observed within overall performances

“Within” perfomance is based on a short term estimate of sigma (for example R-bar/d2) typically derived from a control chart. This will characterise the past and future performance for a STABLE process (i.e. one that does not exhibit any special cause variation) It will not characterise the past or the future performance of an unstable process. Indices derived from sigma are typically Cp and Cpk.
“Overall” performance is based on a global estimate, usually denoted as S, (typically derived using the stdev() calculation in Excel, for example). For a stable process this will be equivalent to the within performance. For an unstable process, the overall performance will characterise the past performance of your process, but not the future performance (UNSTABLE is equivalent to UNPREDICTABLE). Indices derived from S are typically Pp and Ppk.
The best measure of capablility is actually the observed performance in terms of ppm. Everything else depends on assumptions. For example, it is possible to get a process with a Cpk of 0.8 which is 100% conforming, and it is also possible to get a six-sigma process (Cpk=2) which is 100% non-conforming. 
Take a look at Don Wheeler’s books “Beyond Capability Confusion” and “Guide to Data Analysis” for more information.
Hope this helps
Phil

Philip-
You wrote:
“For example, it is possible to get a process with a Cpk of 0.8 which is 100% conforming, and it is also possible to get a six-sigma process (Cpk=2) which is 100% non-conforming.”How?

Situation 1:
A stable process having a skewed distribution, can give you a capability less than 1.0, whilst having no product outside the specification limits (example given in “Beyond Capability Confusion”) The correct interpretation of a capability index less than 1.0 is that the process MAY be incapable IF the process is symetrical about the mean – only by plotting the control chart, and the histogram can you tell.
Situation 2:
A process which is higly unstable may have very low short term variation, and a mean exactly centered between the spec limits, but still have every result outside the specification limits. The key here is that neither the mean, nor the standard deviation, nor any other summary statistic, will adequately characterise the output of an unstable process, and it is complete nonsense to estimate the capability of an unstable process.

Marlon,
You are right…I agree t you..This is something very basic.
Monk

Monk
Thank You

I still don’t understand the relevance. So all I can do is respond to what I assume Marlon’s comment meant …
The discussion is revolving around the presence or absence of instability in a process. In the presence of instability, SD does not exist, and therefore it is meaningless to try to minimise it. The correct approach to any process problem is
a) eliminate special cause variation (until you have done this you don’t have a process to improve or measure)
b) centre the process on the target (because this is easier than reducing common cause variation)
c) if this still doesn’t give you what you want reduce common cause variation by re-engineering your process (dissagregate, stratify, experiment).

You twerp.  I’m sure you’ve never read Wheeler.  I’ll bet you still chew the corners of your picture books.