*PROC CAPABILITY and General Statements* |

## Assumptions and Terminology
for Capability Indices

One of the fundamental assumptions in process capability
analysis is that the process must be in statistical
control.
Without statistical control, the process is
not predictable,
the concept of a process distribution
does not apply, and quantities related to the distribution,
such as probabilities, percentiles, and capability indices,
cannot be meaningfully estimated.
Additionally, all of the standard process capability indices
described in the next section require
that the process distribution be normal,
or at least approximately normal.
In many industries,
statistical control
is routinely checked
with a Shewhart chart
(such as an and *R* chart)
before capability indices such as

are computed.
The control chart analysis yields estimates for
the process mean
and standard deviation ,
which are based on subgrouped data and
can be used to estimate *C*_{pk}.
In particular, can be estimated by

rather than
the ungrouped sample standard deviation

You can use the SHEWHART procedure to carry out the
control chart analysis and to compute capability
indices based on *s*_{R}.
On the other hand,
the CAPABILITY procedure
computes indices based on *s*.
Some industry manuals distinguish
these two approaches.
For instance,
the ASQC/AIAG manual
*Fundamental Process Control*
uses the
notation *C*_{pk} for
the estimate based on *s*_{R},
and it uses
the notation *P*_{pk}
for the estimate based on *s*.
However, assuming that the process is in control
and only common cause variation is present,
both *s*_{R} and *s* are estimates of the
same parameter ,and so there is fundamentally
no difference in the two approaches^{*}.

Once control has been established, attention
shuld focus on the distribution of the process
measurements, and at this point there is no
practical or statistical
advantage to working
with subgrouped measurements.
In fact, the use of *s*
is closely associated with a wide variety of
methods that are highly useful
for process capability analysis,
including tests for normality,
graphical displays such as
histograms and probability plots,
and confidence intervals for
parameters and capability indices.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.