it to tell us where to move to next.
We can see here that we should be moving towards the right,
to increase out objective.
Now we can never expect the model to tell us exactly or
perfectly what will happen over there on the right as we move towards that region.
There is no way that this simple model summarizes all the laws of physics,
heat transfer, and
the complex chemical reactions taking place when popcorn is popping.
This simple model, also referred to by the name of an "empirical model",
is a great approximation, and provides good guidance on where to move to next.
That is what response surface methods (RSM) are about, in a nutshell.
Efficient sequential experiments to reach an optimum, using only
the important factors after you've done a preliminary screening design.