Welcome back. In this tutorial, we're going to discuss a chemical process. This will be a response surface design and we'll discuss multiple responses for this design. We have a chemical engineer that's interested in determining the operating conditions that maximize the yield of a process. There are two controllable variables or factors, time and temperature and they decide to run a central composite design. So we'll have time and temperature coded at one and negative one value. So we'll have four factorial runs for time and temperature, and then also axial values are plus and minus 1.414 or the square root of two, and then five center points, giving us a total of 13 runs for this CCD. The engineer is also interested in two additional responses; viscosity and molecular weight. So in addition to trying to maximize yield, they're trying to keep viscosity between 62 and 68 while also keeping molecular weight less than 3,400. So we'll talk about how we can analyze this design and try and keep all of these responses within their targeted range at the same time. So let's look at the design. In this table, we have our natural variables and the coded variables. We can see that the first four runs are those factorial points, the quarter points and then the next five runs are our center points, and then the last four are our axial runs with that square root two as our axial value. So we have the positive and negative for time and then the positive and negative for temperature. Then, on the right part of the table, we have all three of our responses; yield, viscosity and molecular weight. I'm going to show you how we can create this design from scratch in JMP and then, also how we can just analyze yield and then we'll bring in the other two responses and analyze all three at the same time. So let's open up JMP. So to create this design from scratch, we're going to go to our DOE menu and we'll go to Classical and we'll select the response surface design from this menu. In our response surface box here, we'll add our two or three responses. Our first one was going to be yield and we want to make sure that we're trying to maximize yield and we'll put a lower limit of 70 and we don't really have an upper limit. We'll also add a response for viscosity. We'll keep this as a match target with a lower limit of 62 and an upper limit of 68. Then lastly, we'll add our molecular weight variable or response molecular weight and we're trying to minimize this. We're trying to keep it below 3,400. So I'm going to add in an upper bound limit for that. So we have all three of our responses taken care of. Now, let's move on to the factors. We have time and our low level, our negative one coded level for time is going to be 80 and the upper will be 90, and then for temperature, our low limit is 170 and the upper 180. Make sure that we're using the coded negative one and one values and not the axial values. So I'll click Continue. Here we're going to select a central composite design. We'll select the CCD uniform precision. That means that we'll use five central points. So we'll click Continue. Our next choice for the response surface is to come up with our axial value. We've decided to use the rotatable value of the square root of two, so 1.414. You can see there's other options here for an orthogonal value or a face value, but we're going to stick with the rotatable square root two. Below here we have the number of center points as five. So we can easily change this but we'll keep it as five right now. Then, we'll keep this as a randomized run order and we can make the table and here now we have our design, our time and temperature values and then columns for yield viscosity and molecular weight. If you'll notice, there are some features for each of these columns or column properties and we'll notice that the columns are coded. So we say that an 80 is negative one and a 90 is one for time. We'll have the same idea for temperature. If we go to coding, we'll see where they're coded for negative one and one. All of our responses now have a property of response limits and we've entered whether we're going to maximize, minimize, match target and then what the values that we're trying to achieve look like. If we needed to add any of these by scratch, we can always just go to column properties and select the property we're interested in adding. So this is how we can create the design on our own. I've already created this design in a table for us, so I'm going to open that up. I have my time, temperature and then my three responses yield, viscosity in molecular weight and as I just mentioned, I have all the column properties setup. So I have the correct coding for my factors and I have the correct response limits for my responses. So I'm going to start with just analyzing yield. I go to Analyze and Fit Model and we'll cast just yield in as our y response and then I'm going to select time and temperature, my two factors and come down and use one of these macros. I'm going to use the response surface macro and this will add a response surface effect for time, a response surface effect for temperature. There are two quadratic effects and the two factor interaction. If we needed to tell JMP that this was a response surface, we could also do this manually by going to attributes and selecting a response surface effect but the macro does this for us. So this looks great and I'm going to click run and we'll see we have our fitted model for yield. We have our parameter estimates, our effects tests and we have a response surface feature now. So if I open up this, if I expand this, we can see we have our response surface solution here. Our critical value JMP tells us that the solution is a maximum and it gives us our predicted value. We also can get the eigenvalues and eigenvectors from the canonical analysis. So you see that since both of our eigenvector values are negative, we have a maximum and this is telling us that the maximum of this response service is when time is at 86.9 and when temperature is at 176.5 and this should give us a predicted value of about 80 percent yield. If we wanted to, we could also kinda figure this information out from the prediction profiler since I've set up my desirability function or basically my response limits for yield. If I click this red triangle and go to optimization in desirability and select maximize desirability, this will also give me that maximum point on the response surface to give us our 80 percent yield. We might also be interested in looking at a contour plot or surface plot. If we go to factor profiling, we can add a contour profiler and if I add my low limit maybe of 70 and my high limit maybe, let's say 78.5, we can see where these contours lie. Maybe I want to add in the 80 contour and we can see right here this is the very top of that surface. We can also look at a surface plot and this will give us a similar output. If we go to factor profiling, surface profiler and I add the AD response, we can add this grid to our surface. So we'll see that that's where we get the maximum value and we see where those values occur for time and temperature. We can move this grid through the response to see what our y is. So those are both really nice plots when we're dealing with response surface designs. So now that I have just analyzed yield, I want to say what happens if I'm interested in yield, viscosity and molecular weight. I want to try and find time and temperature conditions that satisfy all three of these responses. So I'm going to go back to analyze and fit model and I'm going to add all three; yield, viscosity, molecular weight in sy, put them all in there. I'll again add time and temperature as a response surface through this macro, giving me my main effects my two quadratic effects and my interaction. I'll run and now I have a response for yield, a model that was fit for yield. I have a model that was fit for viscosity. We can even see that this was also a maximum and then also a model for molecular weight. This was actually a saddle point. So I have all three models fit and now I can look at all three of these responses in this profiler at once. So we can see we can change time and temperature and see how that affects all three of our responses at the same time. Since in the column properties I've entered what response limits I have for each one of these and whether or not I want to maximize, minimize or match a target, my desirability functions are all set to go. So if I click the red triangle and select optimized desirability, maximize desirability I'll get a solution given by JMP. If you wanted to create your own desirability you can also just go here and set desirability. So I'm going to click maximize and it gives me a time in a temperature that gives me a somewhat high yield, viscosity within our range and molecular weight below the upper limit. So this could be a solution. However, we know that yield on its own had a maximum value of around 80 percent. So maybe the 76.7 percent is not quite as high as we would like it. Another option is to look at analyze this graphically. So we can go to the profilers and go to the contour profiler and now I can look at an overlaid contour plot of all three responses, looking at time and temperature on my x and y axis. So for yield, lets say that we have a low limit of 75. Well, we really just have a high limit. A low limit. Let's say we want to be at least 78.54 and for viscosity, how about between 62 and 68? Then for molecular weight, we'll say, we want to be below 3,400. So we can add all these contours to our plots and if we notice, there's an area of white that gives us time and temperature values where all three of the responses are met. So if we come down here, there's an area right here where all of those conditions are met and we also have one small area right here. So depending on maybe if you were also trying to perform the process in his short amount of time as possible, maybe you would select this time and temperature value for your process or maybe if you were interested in having a larger process window, you would select something in the middle of this region over here. So this is a really nice way that you can look at all three responses at the same time and try and find process conditions that meet all your criteria simultaneously. So that is how we can create and analyze response service designs and also how we can analyze multiple responses in JMP. Thanks.
