Functional Data Meets Mixture DOE in a Food Production Case Study (2026-US-30MP-2974)

All right. Hi, my name is Curtis Park. I'm a Principal Scientist here at HP Hood. We're a food and beverage manufacturer located in the Northeast, in the New England area, but we also have a reach across the country. I'm going to talk to you a little bit today about how I've used functional data, in particular, the Functional Data Explorer in JMP Pro, when working on a tricky problem that had a lot of interesting aspects to it. We used mixture DoE, actually, to solve this problem. I'm going to give you a little bit of backstory. We had a supply chain issue where an ingredient that we were using in a food product was not going to be available. I think we had around 6 months notice. And that was because the company making the product was closing the plant where it was being made. We had a tight deadline, and so we needed to figure out what were our alternatives to this. We did some initial formulation work. We got some alternate ingredients from other suppliers making the same ingredient, but there was just something special about the one we were buying where we couldn't just substitute it one for one.

It became pretty clear to us that we'd have to take other ingredients in the formula and adjust them to make sure that this product still met consumer needs or liked by consumers. Our ultimate goal would be that the transition would be seamless and that nobody would be able to tell the difference. As a food scientist working in product development, there are a lot of different things that we have to think about. Number one is usually flavor. If it doesn't taste good, people aren't going to buy it. People won't want it. No matter how healthy it is, if it doesn't taste good, people won't eat it. Same thing with texture. Texture is also very important. But we also have other things to consider. We have to consider the label, the food ingredient declaration, the Nutrition Facts Panel, making sure that we're in compliance with state, local, and federal laws. But also, we have to think about cost, like everybody does. There's another aspect that we're going to talk about is we have to be considering, how is this going to be made? How can we scale it up to make sure that we can make it consistently and safely?

This is where we're going to focus today. I'm showing you a picture of this gentleman here. The question is, well, who is he? What does he have to do with this talk? Well, this man is Louis Pasteur. Louis Pasteur was very famous for having discovered that it was microbes that were spoiling food. At the time, I think the general consensus was there's just something in the air, the miasmas, that was causing food to spoil and other things to decompose. But Louis Pasteur actually discovered it and proved that it was microbial life that was causing spoilage. As a result, he actually developed his own process to be able to prevent spoilage in food products. This process involves heating food products to kill those spoilage organisms so they no longer will spoil it. In honor of his name, we have a process called pasteurization. It's been in the dairy industry for over 100 years now, but it's basically what we're doing is we're heating product up, we hold it for a certain amount of time, and then we cool it back down.

If we think about, let's just say, milk as an example, you have your raw milk, it'll be preheated to a certain temperature. Well, just to make up a number right now, we'll just say like 130, 140 degrees Fahrenheit. In a typical milk processing facility, they would then flow through a homogenizer, which I like to think of homogenizer like when you take your garden hose and on the end, open-ended, and you stick your thumb on it, and you make the hole go from really big to really small, and how it squirts out much, much faster. We're doing that to milk, and the purpose of that is so that we can make the little fat droplets even smaller so that they won't rise to the top and separate. After we've homogenized, we go through a final heating step. This is where we get to the right temperature to be able to kill the spoilage organisms and pathogens and make the product safe. You have to hold it for a certain amount of time once you get to that temperature. We have this holding tube part. Then we can finally cool it back down to the refrigeration temperature, let's say less than 40 degrees Fahrenheit, in between 32 and 40. This process is actually really interesting in that about 90% of the energy that is used to heat and cool the milk in this process is conserved.

How is it conserved? Well, we use what we call plate heat exchangers. They're all over the dairy industry, food industry, many, many different industries. Because they're so efficient. What happens is you have a series of metal plates, stainless steel plates, that are stacked together. On one side of the plate, you'll have hot product or hot water, depends on where in the process you are. You have hot product that is on one side, and then you have cold product on the other side. What happens is the cold product is cooling down the hot side, and the hot side is heating up the cool side. You're conserving that energy. These heat exchangers are very important to our process. Here's a picture of one. Now, if the product that we're trying to pasteurize is too thick, let's say, we can have issues. It'll create too much pressure in here. Because as you can imagine, if you're flowing really fast through small gaps in these plates, you'll get too much pressure, and the gaskets can start to fail, and you can get product leaking out in between the plates. That's not good, as you can imagine.

Not only makes a mess, but it also could be a safety concern if you have hot product being squirted out at the same time. What can we do about this? Well, we have to make sure that the pressure does not exceed a certain threshold, and we know that the gaskets will not fail. When we were doing our formulation work, we needed to find a sweet spot for this product where the viscosity is high enough for consumer appeal. This is a key characteristic of the product that it be thick enough to where it's got the mouthfeel and consistency and whatever what have you that I'm used to. But at the same time, we don't want it too high where we can't pasteurize it consistently and safely. We have to find that sweet spot like Goldilocks. What we did was we used a mixture DoE to understand what formulations did we have that were available. The design that we chose, there were three factors. We used a subset of the overall recipe or formula because we knew that there were a few ingredients that would be more important than others, and we were able to actually let them vary between 0 and 100%.

Now, this is not 0 to 100% of the whole formula, this is just of a scaled-down portion of the formula, and then we'd apply our factor later on to know exactly how much to put in the final formula. This is a picture of the design. If you're not familiar with ternary plots, we have X1 on this bottom axis, X2 over here on this diagonal over here, and X3 on the diagonal on the right. All these correspond to 100% and so on for each of these. That was the design that we chose. There were other designs. What were we going to measure? With our pilot scale pasteurizer that we have, we can measure the pressure in these two green areas. We can measure it at the holding tube, and we can measure it at the final cooling section. We can also measure the viscosity after we have pasteurized the product and put it into a container. These are not curves, right? These are just single points, but we can get at least some information from them. But how could we get more information? We have what's called a rheometer in our lab that allows us to mimic this pasteurization process while measuring the viscosity the entire time.

You can think of it as like a mini lab scale pasteurizer, although that's not what it's designed for. It certainly can do it. What this does is it actually generated for us some curves, because we're constantly measuring viscosity while things are happening, while the temperature is increasing and while time is increasing. We can get curves, maybe something that looks similar to this, where this is just one of the treatments. We have I'm just showing you the entire sequence, and I'll show you there are a few other ways to look at this, which we'll get into in a second. On the x-axis, this is just time throughout the pasteurization process that we used on the rheometer, and on the y-axis is the viscosity. Then I colored this based on what the temperature was at that time. You can see if we go track this from the beginning to end, we're colder, and as it warms up, viscosity goes down. This should make sense to a lot of people, whereas things get they get hotter and they get thinner. But in this product, up until a certain point where we reach a certain temperature, and then the viscosity starts to increase.

We have things happening. The interactions between food ingredients are happening. That's really what we want to capture. We want to understand how do these three ingredients that we're changing, how do they affect these flow properties. Then as we hold it at that certain temperature, and now we start cooling it, as you can see, as it goes to the right, and we get colder and colder, viscosity shoots way up. We started down here, and we ended way up here, same temperature. What we want to understand is what influence do our DoE factors have on these flow curves. I'm going to get out of PowerPoint here. We're going to go into JMP. We'll start by just analyzing the data as is like we traditionally would. We have our treatment, these are our factors, and then our responses. I had already made some prediction formulas. What we can get out of this is I would start with a graph to look at first. And this should make intuitive sense, but as the back pressure increases, viscosity of the resulting product increases. That makes sense to us. It's nothing too new there. The reason why I show this is because not all data points are following that line.

It's not just a straight line. We do have something like this point over here where we had low back pressure, but high viscosity. That's like the sweet spot. That's the gold that we're searching for here. How does that happen? Because I had already made prediction formulas and saved them as a column, anytime you make a model, there's a red triangle option to save columns, the prediction formula. I have the prediction formula for back pressure, prediction formula for viscosity. Now, we can take that same ternary plot and apply a contour formula where we can see what the back pressure is given our three ingredients, one, two, three. You can see we have… This is what I'll call our danger zone in red. This is where we need to stay out of. As it gets more and more blue, that's a really good place to be. But then if we also look at viscosity, it looks a little different. Where in this case, the red zone is where we want to be when we're talking about viscosity. Let me pull that back up. If we can find an area where the viscosity is high, but the back pressure is low, well, maybe we have something.

Then we did locate this, and it's pretty easy to find right in this area. That's good. But what else can we understand from the rheometer testing that we don't understand by just looking at one data point? That's where we're going to go next using the Functional Data Explorer. Okay, so this is what the data comes in for us. We have X1, X2, X3. These are just the factor settings. Action name, just like what I showed you before for the different aspects of a preheat of the pasteurization process, I made some action names where it's preheating, and then there's a homogenization step, which I don't have included here, but then we go to the final heat, there's a hold time, and then there's a cooldown section. We'll get into these last two actions later, but just to show you what the data looks like, we're going to really use temperature and shear viscosity over here. What do these curves look like? If I just plot temperature versus viscosity, this is what you get. It loops around itself because we started at a low temperature, and we ended at a low temperature. If we follow these purple dots, we're going through the preheat section, and then here's the final heat section in red, the hold time is in green, and then the cooldown in blue.

If I cycle through these, you can see that based on how we changed these formulas, it made drastic changes to the final profile that we see, which means that these will give much different profiles in back pressure in our production system. We want to know, what are these individual ingredients doing, and are they all doing the same thing? We could do the Functional Data Explorer for the curves as is using time as our x-axis and viscosity as the y, but there are some limitations. I'm not going to go through what model to choose or how to choose it because, to be honest, I'm not an expert in that area. I know that what I'm going to show you makes sense from a scientific standpoint and that the models functionally work for what I'm trying to do. Could there be a better model? Probably, maybe. But in this case, I used B-splines. Down here, if we look at the profiler, I'm now able to change the amount of X1 and see what is the result on the overall curve. Our curves, remember, time on the x-axis, viscosity in the y, is not as useful to me right now because I don't know at what time was what step, what was happening during that time.

I'm just showing that just to show that that is one way to look at the whole curve. We ended up needing to do this a little differently, because I'll show you, if I did the Functional Data Explorer, where temperature is really the X that I want, and the shear viscosity is the Y, we put our treatment as our ID function, and then our supplementary here are our three factors or three ingredients. If I run this, and I'm going to filter out the shear rate action names. Now, this is my family of curves. They're not They're not something that, at least I know how to model, because they're not in continuous form. Just as an example, if I tried to model this with a B-spline, it doesn't know what to do because it can't make a loop-de-loop like this. I'm just going to do that just to show you why I actually split this up by action name. Then, if we look at the data, we can see we're going to start in the preheat section. It turned out that some of the curves that made a lot of sense to me that seemed pretty simple was using direct functional PCA, but there are a lot of options in there.

If we now look at our resulting curve, I'll make this a little bigger down here. Here. This is our preheat. We start up here around 32-ish center poise. As I decrease the amount of X1, and in this case, it was just increasing X2, you can see how that decreased. I increase X1, it increases. If we look, I can see a lot of I can do a lot of options to see what happens when I change these different ingredients. For us, for the preheat, what I'm most concerned about is that it's not too thick, because of the type of pumps that are used to pump the raw product, I know I don't want it too thick. We can handle thick elsewhere in the process, but at the very beginning, I want it thinner. I now know that X1 contributes to thickness right here. Maybe one thing you could do with the desirability, if I just say I want to maximize the shear viscosity at this point, it's pretty obvious. It's saying actually X3 is the way to do that, which does make sense to me. If I wanted to minimize to understand what might go on, now it's saying, okay, use X2.

But obviously, this is just one piece of the puzzle. That's preheat. What if we go into the heat section? Now, what I notice, okay, there's some almost like an activation energy, a temperature at which things start to happen. It looks like somewhere around 170 to 175, things start to happen. They start to happen more when I add more of X1. Then, what if I add more of X2? X2, it tones the whole thing down. X3 brings it up, but it flattens it out. I can understand in that final heat section in the plate in the plate heat exchanger, if we're trying to minimize back pressure in that particular section, then it looks like our solution probably lies with a formula that has X2 and X3. But once again, that's not everything. We're not going to do the hold, because that one temperature no longer makes sense to be our X, it actually needs to be time. I'll show you that one in a second. We'll look at the cooldown section, where if you Now, this is where typically more of the pressure is going to be built because the product is thicker in the cooldown section.

I wanted to I want to understand what is really driving the viscosity here at the end. Because now, remember, this time we're going right to left during the process because we're going from a high temperature to a low. You see right away with the shapes of these curves, X3 seems to lower that, which it does quite a bit. X2, on the other hand, increases it to a certain point along with X1. There's some synergy in between those. We didn't go over that, but that does happen. If we're trying to minimize that, we can understand how this behavior happens as well. This is really interesting because X1 increases the viscosity in the heat section, but not really in the cooling section, whereas X2 is the opposite. The more we use it, it doesn't really do much in those other two sections, but once it's been heated and cooled, all of a sudden, it goes bananas. This is the important information for us to know in the future, what options do we have, what could we do. Now, there are plenty of other things at play in the formulation. This is one aspect of it, but we definitely gained some really critical insights into how to make this work to where we don't have what they call blowing the press or just squirting out because the pressure is too high.

Looking at the hold tube, once again, this is just time now. I'm looking at just during the hold tube section. This was an interesting insight. We noticed, so if you notice as I use more of X1, it increases in viscosity with more time, but if I, let's say, use more of 2 and 3, not so much. We don't really gain anything by holding it for a longer time. That's a key insight because we could offer opportunities to process it a little differently, shorter time, whatever, if we found the right formulation. Once again, this is just giving you insights on what you can get when you use functional data instead of just looking at a single point. Just to wrap up this data exploration, I'm just going to show you the more you look, the more curves you find. We also generate just a bunch of lines. If you were to plot the shear rate, so this is We did our pasteurization process, and then we measure the viscosity at different shear rates. Think of it as different amounts of force. You could think of it and see how thick is it when you apply different amounts of force.

When we do this, typically, even in rheology, you're plotting log-log plots, so log shear rate versus log viscosity. You get these nice straight lines. Here's another type of curve that we could look at. I did a fit just to show how changing, and this is of the resulting product at the end, how changing the amount of the ingredients, once again, changes not only the slope of the line, but also just a few other characteristics. I did try modeling, fitting regression lines to all of those individual lines, and then using the coefficients for the slope and the intercept and then modeling those with the mixture DoE, and it didn't really show me a whole lot. Whereas using the Functional Data Explorer just like this, I can easily see what each of these has, how they affect the final flow properties. We use these to understand where we need to go. We can also put in a target flow property of maybe our old product, the existing one before we had to make the change, so that we can then match it. One last example of curves, at least in the realm of rheology. I don't know what happened there, but I'll show you.

If we plot the shear rate and the shear stress by treatment, and we are just looking at this particular example, this particular action, now we have another generation of curves, and these actually follow the power law model, so they should fit well. They give us information on how shear thinning is the product that could be important for us for a variety for a variety of reasons. Is it shear thickening? The vast majority of food products would be shear thinning. This is just another type of curve I could easily model in the Functional Data Explorer as well. With that, I'm going to conclude with a few final thoughts. I can't say enough about using the Functional Data Explorer. It's a very useful tool. I really like the fact that it's named Explorer because it does really allow you to explore the data, and especially when you have DoE along with it, you're able to understand how are all these factors contributing to what the curve looks like.

At the end of the day, because we could simulate our process on the rheometer, we gained these insights that we couldn't get otherwise. At the end of the day, we did find a solution that worked, that got us what we needed, and we were able to have a smooth transition and keep customers happy. I thank you for listening to the talk, and I hope that you got a little more insight into the Functional Data Explorer and get excited to find more curves. Thanks.