Lele, a lively and cheerful 5-year-old boy, is worried about his mother's birthday gift. He and his father discuss what birthday gift to give to his mother.
Dad mentioned that mom likes to drink hand-cranked drinks, so Lele thought of making bubble milk tea for her mom. However, his father reminded him that the key ingredients for making jelly milk are not easy to find. Dad explained that the trial and error method takes a lot of time and the results are uncertain. Dad further proposed using JMP to conduct experimental design to find the pearl milk tea flavor that Mom likes in a more effective way.
Lele: Dad, Mom’s birthday is coming soon. I want to give her a gift, but I don’t know what I should give her so that she will like it.
Dad: Mom will be happy with whatever you give her.
Lele suddenly thought of it and said: Mommy likes to drink hand-cranked drinks, or should I make her a cup of pearl milk tea?
Dad: Yes, but do you know how to do it? For example, what is the temperature for brewing black tea and how to cook pearls?
Lele: I can’t, please help me.
Dad: There should be these production processes on the Internet, but there should be less key information on the Internet such as what temperature and how long to cook it, and everyone has different preferences. Since we want to give mom a special birthday gift, we will give it a special birthday gift. How about making her a cup of bubble milk tea just for her as a birthday gift?
Lele: Okay, but how do we find the flavor she likes? There should be infinite flavors in the world. Should we make infinite cups?
Dad: Yes, the method you mentioned to try all the possibilities is the so-called exhaustive method or trial and error method, but this method will take a long time and may not necessarily allow for comparison. Good recipe combination. We should use JMP for experimental design.
what is JMP experimental design ?
Lele: What is JMP? What is experimental design? It sounds like engineers doing experiments. It feels so awesome!
Dad: JMP is a software that contains many statistical analysis functions, and you are right. One of its powerful functions can help us design efficient experiments. Moreover, JMP's experimental design can also set the type and range of factors according to your needs, add the effect model you think is possible and the number of experiments you can perform, etc. to help us construct the optimal experiment within the capabilities available.
Lele seemed not to understand, and her eyes drifted to the unfinished Lego tree house.
Dad went on to say: All in all, we just need to tell him that we What are the options for black tea bags, the range in which the water temperature can be controlled, the desired time range for making tea, and how many experiments we want it to do, and it will help us design the experimental combination. oh.
Lele: Oh, I understand, just like when we go out to play, Just like using driving navigation to help us design navigation routes, telling him where we want to go and where we are now can help us design the best path. .
Dad: That’s right, but the navigation usually knows our goal, is it to take the least time? Or take the shortest path? It will give me the most recommended combination according to the needs. What we need to do now is In the early stage of data collection, use the set number of experiments to consider all possibilities as broadly as possible and collect its results. Then use these data to calculate the model and get the best prediction .
Lele: So now we are like driving navigation engineers, using JMP to design experiments for analysis, and then using the observed data to find out how to reach the destination the fastest?
Dad: Yes, that’s it. Let’s start our experimental design using JMP now, Pearl Milk Tea Engineer.
Lele and her father decided to use JMP's Design Of Experiment DOE (Design of Experiments) function to find out how to make delicious black tea.
Dad: Let’s find the recipe for making black tea first and see what are the important influencing conditions.
Dad: Let’s check the recommended methods of brewing black tea on the website. First, find out which are the key conditions that affect the taste. With the recommended condition settings, we can narrow the scope of our experiment.
Therefore, Dad and Lele first found the appropriate tea steeping temperature and soaking time, as well as the recommended water/tea volume ratio based on the information on the Internet. In addition, Dad found two brands of tea at a nearby store, and chose tap water or mineral water as the water for making tea. All key parameters were organized as follows (Table 1):
parameter
|
Data type
|
value(range/kind)
|
black tea brand
|
category
|
Brand A
|
Brand B
|
tea water
|
category
|
tap water
|
mineral water
|
Water volume/tea volume ratio
|
continuous
|
20~60
|
Soaking temperature (⁰C)
|
continuous
|
70~100
|
Soaking time(m)
|
continuous
|
5~20
|
Table 1, key parameters and ranges of black tea
After searching for the required key parameters and parameter ranges, Lele and her father returned to the living room and sat down.
Lele: Can we start making black tea now?
Dad: Not yet, because we still don’t know the actual values of the parameters that need to be set for each experiment. We also need a little helper to help us design the experiments.
Dad: We need JMP to help us design the combination of experiments.
So, my father opened the JMP statistical software on the computer.
What is a custom experiment Custom Design
Dad: Look, if we need JMP to help us design experiments, you can click on the "DOE" field on the menu option. There are many DOE methods that can be used and related DOE functions. If you don’t understand the principles behind each DOE and the applicable objects, I suggest you use custom design, that is, customized experiments, as a starting point.
Lele: Why use this customized experiment?
dad: The rationale behind customized experiments is Optimization experiment , he will suggest us the best solution based on the conditions we give him, including the key conditions we think are important, whether these key conditions affect each other, what kind of results we want to get, how many experiments we can do, etc. Experimental combinations.
Lele: Just like navigation.
Dad: The advantage of this is that it is very suitable for ordinary people like us, who don’t know much about DOE, but want to do a good experimental design.
Lele: I will become a DOE expert in the future. I’m just a kid now, so I can’t. When I grow up, I will.
Dad: Okay, okay, but even DOE experts often use customized experiments as the entry point for experimental design if the goal is to design the most effective experiments. So let's take a look now with a custom experimental design.
Use custom experimental design to set parameter names, ranges and number of experiments
Then dad input the parameters and range into the custom design platform (Figure 1).
JMP Custom DesignJMP Custom DesignJMP Custom DesignJMP Custom DesignJMP Custom Design
Figure 1, input response results and parameters into the custom design platform
And add the main effect of the parameter, the quadratic term of the continuous parameter and the effect term of the cross term of the continuous parameter into the model (Figure 2).
Figure 2, input the corresponding effect items into the model
Lele: What are quadratic terms and cross terms, and why should we add them?
Dad: The reason for adding the quadratic term effect is to confirm whether the key parameters will have a recurvature phenomenon, that is, there is a value in the middle of the range that will cause the result to produce a maximum or minimum value. The purpose of adding the cross term is to confirm whether these parameters will have a multiplicative effect on each other, that is, in addition to the main effect of the parameters themselves, certain conditions will have additional effects when combined.
Lele saw the picture below and asked, Lele: Is this setting how many experiments we have to do?
Figure 3, center point & number of repetition settings and input of number of experiments
Dad: Yes, here we can set whether to add repeated experiments or whether to add center points to the experiments. The Number of Runs below can select the number of experiments. The minimum number of times written here is 12 times (Minimum). JMP recommends It is 16 times (Default). You can also set an affordable number of experiments (User Specified). We still use the default 16 times (Figure 3).
Lele: Why 16 times? Isn’t the more times the better?
Dad: Yes, but usually due to lack of time or money, we have a preset number of experiments that can be performed. This is also the advantage of customized design. Customized design can design experiments according to this requirement, while other experimental designs must achieve the specified number of experiments. Another important reason is that you can't drink tea, so I have to drink these 16 cups. Dad is already tense after drinking 16 cups. If he drinks a few more cups, he may not be able to sleep at night.
Generate parameter combinations for making black tea and complete data collection
Lele and her father then completed the custom design and produced the parameter combination for making black tea (Figure 4).
JMP DOE參數組合JMP DOE參數組合JMP DOE參數組合JMP DOE參數組合JMP DOE parameter combination
Figure 4, Experimental combination table
Then Dad and Lele completed the experiment according to this parameter combination table. Dad scored in sequence and completed the 16 scoring results (Figure 5).
Figure 5: Collect the corresponding experimental combination results
After drinking too many cups of tea, my father burped and said: We finally completed the data collection for the experiment.
use JMP Fit Model Perform regression analysis and make model predictions
Then, we can click "Model" in the script storage area on the upper left to do subsequent analysis. JMP is very considerate to help us package all subsequent analysis in this program, that is, we can directly exist JMP Fit model on Platform to perform regression analysis , we can directly press "Model" on the DOE table to analyze (Figure 6).
Figure 6, Model script on the DOE Experimental Portfolio Information Sheet
After pressing "Model", my father continued: Here we can choose whether to add effect terms to the model and choose an analysis method. We will use "Stepwise" Method please JMP Help us pick the right model (Figure 7).
JMP Fit ModelJMP Fit ModelJMP Fit ModelJMP Fit ModelJMP Fit Model
Figure 7, regression model starting platform
After several mouse clicks, Dad completed the report (Figure 8) and pointed out the Effect summary and summary of fit results on the computer with his finger.
Dad: I excluded some items with effect terms p-value exceeding 0.05 from the model in order to obtain a more accurate model, because statistically speaking, if the P-value exceeds 0.05, it means that the effect term has little impact on the model. Have you retained this? There is no difference in the effect terms. in addition, can be seen Summary of fit Here we talk about the accuracy of the model (R-square) Reached 0.997 , which means that this model has a strong ability to explain the sample points, which means that this model is a good prediction model for these data. .
JMP Fit ModelJMP Fit ModelJMP Fit ModelJMP Fit ModelJMP Fit Model
Figure 8, regression model analysis report
Lele looked at it and said: Why is the P value of the soaking time greater than 0.05 but not deleted? And there is an upward indicator next to it.
Dad: Because there are other sub-items that must be retained in the model, you can see that soaking time * soaking time is less than 0.05. This item needs to be retained. As its parent item, soaking time also needs to be retained, and this upward indicator It is telling you which parent projects have such problems and must be retained.
Dad continued to scroll the mouse wheel, displaying the lower half of the report.
observe Prediction Profiler Report observed changes in results for each parameter
Dad continued: We went down to find the report Prediction Profiler( scorer) Report , the model is presented here with interactive pictures, which can help us understand more quickly How will each parameter change affect the taste? . You can see the name of the parameter below. Its axis (X-axis) represents the parameter value we set, and the axis on the left (Y-axis) represents the predicted value of the flavor score. If you want to know the scores of different conditions, you only need to adjust the parameter values below to the values you set to get the predicted taste results. For example, I choose tea A, brew it with tap water, and the amount of water/amount of tea leaves The ratio I choose is 40, the soaking temperature is 80, the soaking time I choose 15, when I change it like this...you see, forecast result It came out, with only 4.83 points (Figure 9).
JMP Prediction ProfilerJMP Prediction ProfilerJMP Prediction ProfilerJMP Prediction ProfilerJMP Prediction Profiler
Figure 9, Prediction Profiler
As his father talked, he dragged the mouse to change the parameter settings. Lele's eyes widened, as if he felt incredible.
Lele: It will directly change the predicted taste score on the picture based on your adjustments. It’s so cool.
Dad: Yes, this interactive function is easier to operate and makes it easier for everyone to understand the model. Let’s take a closer look at this graph. In fact, this graph can roughly tell you which direction to adjust to get a higher taste score, which means it tastes better. For example, let’s look at the first tea leaf picture, B Tea is better than A Tea leaves are high, you can know B Tea has a ratio A The trend of delicious tea ,Similarly, Tea brewed with mineral water tastes better than tea brewed with tap water ,as well as Soaking time is approx. 10~15 It will taste better in minutes , for you to play with.
JMP Prediction ProfilerJMP Prediction ProfilerJMP Prediction ProfilerJMP Prediction ProfilerJMP Prediction Profiler
Figure 9, Prediction Profiler
Lele couldn't wait to start setting various parameters. After playing with it for a while, he raised a question.
Lele: Dad, look, when I change the ratio of water volume/tea volume, other parameters will change accordingly. Some will become higher or lower as a whole, and some will change their shape slightly. It’s so strange.
Dad: Hey, you are very powerful. You have noticed this small change. These small changes come from Effects of adjusting parameters , so other parameters will rise with the same shape. If you find that as the original parameter value changes, the shape of other parameters has obvious changes. For example, the original left upper right and lower right becomes the left lower right upper, which means that the The impact of cross-terms is powerful. In addition, you can see that the trend lines of some parameters are not straight lines, but curved lines. If there is a maximum or minimum value, it means that the effect of the quadratic term is very high.
Lele nodded in understanding, and then asked: So can I predict all possible results in this way?
Dad replied: This is a good question. What we have just done is to ask JMP to provide us with an estimated model based on the data we collected. However, these data are based on broad and uniform points within the range we defined at the beginning. Try to look at the performance of each point in all ranges as much as possible, but for parameter combinations outside the range, the prediction ability of this model will be poor, so we try not to make predictions outside the original experimental design range. But for within the range For most of all parameter combinations, we can use this model to predict an accurate outcome.
Next, we have to do today’s key steps: Find the best combination of parameters and conditions , you can adjust the parameter settings on the scorer and see what combination you find that gives you the highest score.
Lele nodded, and there was another round of parameter setting adjustments on the Prediction Profiler.
exist Prediction Profiler , find the best parameter combination
Lele: Dad, I found one with a score of 9.47. I chose tea B and brewed it with mineral water. The ratio of water volume/tea volume was 60, the soaking temperature was 89.5, and the soaking time was 11.9. The result is a taste score of 9.47, which is very good. That's awesome.
Dad: Not bad. It’s already very high. Do you think there will be a higher score?
Lele: Maybe, because I haven’t set all of them to see his scores.
Dad: This is the time to show the magic of JMP. You see, I can open set desirability on the JMP Prediction Profiler and set goals. For example, the higher the score on this topic, the better. Then we can choose Maximum To set the result as large as possible, that is, the bigger the better . and use Maximize Desirability function to find the best parameter combination to achieve the goal (Figure 10). Or choose Maximize and Remember to find the best parameter combination and record it in the report.
Figure 10, (left, middle) Set Desirability sets the desire value function, (right) maximizes the desire value Maximize Desirability
Dad presses Maximize and Remember on the Profiler to quickly find the best parameter combination and record it in the report (Figure 11).
Figure 11, Maximize and Remember results
Lele: This is too fast and convenient!
Dad: Yes, Usually data analysis takes the most time to collect data. JMP It can save more analysis time, so many companies that need to use data for statistical analysis will use this software to speed up analysis time. . In fact, comparing the parameter combination you obtained manually is only a little bit different from the best combination, you are also very good. In addition, continuous parameters, such as soaking temperature, 91.02894, are actually not easy to control. Maybe we can use 91 or 90 to replace the setting.
Lele and her father then discussed the setting of each parameter condition. Finally, they used B tea, mineral water, the ratio of water volume/tea volume is 55, the soaking temperature is 90, and the soaking time I chose 12.5, which is the final key parameter condition setting. (Figure 12).
Figure 12, the best prediction results based on the experimental design
Lele: Yeah! So shall we make milk tea and pearls next?
Dad looked at the time and then said: Mom will be back soon. If we want to treat it as a surprise for Mom's birthday, let's put away the experimental equipment quickly or we will be discovered. We will experiment with milk tea and pearls next time to find a good formula combination. This will apply other DOE techniques.
Lele said happily: "Okay, let's collect it quickly. I'm looking forward to it."
Dad and Lele rushed to clean up the experiment before mother came home, but a small DOE seed slowly sprouted in Lele's heart.
>>The next episode will share how to make delicious pearls through the JMP DOE experimental design platform. <<
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