# Cpk vs Ppk to look at the Capability by Fixture

#### bkirch

##### Involved In Discussions
For long term capability studies, if I wanted to look at the capability by fixture, would it be best to use CPK or PPK, and why?

H

#### hangguanglei

i think PPk which is adequate. can you decribe your fixture ? proof fixture or just a fixture .

#### bkirch

##### Involved In Discussions
The fixtures are in a machining facility holding the parts while they are machined. We have multiple machines and fixtures that perform the same process. I think to get a proper understanding of capability, we would want to look at the capability by machine and fixture.

#### Ron Rompen

Trusted Information Resource
Although Ppk will give you a good immediate snapshot, based on a small initial sample size (say 30 pcs per fixture/machine combination) to demonstrate long-term capability you should use Cpk.

The reason for the difference is the value used to calculate the distance from the closest limit (either UCL or LCL).
For Ppk you would use (UCL-Xbar)/n or (Xbar-LCL)/n (where n = the number of samples taken)
For Cpk, you would use (UCL-XBar/(n-1) or (Xbar-LCL/(n -1)

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Although Ppk will give you a good immediate snapshot, based on a small initial sample size (say 30 pcs per fixture/machine combination) to demonstrate long-term capability you should use Cpk.

The reason for the difference is the value used to calculate the distance from the closest limit (either UCL or LCL).
For Ppk you would use (UCL-Xbar)/n or (Xbar-LCL)/n (where n = the number of samples taken)
For Cpk, you would use (UCL-XBar/(n-1) or (Xbar-LCL/(n -1)
hmmm. perhaps you are confusing the large vs small sample standard deviation formula with the use of the within (short term) vs Total (Long term) standard deviation used in the denominator of the capability indexes?

to answer the OP's question: it depends on which formula you are actually using for Cpk and Ppk.

the correct formula for long term capability (Ppk) is the lesser of (USL-Xbar)/3*Total SD or (Xbar-LSL)/3*Total SD.

...some references use this formula for Cpk and all use it for Ppk.

Some references use the following formula for Cpk when calculating short term capability: the lesser of (USL-Xbar)/3*within subgroup SD or (Xbar-LSL)/3*within subgroup SD.

...some references will use the Ppk formula for short term estimates but require that 30-100 consecutive samples created under the same conditions (equipment, material, operator, environment, etc) be used.

most statistical software use the formulas in blue...software can't differentiate the conditions of your testing so the use of Ppk for short term variation must be chosen deliberately by the analyst ...

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