When you analyze the data, what is the first step?
Do you use the powerful interactive JMP Graph builder for visual analysis?
Or use JMP's Distribution platform to do narrative statistics analysis?
Or use JMP's various predictive modeling tools to find the most appropriate predictive model?
Although these are all popular JMP functions, as the first step in using JMP analysis, in addition to the above platforms, you may wish to consider using Explore Outliers and Explore Missing Values. ) Platform, clean and organize your information.
Maybe you think it is understandable to explore the missing value, after all, it is more reasonable for the subsequent analysis to cut the null value first. But why do we need to exclude outliers? If such outliers represent the status of the data matrix, will it affect our analysis? Moreover, outliers are difficult to catch, can't we ignore this effect first?
To clarify these issues, we need to know what outliers are.
What is an outlier?
Let's discuss the one-dimensional situation first, and randomly generate 1000 standard normal distribution Nor(0, 1) values, as shown in Figure 1. The red points are marked as outliers beyond the range of [-4,4]. The probability of occurrence is 0.0063%, which is a very small probability, so the point that occurs in such a small probability area is regarded as an outlier.
Figure 1 A randomly generated normal distribution point map
Then we look at the situation of two variables, using Graph builder to analyze, regardless of whether the data points have the same mean and variance between the two variables (X2 vs. X1) or have different mean and variance (X3 vs. X1), as shown in Figure 2 below, we can see with the naked eye that these outliers (red dots) seem to have a different trend from other points and are far away from the center point of the data.
Figure 2 (Left) Scatter plot of 2 variables with the same mean and variance (right) Scatter plot of 2 variables with different mean and variance
And when there is a strong correlation between the two variables, it can also be found that some outliers are farther away from other sample points (red dots in Figure 3). In addition, using the histogram boarder function of the Fit Y by X platform to observe the distribution of the two variables (Figure 3), we found that if we only focus on a single variable, we will not be able to detect some outliers. As shown in the figure below, this is also a A good example shows that when we consider the outliers of multiple variables, we will catch some potential outliers to avoid the misjudgment of only observing and controlling a single variable. Fortunately, JMP provides such a multivariable outlier observation platform.
Figure 3 Scatter plot with strong correlation between two variables
At this point, we can understand the concept of outliers, which is to find out points that are farther from the center of the sample than other sample points, or where the location of the point does not match the overall "trend" of the sample. Interestingly, outliers do not represent problematic points, but rather represent gaps with other samples without the same "trend". Therefore, outliers may represent problematic people in a good society, or they may represent a clear stream in the evil city, depending on where your sample comes from.
Make good use of JMP to analyze WAT data and solve semiconductor process problems
Having said that, we use a semiconductor manufacturing electrical test data as an illustration.
The component parameters of semiconductor wafer manufacturing have their corresponding electronic characteristics. Therefore, the quality of the corresponding process can be inferred through the results of electrical testing of these parameters. Wafer foundries generally call electrical parameter testing called WAT (Wafer Acceptance Test), and their customers need to review WAT test data to confirm manufacturing quality. In the new process research and development stage, it is necessary to collect a large amount of WAT data to solve process problems or find the optimal factor configuration.
We use a set of simple WAT data as a demonstration, which contains 10 observation parameter data. When we directly analyze the data of production line 3, using the Analyze>Distribution function, we can make the corresponding histogram and Outlier box plot to observe whether there is a deviation. The group value, as shown in Figure 4 (left), the red line on the Outlier Box marks the most concentrated area covering 50%, from here we can find that the data is concentrated in the middle section. Similarly, you can also use Graph Builder's histogram function to complete the histogram drawing, as shown in Figure 4 (right).
Figure 4 (left) Histogram of Distribution platform; Outlier box plot (right) Box plot of Graph builder
According to the Quantile Range outlier test, we found that there is an outlier (red dot) in parameter 1. The outliers can be found by using the Quantile Range Outliers function in the Analyze>Screening>Explore Outliers platform of JMP (Figure 5), and The data can be marked, excluded, and regarded as missing values.
At the same time, you can also adjust the rules for determining outliers, you can adjust the tail quantile value (Tail Quantile) and its multiple (Q), with the common IQR outlier test, the upper limit is Q3+1.5*IQR, the upper limit Take Q1-1.5*IQR as an example, Tail Quantile is 0.25, and Q is 1.5. And when your data is less in line with the normal distribution, you can consider using Robust Fit Outliers as an outlier screening platform.
Figure 5 Quantile Range Outliers in Explore Outliers platform
But when we consider more comprehensively and include the data of all production lines, you will find that production line 3 has a higher parameter 1 test result, as shown in Figure 6. The original outlier value of 8.01 on production line 3 is more consistent with most of the data. The actual outlier values are converted to the three highest values of production line three (red dots in Figure 6). This result also echoes the importance of the source of the aforementioned samples, and extensive access to representative maternal data is correct for screening Outliers play a pivotal role.
Figure 6 Box plot of all production lines
When considering the influence of all parameters and finding outliers under the influence of all parameters, JMP also provides Robust PCA Outliers or K Nearest Neighbor Outliers functions for you to use. You can find these two functional platforms under Analyze> Screening> Explore Outliers. Here, use the K Nearest Neighbor Outliers platform to find outliers, and use compound to select sample points with higher distances and mark them as outliers (Figure 7).
Figure 7: Distance map under K Nearest Neighbor Outliers platform
Using Graph builder to confirm the distribution position of the data points selected as outliers on each parameter, it can be found that not all points belong to the outliers of a single parameter (such as data points 290, 295, 296, 297, 298). , 299), this result is also the same as mentioned above. With JMP's multivariate outlier screening platform, many potential problems that are ignored under observation of univariate can be caught (Figure 8).
Figure 8 Use Boxplot to compare the distribution of outliers on the variables
Remove outliers and construct a more accurate prediction model
We know that JMP has a good platform to help us filter out outliers, but what impact will it cause if we don't filter out outliers? To simplify the complexity, let's first look at the influence of outliers between the two parameters.
We observe the R-square value estimated by the second-order effect regression between the first-level parameter and the second parameter of the WAT data. Before removing the filtered outliers, the R-square value is 0.602, as shown in Figure 9(a) , And after removing the outliers, the R-square value rises to 0.740, as shown in Figure 9(b), which shows that removing the outliers can construct a more accurate model with a smaller estimated value.
When we use these parameters to construct prediction results, such as yield estimation or CP/FT test estimation, we can detect defects more effectively, reduce costs, and increase benefits.
Figure 9 (a) Quadratic regression estimation without removing outliers (b) Quadratic regression estimation with removing outliers
Then zoom in and consider all the parameters, and use these parameters to estimate the subsequent Bin value results to find the key factors. And find the optimal factor setting value under the setting of minimizing the Bin value. Similarly, we first consider not removing outliers and find the most suitable regression model. Using the Fit model platform, we get a regression model R-square of about 0.971, which contains many factor effect terms, and many of them can be seen The interaction term effect is stronger than the main effect, which seems more confusing, and observing the Residual by Row Plot, we can find that the gaps in the samples selected as outliers are relatively large (Figure 10).
Figure 10 does not remove the outlier regression formula R-square, Residual by Row Plot and influencing factor effect terms
The next step is to remove the outliers and do a regression estimation again. We found that not only did R-square rise to 0.999, but the key factor was also reduced to four factor effect terms. Observing Residual by Row Plot, there was no significant difference. Sample (Figure 11). According to this regression formula, the predicted result will be more accurate and avoid making wrong judgments.
Figure 11 does not remove the outlier regression formula R-square, Residual by Row Plot and the influencing factor effect term
Collect a little more data for subsequent testing of the accuracy of the regression. We can compare the estimated value of the regression with the actual Bin value under the platform of Analyze>Fit Y by X. The new data can still have a good standard. R-square has an accuracy of 0.999, and there are no special points with excessive differences.
Figure 12 Comparison of the estimated value of the regression formula and the actual Bin value
With JMP's Explore Outliers platform, we can easily and quickly eliminate outliers, and avoid being affected by outliers and avoiding the correlation between misjudgment factors or making wrong model predictions, leading to wrong estimations and decisions. As an outpost for analysis, JMP's Explore Outliers platform can provide an appropriate platform to help users find outliers and quickly achieve the purpose of data cleansing for different scenarios, regardless of whether the data is normal or not for single variables or multiple variables. .
Yan Shen reading:
How to make a wafer map in JMP in 30 seconds (English)
Image and wafer analysis using functional data analysis
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