When you analyze data, what's the first step?
Do you want to use the powerful interactive JMP Graph builder (Graph Builder) for visual analysis?
Or use JMP's Distribution (distribution) platform to do narrative statistics analysis?
Or use JMP's diverse predictive modeling tools to find the most appropriate predictive model?
Although these are well-known JMP functions, as a first step in using JMP analysis, in addition to the above-mentioned platforms, you may wish to consider using Explore Outliers (explore outliers) and Explore Missing Values (explore missing values) Platform, clean and organize your information.
Maybe you think it is understandable to explore missing values. After all, it is reasonable to shave off null values first for subsequent analysis. But why do you need to exclude outliers as well? If such outliers are representative of the data population, will it affect our analysis? Moreover, outliers are difficult to capture. Can't we ignore this effect first?
To clarify these issues, we need to know what an outlier is.
What are outliers?
Let's first discuss the one-dimensional situation, and randomly generate 1000 values of the standard normal distribution Nor (0, 1), as shown in Figure 1, where the points marked in red are outliers beyond the range of [-4,4], such The probability of occurrence is 0.0063%, which is a very small probability, so we regard points that occur in such a small probability area as outliers.
Figure 1 Randomly generated normal distribution point map
Then we look at the situation of two variables, using Graph builder analysis, regardless of whether the data points have the same mean and variance between the two variables (X2 vs. X1) or with different means and variances (X3 vs. X1), as shown in Figure 2 below, we can see with the naked eye that these outlier points (red points) seem to have a different trend from other points, and are far away from the data center point.
Figure 2 (left) 2 variables have the same mean and variance scatter plot (right) 2 variables have different mean and variance scatter plot
And when there is a strong correlation between the two variables, it can also be found that some outliers are far 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, which is also a A good example shows that when we consider multivariate outliers in an all-round way, we will catch some potential outliers and avoid misjudgment of only observing and controlling a single variable. Fortunately, JMP provides such a multivariate 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 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 represent a gap from other samples without the same "trend". Therefore, outliers may represent problematic characters in a good society, or they may represent a clean stream in a wicked city, depending on where your samples come 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, so the quality of the corresponding process can be deduced through the results of electrical testing of these parameters. Wafer foundries generally call the electrical parameter test WAT (Wafer Acceptance Test), and their customers need to check the WAT test data to confirm the manufacturing quality. In the new process R&D 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, we can use the Analyze>Distribution function to make the corresponding histogram and Outlier box plot to see if there is any deviation. Group values, as shown in Figure 4 (left), the red line on the Outlier Box marks the most concentrated area covering 50%, from which we can find the data is concentrated in the middle section. Similarly, you can also use the histogram function of Graph Builder to complete the drawing of the histogram, as shown in Figure 4 (right).
Figure 4 (left) Histogram of the Distribution platform; Outlier box plot (right) Box plot of the Graph builder
According to the Quantile Range outlier test, we found that there is an outlier (red dot) in parameter 1. Use the Quantile Range Outliers function in JMP's Analyze>Screening>Explore Outliers platform to find its outlier (Figure 5), and Actions such as marking, excluding, and treating data as missing values can be performed.
At the same time, you can also adjust the rules for judging as outliers. You can adjust the tail percentile value (Tail Quantile) and its multiple (Q), and use the common IQR outlier test. The upper limit is Q3+1.5*IQR, the upper limit Taking Q1-1.5*IQR as an example, Tail Quantile is 0.25, and Q is 1.5. And when your data is not in line with the normal distribution, you can consider using Robust Fit Outliers as an outlier screening platform.
Figure 5 Quantile Range Outliers in the Explore Outliers platform
But when we consider it 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 in line with most data However, the actual outliers are converted to the three highest values of production line 3 (red dots in Figure 6). This result also echoes the importance of the source of the aforementioned samples. Extensive acquisition of data that can represent the mother population is essential for screening correct 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 composite to select sample points with higher distances and mark them as outliers (Figure 7).
Figure 7 K Nearest Neighbor Outliers distance map under the platform
By confirming the distribution position of these data points selected as outliers on each parameter by Graph builder, it can be found that not all points belong to outliers of a single parameter (such as data points 290, 295, 296, 297, 298 , 299), this result is also consistent with the above-mentioned multivariate outlier screening platform of JMP, which can capture many potential problem points that are ignored in the observation of single variables (Figure 8).
Figure 8 uses Boxplot to compare the distribution of outliers on variables
Remove outliers and build more accurate predictive models
We know that JMP has a good platform that can help us filter out outliers, but what will be the impact of not filtering out outliers? To simplify things, let's first look at the impact of outliers between the two parameters.
We observe the R-square value estimated by the regression formula of the secondary effect between the first-level parameter and the second parameter of WAT data. Before removing the screened outliers, the R-square value is 0.602, as shown in Figure 9 ( a), and after removing outliers, the R-square value increased to 0.740, as shown in Figure 9(b), which shows that removing outliers can construct a more accurate model with a smaller gap in estimated values.
When we use these parameters to construct forecast results, such as yield rate forecast or CP/FT test forecast, we can detect defects more effectively, reduce costs and increase benefits.
Figure 9 (a) Quadratic regression estimation without outliers removed (b) Quadratic regression estimation with outliers removed
Then zoom in and consider all the parameters, and use these parameters to predict the subsequent Bin value results to find the key factors. And find the best factor setting value under the setting of minimizing Bin value. In the same way, we first consider not removing outliers to find the most suitable regression model. Using the Fit model platform, we get a regression model with an R-square of about 0.971, including many factor effect items, among which we can see many The effect of the interaction term is stronger than the main effect, which seems to be more chaotic, and observing the Residual by Row Plot, it can be found that the gap between the samples screened as outliers is relatively large (Figure 10).
Figure 10 Regression R-square, Residual by Row Plot and affected factor effect items without removing outliers
The next step is to remove the outliers and do a regression estimate again. We found that not only did the R-square rise to 0.999, but the key factors were also reduced to four factor effect items. Observing the Residual by Row Plot, no significant difference was found Sample (Figure 11). The results predicted according to this regression formula will also be more accurate, avoiding wrong judgments.
Figure 11. The outlier regression formula R-square, Residual by Row Plot and the affected factor effect items are not removed
Collect a little more data to do follow-up testing of the accuracy of the regression formula. We can compare the estimated value of the regression formula with the actual Bin value under the platform of Analyze>Fit Y by X. The new data can still have a very good level. R-square has an accuracy of 0.999, and no particular point has excessive variance.
Figure 12 Comparing 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, avoiding the influence of outliers to misjudge the correlation between factors or make wrong model predictions, leading to wrong estimates and decisions. As an outpost for analysis, JMP's Explore Outliers platform can address different scenarios, whether univariate or multivariate, whether the data is normal, and can propose an appropriate platform to help users find outliers and quickly achieve the purpose of data cleaning .
Extended 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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