Process Capability

The capability of a process is some measure of the proportion of in-specification items the process produces when it is in a state of statistical control.

Process Capability vs. Batch Performance

Process capability is different than batch performance. With batch performance, you are interested in what actually was produced. With process capability, you are interested in what the process is capable of producing when in statistical control. This may not sound like a big difference, but it can be very important.

Process Capability Assumptions

For valid process capability calculations, all data must be from an in-control process, with respect to both the mean and standard deviation. Make sure to check this data in a variables control chart to make sure that all points in the x bar, s or R charts are in control. If they aren't, your capability indices in the statistics dialog box are not valid.

Process Capability: Indices

You can tell a lot about your process by using histograms and control charts together. It is also a widely-accepted practice to express process capability using the following indices:

  • Cp is the simple process capability index. It is the process width divided by 6 times sigma, its estimated within-subgroup standard deviation, where the process width = Upper Spec Limit minus Lower Spec Limit. If Cp < 1, the process is wider than the spec limits, and is not capable of producing all in-specification products. Cp could be greater than one, but bad parts could still be being produced if the process is not centered. Thus, there is a need for a capability index which takes process centering into account: Cpk.

  • Cpk is the difference between x double bar and the nearer spec limit divided by 3 times sigma. If Cpk >=1, then 99.7% of the products of the process will be within specification limits. If Cpk <1, then more non-conforming products are being made.

Bear in mind that specification limits are not statistically determined, but rather are set by customer requirements and process economics.

The histogram pictured here illustrates the idea of process capability. The process is wider than the spec limits. The process appears to have a low capability for making good, in-spec products.

In the PathMaker software, the following process capability indices are calculated if specification limits are applied to histograms:

Cp The distance between the upper specification limit and the lower specification limit, divided by (6 times the standard deviation). If Cp < 1, the process is wider than the spec limits, and is not capable of producing all —in-specification products. Cpcould be greater than one, but bad parts could still be being produced if the process is not centered. Thus, there is a need for a capability index which takes process centering into account: Cpk.
Cu The difference between the process mean and the upper spec limit, divided by 3 sigma, or 3 times the standard deviation.
Cl The difference between the process mean and the lower spec limit, divided by 3 sigma, or 3 times the standard deviation.
Cpk Cpk is the difference between the process mean and the nearer spec limit divided by 3 times sigma. (Cpk is the lesser of Cuand Cl.). If Cpk>=1, then at least 99.7% of all products of the process will be within specification limits. If Cpk<1, then some non-conforming products are being made, and you may need to study your process to see how it can be improved.

A final note on capability indices: Look at the Charts!

For most people, looking at a histogram with specification limits give a clearer picture of what is going on in a process than the indices will. The indices can be used to add precision and may be easier to use as ongoing checks on a conforming process, but they are not terribly intuitive, and may be overkill in straightforward situations

View a video tutorial on PathMaker's data analyst tool.View a Video Tutorial on PathMaker's Data Analyst Tool.


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