# Process Capability - Long-term vs. Short-term

T

#### Tamashiro

In the Statistical process Control Reference Manual published by AIAG, capability falls under 2 categories; long-term and short-term. On page 59, Long-term capability is denoted as Cpk and uses an estimated process standard deviation while short-term capability is denoted as Ppk using the calculated standard deviation. It has been argued and published by many statistical program companies that Ppk is long-term and Cpk is short-term. the reasoning for this confusion relies on the definition of what long-term and short term is and how it relates to the standard deviation. What is the definition of Cpk and Ppk and why do most software companies publish process capability contrary to the statements in the AIAG manuals?

L

#### Lassitude

why do most software companies publish process capability contrary to the statements in the AIAG manuals?
Because the AIAG is not the only 'expert' or business in the world. Software companies are looking to sell to the world, not just Ford, GM and Chrysler.

Specifically which software package are you talking about?

#### Marc

##### Hunkered Down for the Duration with a Mask on...
Staff member
I have no experience with minitab to know. Can you cite the specific equation differences (or other details of the differences) you are asking about?

T

#### Tamashiro

The equation for process capability is exactly the same as indicated in the AIAG reference manual. The clarification I'm looking for is in the definition of long term and short term. The AIAG reference manual does not define long term or short term, but seems to imply long term using Cpk. Cpk uses an estimated sigma, which implies it estimates capability based on trend and therefore may predicate future capability. Ppk, however uses a finite source of data for sigma, which implies capability for that particular set of data.
In some of the software packages, I've noticed Cpk is referenced as short-term and Ppk as long-term. What is the definition of long-term and short-term capability and is long-term represented by Cpk or Ppk?

D

#### Don Winton

I am not familiar with Minitab either. I also do not have a copy of the AIAG manual. But, as I elaborated on in the forwarding thread I referenced above, I believe AIAG has produced more problems by creating this Ppk thing. I had never heard of it before the forwarding thread above, nor had I heard of short-term or long-term capability studies.

All process capability studies should use an unbiased estimate of standard deviation or calculated standard deviation as detailed in the CPK.PDF file located at the PDF Zone section of the Cove. It states:

"To obtain an accurate estimate of the process spread (standard deviation), at least sixty data points are needed. If less that sixty data points are available, use the following formula with error correction factors given in Table 1."

Basically, if there are less than sixty data points, you use an unbiased estimate of standard deviation corrected by the formula. If greater than sixty data are available, use the standard deviation calculated from the data.

BTW, which symbol (s, sigma-hat, s-hat, etc.) does the AIAG manual use in the formula for Ppk and Cpk to represent process spread?

Regards,
Don

------------------
Just the ramblings of an Old Wizard Warrior.

B

#### BRoyal

Davis Bothe addresses the difference between Cpk and Ppk in his book "Measuring Process Capability." McGraw-Hill is the publisher. Be aware that this book will probably tell you more than you want to know about process capability

Ben Royal

B

#### Batman

Hi Don!
The AIAG manual uses [Greek]lower case Sigma with a hat for Rbar/d2 estimate from the X-R chart.
Lower case 's' for the sample standard deviation (n-1) from a random sample.

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