# Cpk and Ppk Differences and Questions

#### sushant_kulkarni

##### Involved In Discussions
Dear all,

Cpk used for Short term capability with Std. deviation with in sud-group variation.

Ppk used for Long term capabi;ity of system with Std. deviation from long time and actual process variation and sample size.

Though we are calculating Cpk or Ppk with system only stat. control then standard deviation for both the capability would be same?

How can Ppk will be less or standard deviation will be higher for Ppk.

Will it affect by common causes as well as special cause of variation?

and if it will be how can we say that system is in the stat. control?

If system isnot in the stat. control then to calulate Cpk and Ppk will be wrong.

Sushant

#### bobdoering

Trusted Information Resource
Re: Cpk and Ppk differance

First - and most important question: is Cpk or Ppk even applicable? What is the process and the characteristic? Is it normal? Should it be? If not, it does not apply.

After that, yes, the process is assumed to be normal and in control (no special causes) before calculating the indices. But, that is rarely the case...it is nearly impossible to remove all special causes - although you can do it mathematically (do not include it in the capability study data). Then the difference in Cpk and Ppk depends on the source of variation.

D

#### Darius

Re: Cpk and Ppk Differences

Though we are calculating Cpk or Ppk with system only stat. control then standard deviation for both the capability would be same?

How can Ppk will be less or standard deviation will be higher for Ppk.

Will it affect by common causes as well as special cause of variation
The mathematical difference between Cpk and Ppk is the standard deviation estimate, the stdev estimate for Ppk could be greater or equal to Cpk stdev estimate (equal is there are no special causes and no trend). SPC control Chart uses the same estimate as Cpk.
The special causes affect more Ppk stdev estimate that Cpk and Control Chart stdev estimate. But all stdev estimates are affected by special causes (bigger).

how can we say that system is in the stat. control?
The ausence of patterns, but as bob said, it could happen even with simulated data.

If system isnot in the stat. control then to calulate Cpk and Ppk will be wrong.
Cpk could be wrong (many could say this) and as Wheeler said Ppk could be also wrong because is useless obtain a value that could change too much.

I will say, as I readed somewhere: "To manage, You must measure"

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Unless of course you have a negative variance component. Remember Cpk is based on the within lot variability. PpK is based on total variation which is the sum of lot to lot and within lot variability. If the lot to lot variance is negative (a statistical anomoly), it is possible to have a Ppk that is larger than Cpk.

Hmmm....why do we use Cpk and PpK?

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Unless of course you have a negative variance component. Remember Cpk is based on the within lot variability. PpK is based on total variation which is the sum of lot to lot and within lot variability. If the lot to lot variance is negative (a statistical anomoly), it is possible to have a Ppk that is larger than Cpk.

Hmmm....why do we use Cpk and PpK?
oooh a great question: because someone mistakenly thought that within subgroup variation (which in standard charts is piece to piece variation) represents the true common cause variation and again mistakenly mis-interpreted this to mean that Cpk was the potential capability (besides centering) of your process and that it woudl be difficult to impossible to improve upon that performance without changing the technology. Nice try but wrong on so many levels. Unfortuantely it got written into articles, then company manuals then books and now since it's published, well by golly it must be true! Statistical Sillyness...

the Ppk > Cpk (negative variance component) can happen when we use the Range method and we have 'chunky' data. This overestimates the within standard deviation making it larger than the total standard deviation. I don't see it frequently, but it's not uncommon.

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
oooh a great question: because someone mistakenly thought that within subgroup variation (which in standard charts is piece to piece variation) represents the true common cause variation and again mistakenly mis-interpreted this to mean that Cpk was the potential capability (besides centering) of your process and that it woudl be difficult to impossible to improve upon that performance without changing the technology. Nice try but wrong on so many levels. Unfortuantely it got written into articles, then company manuals then books and now since it's published, well by golly it must be true! Statistical Sillyness...

the Ppk > Cpk (negative variance component) can happen when we use the Range method and we have 'chunky' data. This overestimates the within standard deviation making it larger than the total standard deviation. I don't see it frequently, but it's not uncommon.
What really irks me is that it continues to gain traction. I have a client who uses Cpk and Ppk values as an acceptance criteria for a lot. When I explained that those same values can be distilled to a CV specification, they thought I pulled some statistical vodoo out of my hat. The funny part is that they tend to fail the Ppk criteria (their run to run variability is awful) but have stellar Cpk (their within run is actually very tight).

Anyway, excellent observation Bev!

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