Following< Use experimental design DOE Custom design to find the best milk tea recipe >、< Using JMP split-plot experimental design to create delicious pearls > After Lele and her father found the best milk tea flavor and pearls, there were only two weeks left before her mother’s birthday. Then they hoped to find the proportion of these ingredients that her mother loved most with milk, as well as the appropriate ice cubes and The sweetness configuration gives mom a birthday surprise – give her a cup of delicious pearl milk tea.
Lele: Finally, we have to find the recipe for pearl milk tea. How do we know which flavor mom likes?
Dad: We are here to collect mom’s taste ratings without being discovered by her, so I plan to give her the experimental version of pearl milk tea one after another in the past two weeks, and not too many cups at a time, otherwise mom will Discover.
Lele: There is another big problem. We need to mix black tea, milk and pearls. The total amount of these must be a fixed amount. The experiments we did before did not have such restrictions.
Dad: You are very powerful. You have noticed this problem, so this time we have to use the help of JMP to set the constraints of this experimental design.
Lele: I didn’t expect JMP to be so powerful that it could handle this problem. Then let’s quickly ask JMP to help us design experiments!
Dad took out his computer and started JMP. He continued: Let’s first sort out the factors considered and the response results. Of course, the response result is the taste score of pearl milk tea, and the factors include the proportion of black tea, milk, and pearls, as well as the amount of ice cubes and sugar. Input these response results and factors into the custom design platform (Figure 1). However, when inputting, you can set black tea, milk, and pearls as the mixing factor (Mixture). This means that black tea + milk + pearls = 1, that is, you need to find Fix these three to add up to one cup, and find which proportion is the best combination .
Figure 1, response results and factor settings of the pearl milk tea experiment
Lele looked at the factor settings and asked her dad: Why are the settings for Bing and Tang not continuous factors, but discontinuous numerical factors (Discrete Numeric)?
Dad: Because I think it is difficult to measure the exact amount of ice cubes and sugar. Like ice cubes, I can use 1 ice cube, 2 ice cubes, or 3 ice cubes to adjust, but it is difficult to add exactly 2.5 ice cubes. Ice cube, so I first set it as a discontinuous numerical factor. In addition, I also adjusted the appropriate ranges of black tea, milk, and pearls so that there would not be too much or too little of these three ingredients.
Dad continued to press Continuous to expand the Model project, and then said: Here, because we hope to see the optimal amounts of ice and sugar, we add the quadratic terms of ice and sugar (Figure 2) to see if there is any The phenomenon of recurvature.
Figure 2: The model adds quadratic effect terms of ice cubes and sugar.
Dad then scrolled down the custom design platform to Design Generation, checked Group runs into random blocks of size, filled in 3, and entered 2 after Number of Center points (Figure 3).
Dad: Look, I filled in 3 in Group runs into random blocks of size, which means that my data is divided into many blocks, and each block contains three experiments. Because if we want my mother to test the taste of bubble milk tea, we can’t give her too much at one time for fear that she will become suspicious, so I divided it into four days and gave it to her, and then drank three experimental results each time, so that she would be less likely to get sick. suspicion.
In addition, 2 center points are specified after the Number of Center points, so that you can see the status of the center points more accurately, and select the preset number of experiments 12 times.
Figure 3, Block, center point, number of repetitions and number of experiments settings
After all settings were completed, Dad pressed make design to start the experimental design, and then pressed make table to complete the table creation of the experimental combination (Figure 4).
Figure 4, Experimental design combination generated using JMP
Dad said: Lele, look, in the designed experiment, the black tea + milk + pearls in each experiment are equal to 1, so this experimental combination represents the proportion of these three materials to make pearl milk tea, and the Random Block represents our The experiments are divided into 4 clusters, each cluster contains 3 experiments. Then we will do experiments based on this table and give it to my mother.
In the next two weeks, based on the combination of experimental tables made by JMP, my father completed the experiments in four days. He asked his mother to drink the pearl milk tea from these experiments as a treat to his colleagues, and obtained her mother's taste ratings for these experiments. .
The day before my mother's birthday, my father and Lele gathered around the dining table to find the bubble milk tea recipe that best suited my mother's taste based on the collected information.
Dad: Okay, I have finally collected the data for analysis. Next, let’s use the analysis function of JMP to do the analysis.
Lele pointed to the JMP data sheet and said: I remember you said that you can press the Model on the left to perform analysis. (Picture 5)
Figure 5. The Model script on the left can perform regression analysis based on the collected experimental design results.
Dad: You are getting better and better. You even know how to perform analysis. Yes, you just need to press this Model script to perform subsequent analysis. Then dad pressed the Model script.
Dad: Look at the starting platform of the regression analysis (Figure 6). It has taken into account the items that we previously set as model effect items in the customized design into the constructed model effect items. In addition, there is also a Random block item. , this is a factor used to confirm whether dividing the experiment into multiple days has any impact.
Figure 6, regression analysis starting platform
Dad then pressed Run to complete the regression analysis report.
Dad: First, you can see the effect summary (Figure 7). Here you can see that some effect items have P values exceeding 0.05. After deleting unimportant effect items in order, we deleted the quadratic effect terms of sugar and ice. Effect term, this also means that ice and sugar do not recurve, that is to say, the optimal formula of ice and sugar does not obviously occur at a certain value in the middle of the range. The P value of the main effect of sugar is 0.066, which is not far beyond 0.05, so it is still retained in the model.
Figure 7, regression analysis report-effect summary
Dad scrolled down the report and continued: We will then use the REML Variance Component Estimates report (Figure 8) to see if there will be any difference in collecting data on different days. It can be noticed here that the Wald p-value is much greater than 0.05. It means that different Blocks will not cause differences, which means collecting data on different days will not affect the judgment of taste.
Figure 8, Regression analysis report-REML Variance Component Estimates report
Lele: So we can directly use this result to find the best bubble milk tea recipe combination?
Dad: That’s right. Which tool should we use next to find the best combination?
Lele: I know, Profiler.
Dad: Yes, do you remember how to use it?
Lele: I know that you need to set the desired value first, and then optimize the desired value.
Dad: Yes, you are very powerful. First we can go to Set Desirability to set the desire value. For example, look at the big and small, or look at the eyes, and then Maximize Desirability to optimize your desire value, you can find the recipe settings when you want to get the best results.
After some operations, Lele ran out the result, Lele: I found it. black tea : milk: Pearl=0.6:0.2:0.2 When you drink it, mix it with a piece of ice and a teaspoon of sugar to get your mother’s favorite bubble milk tea recipe (Picture 9).
Figure 9, the best bubble milk tea recipe combination obtained using Profiler
Dad: Great, we finally found Mom’s favorite bubble milk tea recipe. Mom will be surprised and happy tomorrow when she receives the cup of bubble milk tea you specially made for her.
At the birthday party the next day, Lele's pearl milk tea was well received by her mother. While Lele was proud and happy, she also silently thanked JMP for helping him make this exclusive cup of pearl milk tea full of love. Now Try JMP for free for 30 days .
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