I'm embarrassed to answer after 3 years or so, so I guess we're belatedly even...
I was reviewing some posts during a search and found this oldie. Well, most questions get answers (sooner or later)...
I can't give you a statistical rational - maybe Don will see this and comment.
The differences are:
Pp
The Pp index is used to summarize a system's performance in meeting two-sided specification limits (upper and lower). Like Ppk, it uses actual sigma (sigma of the individuals), and shows how the system is actually running when compared to the specifications. However, it ignores the process average and focuses on the spread. If the system is not centered within the specifications, Pp alone may be misleading.
The higher the Pp value...
...the smaller the spread of the system’s output. Pp is a measure of spread only. A process with a narrow spread (a high Pp) may not meet customer needs if it is not centered within the specifications.
If the system is centered on its target value...
...Pp should be used in conjunction with Ppk to account for both spread and centering. Pp and Ppk will be equal when the process is centered on its target value. If they are not equal, the smaller the difference between these indices, the more centered the process is.
Ppk
Ppk is an index of process performance which tells how well a system is meeting specifications. Ppk calculations use actual sigma (sigma of the individuals), and shows how the system is actually running when compared to the specifications. This index also takes into account how well the process is centered within the specification limits.
If Ppk is 1.0...
...the system is producing 99.73% of its output within specifications. The larger the Ppk, the less the variation between process output and specifications.
If Ppk is between 0 and 1.0...
...not all process output meets specifications.
If the system is centered on its target value...
...Ppk should be used in conjunction with the Pp index. If the system is centered on its target value, Ppk and Pp will be equal. If they are not equal, the smaller the difference between these indices, the more centered the process is.
Pr
The Pr performance ratio is used to summarize the actual spread of the system compared to the spread of the specification limits (upper and lower). The lower the Pr value, the smaller the output spread. Pr does not consider process centering.
When the Pr value is multiplied by 100, the result shows the percent of the specifications that are being used by the variation in the process. Pr is calculated using the actual sigma (sigma of the individuals) and is the reciprocal of Pp. In other words, Pr = 1/Pp.
Cp
The Cp index is used to summarize a system's ability to meet two-sided specification limits (upper and lower). Like Cpk, it uses estimated sigma and, therefore, shows the system's potential to meet the specifications. However, it ignores the process average and focuses on the spread. If the system is not centered within the specifications, Cp alone may be misleading.
The higher the Cp value...
..the smaller the spread of the system’s output. Cp is a measure of spread only. A process with a narrow spread (a high Cp) may not meet customer needs if it is not centered within the specifications.
If the system is centered on its target value...
Cp should be used in conjunction with Cpk to account for both spread and centering. Cp and Cpk will be equal when the process is centered on its target value. If they are not equal, the smaller the difference between these indices, the more centered the process is.
Cpk
Cpk is a capability index that tells how well as system can meet specification limits. Cpk calculations use estimated sigma and, therefore, shows the system's "potential" to meet specifications. Since it takes the location of the process average into account, the process does not need to be centered on the target value for this index to be useful.
If Cpk is 1.0...
...the system is producing 99.73% of its output within specifications. The larger the Cpk, the less variation you will find between the process output and specifications.
If Cpk is between 0 and 1.0...
...not all process output meets specifications.
If the system is centered on its target value...
...Cpk should be used in conjunction with the Cp index. Cpk and Cp will be equal when the process is centered on its target value. If they are not equal, the smaller the difference between these indices, the more centered the process is.
Cpm
The Cpm index indicates how well the system can produce within specifications. Its calculation is similar to Cp, except that sigma is calculated using the target value instead of the mean. The larger the Cpm, the more likely the process will produce output that meets specifications and the target value.
Cr
The Cr capability ratio is used to summarize the estimated spread of the system compared to the spread of the specification limits (upper and lower). The lower the Cr value, the smaller the output spread. Cr does not consider process centering.
When the Cr value is multiplied by 100, the result shows the percent of the specifications that are being used by the variation in the process. Cr is calculated using an estimated sigma and is the reciprocal of Cp. In other words, Cr = 1/Cp.
[This message has been edited by Marc Smith (edited 15 February 2000).]