# Pp/Ppk & Cp/Cpk - Which is appropriate for Long/Short Term Study?

S

#### Stefanus Simbolon R

Dear all,
when we have a new product, evaluate for short term study use Pp/Ppk or Cp/Cpk?
For evaluating at normal production (long term study), we use Pp/Ppk or Cp/Cpk?

regards

B

#### Barbara B

Re: using Pp/Ppk or Cp/Cpk when short term study?

This depends on the definitions used for Pp/Ppk and Cp/Cpk. If you describe a little bit more detailed which norm or customer requirements your question is based on, the answer could be more helpful.

Regards,

Barbara

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
In order to answer your question so that you understand why the answer we give is the correct one we must first understand the concepts of Cpk and Ppk.

The first concept is that Cpk and Ppk formulas were originally designed for ongoing processes and was conceived as an extension of SPC. Properly designed SPC charts are constructed using a series of small samples – or subgroups – taken over time. In general, when properly designed the parts within a subgroup are created under relatively the same conditions: same raw material, same operator, same equipment, same settings, same tool/fixture/equipment condition, same environmental conditions, etc. Each subgroup is taken far enough apart that some and eventually all of these conditions change so that all variation is captured.

Within subgroup variation therefore represents short term variation. Cpk uses the within subgroup standard deviation (the average of all of the subgroup Standard deviations)

The total variation (within subgroup plus subgroup to subgroup) is the long term variation. Ppk uses the standard deviation of all of the individual values.

(It is important to note that often people use the notation of Cpk as a generic term for a process capability index. They will specify Cpk when they really mean Ppk.)

When a product – or process – is new, there is often limited variation in the various inputs. So there is no way to determine the long term performance. Short term capability can be assessed. The units are all to be created using essentially the same conditions: same raw material, same operator, same equipment, same settings, same tool/fixture/equipment condition, same environmental conditions, etc. Only the sample size is much larger than one would take for an ongoing sampling of multiple subgroups. Typically, the sample size would be from 30-100 units. In this case since there aren’t multiple subgroups the standard deviation is just the single standard deviation on the individual values. The same standard deviation formula as for Ppk. So the short capability calculation for new products looks like the Ppk formula…

Hope this helps

Note: there are many complicating factors that can influence the sampling and interpretation depending on your actual situation…

M

#### Mr.Happy

Bev,

Good explanation, to make it complete you might explain what the short terms Pp/Ppk and Cp/Cpk stand for.

#### Stijloor

Staff member
Super Moderator
Bev,

Good explanation, to make it complete you might explain what the short terms Pp/Ppk and Cp/Cpk stand for.

Goede Middag!

Dr. Gordon Constable answers as follows:

What do the letters in Cp and Cpk stand for?

There is no authoritative answer. Cp has been around for a long time and many believe it stands for Capability of the Process. Others say Process Capability, but that would reverse the letters.

As for Cpk, in the literature that I first saw about Cpk, k was the amount of the difference in the target value and in standard deviations (the number of standard deviations that the process is off target). Before you ask, Pp generally is said to be Process Performance.

Gordon Constable Ph.D
Prettig weekend!

Stijloor.

B

#### Barbara B

Like it is written in the quotes Stiljoor provided: It depends.

If you are dealing with german companies, they more often use Ppk as potential process capability and Cpk as process capability index, the latter only being used if it has been proved that the process is in a state of statistical control and the first being applicable in case no SPC or other method has been used to evaluate the process. So Pp/Ppk is in Germany often the "short term" and Cp/Cpk the "long term" capability.

They're referring to a german norm, DIN ISO 21747 which was published in 2006 as a replacement for the DIN ISO 55319 (also a german speciality). And both norms have a lot of flaws concerning the statistical methods, so I wouldn't recommend neither of them, but this is a different topic. They define Pp/Ppk and Cp/Cpk exactly the other way round like they are used in most other countries.

M

#### Mr.Happy

Like it is written in the quotes Stiljoor provided: It depends.

If you are dealing with german companies, they more often use Ppk as potential process capability and Cpk as process capability index, the latter only being used if it has been proved that the process is in a state of statistical control and the first being applicable in case no SPC or other method has been used to evaluate the process. So Pp/Ppk is in Germany often the "short term" and Cp/Cpk the "long term" capability.
Hello Barbara,

Because we do business with German customers I would like to thank you for this additional information.

Danke,

M.f.G.

Mr.Happy

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
It is not the letters (C or P) that matter. It is the formula used to calculate the standard deviation and more importantly the time frame and structure of how much variation was included in the study.

In the end it is about gaining understanding of your process variation and no correct or incorrect definition in some 'standard' should affect that.

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