Hello, welcome back. In this tutorial, we're going to discuss a mixture experiment. Our experimenter is trying to optimize the formulation of an automotive clear coat paint. This is a mixture design and it has three components, a monomer, a crosslinker and a resin. There are several constraints on the component proportions. Obviously, we need all three to add up to 100%. So that's our X1 plus X2 plus X3 equals 100, but there's some additional constraints in that the monomer needs to be between 5 and 25%. The crosslinker between 25 and 40% and the resin between 50 and 70%. For this design, we're going to use 14 runs and for replicate points. And we'll use the D-optimal design for a quadratic model. There are some requirements for the response. The customer wants this hardness score to exceed 25 and the percentage of solids to be below 30. Here's a D-optimal design for the paint formulation problem. We have our three components,, the monomer the crosslinker, and the resin and then our two responses, hardness and solids. We can see the different component proportions for each of these treatments. And notice that for each treatment combination, for each component mixture, everything will add up to one. So I'm going to show you how we can create a design like this and JMP. And then also how to analyze this design and use the mixture profiler to look at dual responses. So let's get JMP open. Okay, to create this design on our own we can go to DOE, Classical. And now we'll select Mixture Design from this menu. Good, we'll say we have two responses. One is the hardness. And we're trying to maximize that. We want it to be at least 30. In our second response, we're trying to minimize. That's the percentage of solids, and we want that to be less than 25. And then we have our three components. We have the monomer which we want it to be between 5 and 25%. So we're going to enter this as a decimal value, so I'll say 0.05 to 0.25. For the crosslinker, our second component, the requirement was that it's between 25 and 40%. So we'll enter 0.25 to 0.4. And the last component, the resin, needs to be between 50% and 70%. So we've added in all of our constraints. So I'm going to click Continue. Okay, and we have to choose the mixture design type. Notice that some are grayed out and that's because we have this restricted constrained design region. So we're going to choose the optimal design. I'm going to add in all three two-factor interactions to my model. This will ensure that I get a D-optimal design for the quadratic model. We decided that we were going to have four replicate points and 14 runs total. So this looks good. I'm going to make the design. Takes a second for JMP to find the optimal design through its algorithm, and there we go. There's our design. This is a D-optimal design for the quadratic model for these three components using the specified constraints. So we easily can just make a table and start creating these mixtures and collecting data and analyzing this model. So I already have a D-optimal design, this paint formulation for this paint formulation problem with the monomer the cross Linker and the resin. And we'll see that if I double-click on any of these columns, I have that it's a mixture variable. And then its lower and upper limit. So if that wasn't there, we could easily go to Column Properties and go to Mixture and add this as a property. But I have them all set up and I also have my hardness set up with the response limits. We want it to be at least 25 and the solids that we want it to be less than 30. Okay, so I'm going to go to Analyze, Fit Model. I'm going to select all three components and I'm going to use the factorial degree to degree macro. So I get all three main effects in the three two-factor interaction. And notice that JMP already includes this as a mixture variable because I've already added that as a column property. If it wasn't, we could easily go to Attributes and select Mixture Effect. So we have our mixtures and we have our two-factor interactions. I'm going to add both hardness and solids in as responses. We'll click Run and we'll see that we have fit a response hardness model. And we have fit a response solids model. And then we have this prediction profiler that looks at both solids. And hardness as we look at all three components at the same time. If we want, we could select the red triangle, go to Maximize Desirability. And we can find a component, or a mixture of 50% resin, around 33% crosslinker. And about 17% of the monomer, and that would give us hardness score of 31.5. And a percent solids measurement of 16, so satisfying both the customer requirements. A nice picture to go along with this would be our mixture profiler. So if I go to Profiler, I can come down to the Mixture Profiler. And we'll see this is a photo. If we didn't have any constraints for this mixture, we would have points all along this design space. But since we have constraints on these components we have this reduced design space. So you can see these black dots are the design points from this design and we can add contours. So we want to make sure that our hardness was at least 25. And that this percent solids was less than 30. So enter both those contours. And we can see, right within this area, where exactly we have, Area of operability. Okay, so any values or components mixtures in this area will satisfy all the customer requirements. So this is a nice way we can play around and try and find out your process window. And then find the greatest component mixture for your problem. Okay, that's how we can create and analyze a mixture response with constraints and also multiple responses using JMP.
