by Laura Lancaster LauraL@JMP, Principal Research Statistician Developer, SAS
Process capability analysis is an essential part of Six Sigma and many other quality initiatives that are used in a wide variety of industries. By assessing how well a stable process is performing relative to its specifications, quality practitioners are able to understand the current state of the process. They can make adjustments and reduce process variation, thereby improving quality and consistency.
Because process capability analysis is so important for achieving and maintaining high quality, JMP 12 now includes a Process Capability platform to make this analysis easier and more effective. By adding more options to the platform, it offers increased flexibility and modernized graphs. There were two central ideas that steered our development in the new platform:
Process capability analysis should reflect the type of control chart used in the statistical process control program.
The potential performance of a process (sometimes referred to as short-term capability) and the past performance of the process (sometimes referred to as long-term capability) should be available alongside each other.
In addition to all of the options available in the Capability platform in previous versions of JMP, the Process Capability platform introduced in JMP 12 adds these new features:
A process can be subgrouped by grouping columns or constant subgroup sizes, reflecting XBar control charts.
Both within and overall variation are computed. Within variation – which is computed in XBar and R, XBar and S, and I-MR charts – displays the variation within subgroups and is used to analyze potential performance (sometimes referred to as short-term variation). Overall variation is the variation of the total process and is used to analyze past performance (sometimes referred to as long-term variation).
The capability indices reports and most graphs are available for both types of variation. In the Individual Detail Report, the distributions for both within and overall variation can be graphed on a histogram of the data.
Data table values that are outside of specifications can be selected and colored.
The Process Capability platform is designed to help users analyze multiple processes simultaneously. However, because it is important to analyze process capability in conjunction with process control charts, we have also added the new Process Capability platform’s Individual Detail Report to the Control Chart Builder platform.
Let’s use fictional ice cream manufacturer, Tiger Paw Ice Cream Company, to demonstrate how some of these new features work. Tiger Paw Ice Cream makes a variety of frozen desserts. The company has many specifications that guarantee great taste and creaminess for all of its products, while also meeting FDA requirements. We will examine Tiger Paw’s production capability to meet the percent milk fat specifications for three frozen desserts: Tiger Tracks Ice Cream, Low-Fat Chocolate Ice Cream, and Vanilla Frozen Yogurt. These products have the following milk fat specifications:
In this process capability study, five samples of each frozen dessert were randomly chosen from each of the three product blending machines at the beginning of every hour for eight hours. Figure 1 shows how we set up the launch dialog for the new Process Capability platform. We assigned columns Tiger Tracks % Fat, Low-Fat Chocolate % Fat, and Vanilla Frozen Yogurt % Fat as processes and then assigned Machine and Hour as subgroup columns for each of these processes. (Note: We saved the spec limits as column properties in the data table so that we did not have to enter the spec limits through a dialog.
Figure 1 Process Capability Launch Dialog
Figure 2 shows the initial process capability report after the platform is launched. (The Goal Plot point labels have been pinned open. You can always identify a point by moving the cursor over the point to see the label.) With the Goal Plot and Capability Box Plots, you can quickly visualize how well the processes are meeting specifications.
By examining the Capability Box Plots shown in Figure 2, we quickly see that some of the Tiger Tracks Ice Cream samples did not meet the percent milk fat specifications since there are points that fall outside of the spec limit lines. Its box plot is also rather wide, indicating relatively high variation in the data with respect to the spec limits. Next, we notice that the box plot for the Low-Fat Chocolate Ice Cream is off-center, with most of the data above the target line. The box plot for the Vanilla Frozen Yogurt looks healthy. We would like to examine these processes in more detail, so we turn on the "Individual Detail Reports" from the menu.
Figure 2 Process Capability Initial Report
Figure 3 shows the Individual Detail Report for Tiger Tracks Ice Cream percent milk fat. The histogram suggests that the data is approximately normal. Once again, we can see that some of the data falls outside of the spec limits. The normal density curve that uses the Overall (long-term) Sigma estimate appears to be different from the curve that uses the Within (short-term) Sigma estimate, indicating that the process might be unstable and interpretation of the capability indices might be questionable. If the process were stable, Tiger Paw might be able to achieve behavior that more closely resembles the blue curve that uses the Within Sigma estimate.
As a first step in determining what is making the Tiger Tracks Ice Cream process unstable for percent milk fat, we choose Select Out of Spec Values and Color Out of Spec Values from the main menu. Figure 4 shows a portion of the data table with some of the out of spec values selected and colored. Values that are below the lower spec limit are shaded red, and values that are above the upper spec limit are shaded blue. Examining these outliers and the data, it appears that there are issues with machines 2 and 3.
Figure 4 Out of Spec Values, selected and colored
Further investigation with an XBar chart in Control Chart Builder identifies some issues with this process (Figure 5). Machine 2 appears to be blending in too little milk fat, while machine 3 appears to be blending in too much.
Figure 5 XBar Chart of Tiger Tracks % Fat using Control Chart Builder
Next, we examine the Individual Detail Report for the Low-Fat Chocolate Ice Cream, shown in Figure 6. The histogram suggests that the data is approximately normal. The density curves fall atop one another, indicating a stable process. We also see that the Overall Sigma and Within Sigma estimates in the Process Summary report do not differ much. All of the data is within in the specifications limits, but it appears that the distribution has shifted to the right of the target. This means that the consumer is getting a higher percentage of fat than the label indicates and that Tiger Paw is wasting some of its milk fat. Getting this process back on target would improve consumers’ waist lines and Tiger Paw’s bottom line. The Cpk value of 1.431 and Ppk value of 1.429 indicate that this process is still quite capable despite being off target.
Finally, Figure 7 shows the Individual Detail Report for Tiger Paw’s Vanilla Frozen Yogurt. Once again, the histogram suggests that the data is approximately normal, and the overlaid density curves suggest that the process is stable. The data appears to be centered on the target and well within the spec limits. The Cpk value of 1.333 and the Ppk value of 1.324 indicate that this process is capable.
Tiger Paw Ice Cream Company needs to address the stability issue for its Tiger Tracks Ice Cream process for blending in the correct percentage of milk fat, but the Low-Fat Chocolate Ice Cream and Vanilla Frozen Yogurt processes appear to be capable for blending in milk fat. Even though the Low-Fat Chocolate ice cream process is capable, the company might consider trying to get the percent milk fat blending centered on the target value to save money and reduce the fat content in the low-fat ice cream.