Quality and Process Methods • Process Capability • Additional Examples of the Process Capability Platform
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Additional Examples of the Process Capability Platform
Process Capability for a Stable Process
In this example, you verify the assumptions that enable you to estimate PPM defective rates based on a capability analysis. You access Process Capability through Control Chart Builder and then directly. The data consist of 22 subgroups of size 5. There are 6 missing readings, with 3 in each of two consecutive subgroups.
Process Capability through Control Chart Builder
You can use Control Chart Builder to check process stability and the normality assumption for your process characteristic. You can also obtain Process Capability information directly within Control Chart Builder.
1.
Select Help > Sample Data Library and open Quality Control/Clips2.jmp.
2.
Right-click on the Gap column and select Column Info.
3.
In the Column Info window, select Show as graph reference lines and click OK.
4.
Select Analyze > Quality and Process > Control Chart Builder.
5.
Drag Date to the Subgroup zone.
6.
Drag Gap to the Y zone.
XBar and R Control Chart for Gap
The control chart indicates that Gap is stable over time. Because Gap has the Spec Limits column property, a Process Capability Analysis report appears to the right of the control chart.
Histogram in Process Capability Analysis for Gap
The histogram and fitted normal blue curve suggest that the distribution of Gap is approximately normal. Although the process is stable, the distribution of Gap is shifted to the right of the specification range.
The Process Summary report shows the specification limits that are saved to the Spec Limits column property. It also shows that the estimate of sigma calculated from within-subgroup variation (Within Sigma) does not differ greatly from the overall estimate given by the sample standard deviation (Overall Sigma). This is expected because the process is stable.
7.
Right-click in the body of the Nonconformance report and select Expected Within PPM from the Columns submenu.
Capability Indices and Nonconformance Report
The Cpk value calculated using subgroup variation is 0.966, indicating that the process is not very capable. The Cpl value suggests good performance, but this is because the process is shifted away from the lower specification limit. Defective product generally results from large values of Gap.
Note that the confidence interval for Cpk is wide, ranging from 0.805 to 1.128. This occurs even though there are 104 observations. Capability indices are surprisingly variable, due to the fact that they are ratios. It is easy to reach incorrect conclusions based on the point estimate of a capability index.
The estimates of out of specification product given in the Nonconformance report provide a direct measure of process performance. The PPM values in the Nonconformance report indicate that Gap hardly ever falls below the lower specification limit (1.4 parts per million). However, the number of parts for which Gap falls above the upper specification limit is 1869.0 parts per million.
For an uncentered process, the Cp value indicates potential capability if the process were adjusted to be centered. If this process were adjusted to be centered at the target value of 14.8, then its capability would be 1.264, with a confidence interval from 1.071 to 1.457.
Process Capability Platform
Now that you have verified stability and normality for Gap, you can obtain additional information in the Process Capability platform.
1.
Select Analyze > Quality and Process > Process Capability.
2.
Select Gap and click Y, Process.
3.
Open the Process Subgrouping outline.
4.
Select Date in the Select Columns list and Gap in the Roles list.
5.
Click Nest Subgroup ID Column.
By default, the Within-Subgroup Variation Statistic selection is set to Average of Unbiased Standard Deviations. In the Control Chart Builder example (Process Capability through Control Chart Builder), subgroup ranges were used.
6.
Click OK.
Goal Plot and Box Plot for Gap
The Goal Plot shows the Ppk index for Gap as being essentially equal to 1. The box plot shows that most values fall within specifications, but the preponderance of data values are shifted to the right within the specification range.
7.
From the Process Capability red triangle menu, select Individual Detail Reports.
The report is the one obtained using Control Chart Builder, except that the Within Sigma is based on average standard deviations rather than average ranges. See Histogram in Process Capability Analysis for Gap and Capability Indices and Nonconformance Report.
Process Capability for an Unstable Process
The following example shows a case where the overall variation differs from the within variation because the process is not stable. It uses the Coating.jmp data table from the Quality Control folder of Sample Data (taken from the ASTM Manual on Presentation of Data and Control Chart Analysis). The process variable of interest is the Weight column, grouped into subgroups by the Sample column.
Process Capability Platform
1.
Select Help > Sample Data Library and open Quality Control/Coating.jmp.
2.
Select Analyze > Quality and Process > Process Capability.
3.
Select Weight and click Y, Process.
4.
Open the Process Subgrouping outline.
5.
Select Sample in the left side column list box.
6.
Select Weight in the right side column list box.
7.
Click Nest Subgroup ID Column.
8.
Click OK.
9.
Enter 16 for LSL, 20 for Target, and 24 for USL in the Spec Limits window.
10.
Click OK.
11.
Select Show Within Sigma Points from the Goal Plot red triangle menu.
12.
Select Individual Detail Reports from the Process Capability red triangle menu.
Process Capability Report for Coating.jmp Data
Process Capability Report for Coating.jmp Data shows the resulting Process Capability report. The Goal Plot shows two points representing the mean shift and standard deviation standardized to the specification limits. The point labeled Overall Sigma is calculated using the overall sample standard deviation. The point labeled Within Sigma is calculated using a within-subgroup estimate of the standard deviation.
The point calculated using Overall Sigma is outside the goal triangle corresponding to a Ppk of 1. This indicates that the variable Weight results in non-conforming product.
However, the point calculated using Within Sigma is inside the goal triangle. This indicates that, if the process were stable, Weight values would have a high probability of falling within the specification limits.
Control Chart to Assess Stability
Use Control Chart Builder to determine whether the Weight measurements are stable.
1.
Select Analyze > Quality and Process > Control Chart Builder.
2.
Drag Sample to the Subgroup zone.
3.
Drag Weight to the Y zone.
XBar and R Chart for Weight
The control chart indicates that the Weight measurements are unstable. The process is affected by special causes and is unpredictable. This makes the interpretation of capability indices and nonconformance estimates highly questionable. Even estimates based on Overall Sigma are questionable, because the process is not predictable.
The histogram in Process Capability Report for Coating.jmp Data shows the distribution of the Weight values with normal density curves using both sigma estimates superimposed over the histogram. The normal curve that uses the Overall Sigma estimate is flatter and wider than the normal curve that uses the Within Sigma estimate. This is because the estimate of Overall Sigma is inflated by the special causes that make the process unstable. If the process were stable, the narrower normal curve would reflect process behavior.
You can also compare the Cpk estimate (1.142) to the Ppk estimate (0.814). The fact that Ppk is much smaller than Cpk is additional evidence that this is an unpredictable process. The Cpk estimate is a forecast of the capability that you would achieve by bringing the process to a stable state.
Note: The Individual Detail Reports Cutoff preference determines whether the Individual Reports appear by default. If the preference is enabled, the Individual Reports appear by default if the number of process variables is less than or equal to the number specified in the preference. You can change this preference in Preferences > Platforms > Process Capability.