Quality and Process Methods • Multivariate Control Charts • Additional Examples of Multivariate Control Charts
Previous
 • 
Next
Additional Examples of Multivariate Control Charts
This section contains additional examples of creating multivariate control charts to monitor an individual process and detect change points.
Example of Monitoring a Process Using Sub-Grouped Data
The workflow for monitoring a multivariate process with sub-grouped data is similar to the one for individual data. See Example of a Multivariate Control Chart. You create an initial control chart to save target statistics and then use these targets to monitor the process.
Step 1: Determine Whether the Process Is Stable
1.
Select Help > Sample Data Library and open Quality Control/Aluminum Pins Historical.jmp.
2.
Select Analyze > Quality and Process > Control Chart > Multivariate Control Chart.
3.
Select all of the Diameter and Length columns and click Y, Columns.
4.
Select subgroup and click Subgroup.
5.
Click OK.
Multivariate Control Chart for Sub-Grouped Data, Step 1
The process appears to be in statistical control, making it appropriate to create targets using this data.
Step 2: Save Target Statistics
1.
From the red triangle menu, select Save Target Statistics.
This creates a new data table containing target statistics for the process.
2.
Save the new data table as Aluminum Pins Targets.jmp.
Now that you have established targets, create the multivariate control chart that monitors the process.
Step 3: Monitor the Process
1.
Select Help > Sample Data Library and open Quality Control/Aluminum Pins Current.jmp.
This sample data table contains recent observations from the process.
2.
Select Analyze > Quality and Process > Control Chart > Multivariate Control Chart.
3.
Select all of the Diameter and Length columns and click Y, Columns.
4.
Select subgroup and click Subgroup.
5.
Click Get Targets.
6.
Open the Aluminum Pins Targets.jmp table that you saved.
7.
Click OK.
8.
From the red triangle menu, select Show Means.
The Show Means option gives the means for each subgroup. You can then observe which groups are most dissimilar from each other.
Multivariate Control Chart for Sub-Grouped Data, Step 3
Multivariate Control Chart for Sub-Grouped Data, Step 3 shows indications of instability at subgroups 4-7, 9-11, 18, and 20. This result implies that these observations do not conform to the historical data from Aluminum Pins Historical.jmp, and that the process should be further investigated. To determine why the process was out of control at these points, you might want to examine individual univariate control charts or perform another univariate procedure.
An alternative method to monitoring this process is based on the big principal components. In this example, for the historical data, the first three principal components account for about 98% of the variation. Based on this, you might construct a chart for the first three principal components. Then you would monitor current data using those three components. The control limits for the chart used in monitoring the process should be based on the corresponding chart for the historical data.
Example of T Square Partitioned
Use T Square Partitioned to separate out the more important components from the less important components when studying process behavior. In this example, the coating on each of 50 bars was measured at 12 uniformly spaced locations across the bar. You want to examine the variation in the measurements and determine whether the causes of variation need to be investigated further.
1.
Select Help > Sample Data Library and open Quality Control/Thickness.jmp.
2.
Select Analyze > Quality and Process > Control Chart > Multivariate Control Chart.
3.
Select all of the Thickness columns and click Y, Columns.
4.
Click OK.
The current alpha level is set to 0.05, which corresponds to a 5% false alarm rate. You want to set the false alarm rate to 1%.
5.
Change the alpha level by selecting Set Alpha Level and choosing 0.01 from the red triangle menu.
Initial Multivariate Control Chart for Thickness.jmp
The overall control chart in Initial Multivariate Control Chart for Thickness.jmp suggests that special causes have affected bars 1, 2, 4, 5, and 22. Looking at the Principal Components report, you can see that almost 95% of the variation in the 12 thickness measurements is explained by the first principal component. You want to study the variation associated with this principal component further.
6.
From the red triangle menu, select T Square Partitioned.
7.
Accept the default value of 1 principal component by clicking OK.
T Square Partitioned Control Charts
In contrast to the Principal Components report, the T Square with Big Principal Components chart, which reflects variation for only the first component, shows no evidence of special causes. The T Square with Small Principal Components chart shows that the special cause indications reside in the remaining smaller components. These smaller components do not explain much variation, and likely represent random noise. Therefore, you might conclude that the variation in the thickness measurements is not a major cause for concern.
Example of Change Point Detection
Use change point detection to find the point at which a shift occurs in your data.
1.
Select Help > Sample Data Library and open Quality Control/Gravel.jmp.
2.
Select Analyze > Quality and Process > Control Chart > Multivariate Control Chart.
3.
Select Large and Medium and click Y, Columns.
4.
Click OK.
5.
From the red triangle menu, select Change Point Detection.
Change Point Detection for Gravel.jmp
Tip: You might need to drag the axes to see the density ellipses for the two groups, depending on your data.
In the Change Point Detection plot, values above 1.0 indicate a possible shift in the data. At least one shift is apparent; the change point occurs at observation 24 and the shift occurs immediately after observation 24. The 95% prediction regions for the two groups have approximately the same size, shape, and orientation, visually indicating that the sample covariance matrices are similar.