Experiments 5B - Response surface methods (RSM) in one variable
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/5B
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Now in this video we're going to start optimizing our process, using the idea of a response surface method (RSM) or responsive optimization.

I will say this as encouragement, more than any single other technique I use, the concept of optimization has always led to the most significant increase in profit and value in the companies I've worked with.

Students that have used the concepts from this course in their work have been promoted many times, and I still get emails from them telling me about this.

Now, full disclosure: I didn't invent any of these ideas so I don't deserve the credit, but let me try to explain them to you.

Now people have been asking about linear versus nonlinear systems on the forums. And to address the issue of repeated experiments and noise, we will look at these topics in this example. That's the idea of just-in-time learning.

Now some fair warning,this video is longer than most, but it carries a single case study through and introduces many critical concepts.

So back to the popcorn example from the prior video.

We had a single factor that affects the system, factor A, the cooking type.

And we developed the model: y = 90 + 15x_A

We said that the interpretation of the 15 x_A term in the model is that if we
increase the cooking time from -1 to 0, or from 0 to +1 in coded units,
that's a 1 unit increase, then the number of popped but unburnt popcorn increases on average by a value of 15 units.

This would be a good time to have a discussion about how we connect our
coded values over here in the model to real world values of cooking time.

The simple rule for continuous factors is that we use the 
(coded value) = (real world value) minus the (center point) divided by half the range.

In the cooking time factor here the center point is the middle, between the low value and the high value. That corresponds to 135 seconds.

The range refers to the high level minus the low level. So 150 minus 120 equals 30, and half the range is then 15 seconds. 

Let's try using this formula for the real world units of 135 seconds of cooking time. So that's 135 - 135 = 0, divided by half the range of 15,
which is still 0.

So the coded value for 135 seconds is 0.

The cooking time of 150 seconds should correspond to +1 in coded units.
And the formula shows that that's correct.

You could use the formula in the backwards direction.

What does a cooking time of +2 in coded units correspond to in real world units?

If we work in reverse, we multiply our coded value by half the range. So that's plus 2 times 15, which equals 30. Then instead of subtracting
the center point, we add it. So 30 plus 135 = 165 seconds

So here's a summary of how to go from real-world units to coded units and back again. Keep this close by. We're going to use this many times in this section.

So let's visualize this.

The actual experiments are shown here with black circles. Andd the prediction model is shown as a blue line. Notice at the low level in coded units of -1, the prediction is 75 and it corresponds closely to the experimental values of 74 and 76.

At the baseline where the coded value is 0, we have a prediction using
the model of 90 unburned popcorns. But notice, we never run an experiment actually at the base line. The model simply tells us
that if we did run one, that would be the number of
unburnt popcorn's to expect.

And at a coded value of +1, or 150 seconds in real world units, we make
a prediction of 105 unburnt popcorns. 

Now on the forums, people have been hinting and asking about the idea of whether the linear model is valid. People have been suggesting that all practical systems have non-linear behaviour.

Another way of stating that is to ask, what's going to happen as we extend our blue line prediction model further and further to the right? The blue line indicates that as we cook longer we should obtain more and more white popcorn.

But clearly that is not true.

If I cook the popcorn for longer times I would expect that I'm going to start to burn it. And this outcome variable will quickly start to decrease. Definitely not increase.

But back over here in this region on the left the model is perfectly valid.

This is a great illustration of the famous quote by George Box, who I've now mentioned several times in the course videos. 

He said, "all models are wrong, but some are useful".

He also extended that by asking: " ... the practical question is, how wrong do they have to be before they are not useful?" I paraphrased that last piece and that is exactly what we're dealing with here in the video.

Another way of looking at the issue is to ask, how do we know when the model ...