## 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:

- C
_{p} 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 C_{p} < 1,
the process is wider than the spec limits, and is not capable of
producing all in-specification products. C_{p} 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:
C_{pk.}

- C
_{pk} is the difference between x double bar and the
nearer spec limit divided by 3 times sigma. If C_{pk}
>=1, then 99.7% of the products of the process will be within
specification limits. If C_{pk} <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.

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 C_{p} < 1, the process is
wider than the spec limits, and is not capable of producing all
—in-specification products. C_{p}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:
C_{pk.} |

**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** |
C_{pk} is the difference between the
process mean and the nearer spec limit divided by 3 times sigma.
(C_{pk} is the lesser of C_{u}and
C_{l.}). If C_{pk}>=1, then at least 99.7% of
all products of the process will be within specification limits.
If C_{pk}<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.