More Capability Indices
Over the last several years, some new
process capability indices have surfaced. These indices are the Pp,
Ppk, Cpm, and Ppm.
Pp and Ppk are called Process Performance
As their description implies, Pp and Ppk look at what
the performance could be. Some people refer to them as short-term
capability indices because they do not look at process variation
Another use of the Process Performance Indicators today
is to get a look at how the total variation from the process
compares to the specification. Even special causes are included in
the determination of total variation.
Editorial Note: We believe
that the inclusion of special causes creates some problems for these
indicators. Per AIAG manuals, Pp and Ppk are based on a
“statistically stable” process with process data that form “an
approximately normal distribution.” In our view, it is hard to see
how a process can be statistically stable while having special
causes of variation; we suggest Ppk and Pp are best used as
preliminary process performance indicators.
For Pp and Ppk, the sample standard deviation, s, is
calculated directly from the data using:
For Cp and Cpk, s is
calculated by using R-bar/d2.
Typically there will be less sources of
variation represented in a preliminary process performance study
than in a process capability study so the preliminary Ppk value is
usually greater than the Cpk value for a process.
Cpm is the
process capability measured against performance to a target.
Cpm capability index compares the width of the specification to the
spread of the process output plus an error term for how far the
center of the distribution is from the target.
The process is
penalized for not running on-target. And since the
difference-from-target term is squared in the calculation, as the
distance from the target increases, the penalty increases
For a centered process that is on-target (that is,
the center of the specification is the target), Cp, Cpk, and Cpm
will be equal. When close to center, we often find that the Cpk and
Cpm values are similar. But if the mean is more than one standard
deviation away from the target, then the three indices will give us
very different views of the process capability.
Ppm is a process
performance index based on Cpm.