Following the previous article Later, Dad and Lele found the formula and technique for brewing black tea through custom design. Next, the two people are going to experiment on how to make delicious pearls.
Lele: Fortunately, last week we packed up so quickly that our mother didn’t notice that we were secretly preparing her birthday present.
Dad: Yes, let’s seize the time to try making delicious pearls this week. I looked at the information on the Internet and found that there are several important factors that affect whether the pearls taste good or not, including the brand of pearls, the amount of water to cook the pearls/pearl ratio, the cooking time, the type of sugar and the amount of sugar. Soaking time.
Lele: I remember that there are water temperature control conditions when making black tea. Don’t you need to consider this?
Dad: Yes, the water temperature is the key factor for making black tea, but this time we will boil the water, that is, put the pearls down to boil when it is 100 degrees, so the temperature is always 100 degrees, there is no difference in conditions like this , we don’t need to control it, and we don’t need to use it as a factor in the experiment. In addition, many recommended recipes for boiling pearls say that the pearls must be quickly cooled after cooking to make them elastic. We regard this as part of the standard process, so it does not need to be used as a control factor.
Lele: I see, when are we going to start our experiment? Should we ask JMP to help us design experiments this time?
Dad: Yes, because the pearl brand and water volume/pearl ratio are factors that are difficult to change, so we asked JMP to help us this time Set up appropriate experiments based on the difficulty of changing factors.
Design experiments based on the difficulty of changing factors
Lele: It sounds great. JMP can also provide appropriate experiments based on the degree of ease of change.
Dad: Then I will prepare the materials for making pearls first, and you will do your homework first.
Dad prepared two brands of pearls, a cup to calculate the amount of water and pearls, granulated sugar and brown sugar, and opened JMP. After Lele finished her homework, she returned to her father and said: Are we also using customized experimental design experiments this time?
Dad: Yes, we also treat our target value, which is the deliciousness of the pearls, as the response result. The goal is the more delicious the better, that is, the bigger the better, and then we place the key factors of pearl brand, water volume/pearl Proportion, simmering time, sugar type and sugar soaking time (Table 1).
key factors
|
Data type
|
value(range/kind)
|
pearl brand
|
category
|
Brand A
|
Brand B
|
Water volume/pearl ratio
|
continuous
|
6~8
|
Simmering time
|
continuous
|
20~50
|
Sugar type
|
category
|
granulated sugar
|
brown sugar
|
Sugar soaking time
|
continuous
|
10~30
|
Table 1: Table of key factors in the pearl experiment
Dad fills in the appropriate factors and ranges in sequence on the custom design platform (Figure 1).
Figure 1, response results and factor settings
Understanding the split-plot experiment
Dad went on to say: Because we hope to cook once and then pick up the pearls at different simmering times, this can save some experimental time, so we set the two parameters of water volume/pearl ratio and pearl variety to very high values. It is difficult to change, and then we set the simmering time as a parameter that is difficult to change, and the remaining two parameters remain in their original easy-to-change state. so Set factors at different levels to perform a hierarchical experimental design, which we call a "split-plot experiment" (Figure 2).
Figure 2: Difficulty of changing adjustment factors
Dad pressed the continue button and continued: We adjust the effect term of the Model and add the quadratic term of the continuous variable (Figure 3). This can confirm whether there is a maximum or minimum value in the parameter range, that is Whether extreme values occur in the middle of the range rather than at the ends.
Figure 3, adding model effect items
Dad scrolled down the report as he spoke, and continued: In addition, because we have set the factors at two levels: "very difficult to change" and "difficult to change", under Design Generation, we can select "very difficult to change" and " Is it difficult to change? Is there an independent relationship between the two? That is, the two layers are a nested structure or a cross structure. if Tick Hard to change factors can vary independently of Very Hard to change factors , which means that the two layers are a "cross structure" , if not checked, it means "nest structure" . ( As shown in Figure 4)
Figure 4, adjust whether it is a trough structure, the number of Whole Plots & Subplots, and the total number of experiments
Lele asked: What is a nested structure?
Dad then drew a figure on the paper and answered: Nested structure, also called nested structure, is actually the next layer embedded in the previous layer, so the same combination is completed in sequence before making the next combination. For example, in the picture I drew, I started from group A, which is very difficult to change factors. After finishing the AC combination, I did the AD combination, and then moved to group B.
Figure 5, explanation of cross structure and nest structure, numbers indicate the experimental sequence
As for the cross structure, he will not complete the factors that are difficult to change in order. His order is still starting from group A, which is very difficult to change factors, but then he will create AC, AD, AC, AD, BC , BD, BC, BD in this order, you can find that factors that are difficult to change need to be crossed to complete the experiment (Figure 5).
Lele took the picture drawn by her father and looked at it for a while, then turned to her father's computer. Dad scrolled down the report and continued: We can also specify the number of Whole plots (full area) and Subplots (sub-area). I set 6 times and 12 times here. You can also choose the number of experiments. This time we keep He presets 36 times (Figure 4).
Figure 4, adjust whether it is a trough structure, the number of Whole Plots & Subplots, and the total number of experiments
Lele: Is 36 times too many?
Dad: This part depends on the actual experiment and whether the experimenter can afford it. But I think you can eat this pearl with me today. We will rate it together and use this average score as the result of the taste score. This way, It's also more accurate.
Dad and Lele followed the experimental combinations designed by JMP’s customized experimental platform and completed 36 taste ratings (Figure 6).
Figure 6, collecting experimental results
Lele: Dad, I’m so full.
Dad: Me too, but fortunately you helped me share some of the burden. We finally completed the data collection, and now we can use JMP tools to help us analyze it.
use JMP Perform regression analysis
While talking, Dad pressed "Model" in the upper left corner of the DOE table to start regression analysis. After a few actions, Dad completed the regression analysis report production. Lele took the JMP report completed by Dad and watched it for a while. Ask Dad: Why didn’t you delete the effect term whose P value exceeded 0.05 for the pearl brand?
Dad: That’s right. Did you remember to delete the effect items whose P value exceeds 0.05? However, the specification of P value is set to 0.05 as a reference value, because the P value of the pearl brand is 0.05367. Although it exceeds 0.05, it does not exceed a lot. , and the model does not consider too many effect terms, so I will keep it.
Lele nodded to express his understanding. Dad went on to say, if you look at the Effect Summary report, you can find that the type of sugar and the time of soaking the sugar are the top two. These factors will affect the sweetness of the pearls, especially the type of sugar. many. In addition, the cooking time is also a very important condition (Figure 7).
Figure 7, Regression analysis report-Effect Summary
Lele said: Yes, if you cook it for too long, it will become crumbly and not tasty. If you pick it up too quickly, it will become hard.
Dad: Right, you also feel this way from the experiment process, so many companies have many senior teachers or experienced old employees. They are well-informed, so they will know which parameters are important, but they don’t like them. Use the tools of experimental design. However, in this example, if we don’t do experiments, we still don’t know Types of sugar and Soaking time The taste of pearls is so important, so The experimental design is not to challenge these experienced employees, but to provide a way to help them examine whether there is any improvement in the current process or formula. . For this example, our goal is Find better pearl flavors .
Lele nodded in agreement. Dad turned the report to the REML Variance Component Estimates report below (Figure 8). He continued: There is another important test that needs to be confirmed. You can see that a Wald test was performed on Whole plots and Subplots here to check whether there are differences between different Whole plots and Subplots. The results are all obviously greater than 0.05, so we are more confident that Whole plots and Subplots have good effects on pearl taste. There is not much difference in the scores, and we can safely use the analysis results of the split-plot experiment to construct a model of pearl taste and parameters.
Figure 8, Regression analysis report-REML Variance Component Estimates
Lele changed the topic: But you said that the type of sugar is very important, how do we confirm which kind of sugar is delicious?
Dad opened the Prediction Profiler and continued: Lele, look at the picture of sugar types. It is obvious that the score of brown sugar is higher than that of granulated sugar. In other words, you said that the caramel flavor is cooked with brown sugar ( Figure 9).
Figure 9, Prediction Profiler
Then Dad used the function of Maximize Desirability function of the scorer to get the best parameter combination condition for pearl brand A. The water consumption/pearl ratio is about 6.9 to cook. The cooking time is about 30 minutes. After cooking After soaking in brown sugar for about 26 minutes, you can get delicious pearls with an expected score of 9.7 (Picture 10).
Figure 10, the best combination estimated by Prediction Profiler
Lele: Great, we found the most delicious way to cook pearls. I hope mom will like it.
Dad: He will definitely like it. Next is his birthday. We will combine the best black tea we made last week with the best pearls we made today, milk and some ice cubes, and maybe add some appropriate Fructose, you can get mom’s favorite bubble milk tea.
Lele suddenly thought of a question: What is the ratio between these?
Dad smiled and said: Then we need the help of the birthday girl and JMP to help us find the most suitable ratio!
Lele: I’m looking forward to it!
The next article will explain: How to use the mixture design in experimental design to make perfect bubble milk tea.
Get more resources related to DOE experimental design:
