Experiments 5A - Response surface methods - an introduction
Channel: Kevin Dunn
Date: 2015-08-10

Videos used in the Coursera course: Experimentation for Improvement. Join the course for FREE at https://www.coursera.org/learn/experimentation

These videos are also part of the free online book, "Process Improvement using Data", http://yint.org/pid

Full script for the video: http://yint.org/scripts/5A
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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.

Firstly: I'm always 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 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 eliminate 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.

Then using fractional factorial ideas from module 4 and you can quickly identify which factors are actually related to the issue by running a screening experiment.

And right since the second module in this course, we've been making predictions based on our experimental results, so you're very comfortable with that idea.

Now in this section, we're going to be optimizing our process. Let's go back to a familiar system, making popcorn.

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 so you can quickly see that factor B, the type of oil, has almost no effect on the outcome. Notice that the first
objective of the five was used here. We learned in our system that the type of oil over this range of cooking times seems to have little impact on the outcome. 

It doesn't mean that oil type is totally irrelevant, it simply says that over the range of cooking times used in this experiment, oil type seems to have little effect.

Also notice that we could learn that the AB interaction is not significant. We can see that in the Pareto plots, as well as the contour plot. Visually, this means we could 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 neither factor B, nor the AB interaction is large.

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 ...