# Short Term vs. Long Term SPC Study - Where is Cp and Cpk Defined

#### AMIT BALLAL

Super Moderator
Hello all!

There has always been a confusion regarding whether Cp,Cpk is for short term or long term. Although I came to know that Cp,Cpk is for short term and to be used during preliminary SPC study (Such as development stage), there is no reference available supporting this.

I tried to look for it on AIAG SPC 2nd edition manual, but couldn't find it.
Please help me to find it on this manual / share with me other reference if any, so that I can use it as a reference and to manage the arguments happen between customer / auditors.

Amit

#### Bev D

##### Heretical Statistician
Super Moderator
There are many posts on this recurring question on Elsmar...
here is the text of a summary I posted February 19, 2016 on The Quality Forum Online

On Cpk, Ppk and long & short term capability. A mathematical conundrum.

Besides the fact that Cpk and Ppk are worse than useless and an abomination on the face of the earth (IMHO), the original definitions (and the ones most reputable statistical software use) are this:

Cpk = the ratio of the process spread to the tolerance using the within subgroup standard deviation. This assumes a homogenous process where the between subgroup variation is nothing more than sampling error. It is also referred to as the 'capability' index or short term capability because there is no subgroup to subgroup variation in the index.

Ppk = the ratio of the process spread to the tolerance using the total standard deviation; within subgroup and between subgroup. This is essential when we have a non-homogenous process where the between subgroup variation is more than sampling error. It is also referred to as the 'performance' index or long term capability because there is subgroup to subgroup variation.

IF the process is homogenous then Ppk and Cpk will yield very similar numbers...

Non-homogenous processes can be stable and predictable and capable. The appropriate control chart would require a rational subgroup schema different than the traditionally taught subgrouping based on sequential parts. In these cases, yes Ppk can be predictive if the other assumptions are met. (random representative sampling, Normal distribution, yada yada.)

There is a corruption of these original definitions perpetuated by some automotive and aerospace companies where the Ppk formula is used for short term studies in development phases where 30-60 sequential parts are made under the same conditions (same equipment, material, operators, etc.). (This is a valid method for short term capability)

Adding to the confusion, some companies will specify the calculation of "Cpk" but provide the formula for Ppk. This goes back to the original index which used the total standard deviation and was called Cpk.

So the ‘names’ Cpk and Ppk do not correlate to the phrases “short term” and “long term”. Nor do the formulas, as the Ppk formula using the total standard deviation is good for both short term and long term studies, depending on the study design.

To add even more to the confusion some companies reverse the definition of Ppk and Cpk by using a Ppk formula for short term capability in the pre launch phase of a product because the producer doesn't have multiple subgroups and changing conditions (different lots, different operators, etc) and then they specify the Cpk for full production conditions.

As quality professionals we should take this definition confusion as a sign that these indices are just smoke and mirrors...

#### Miner

##### Forum Moderator
Part of the confusion was that in the early 1980's, Ford Motor Company used the reverse nomenclature, stating Ppk was for process POTENTIAL and Cpk was for process CAPABILITY. After a few years, they reversed it to what is currently used today.

The current AIAG SPC manual defines Ppk as the PERFORMANCE index.

The AIAG SPC manual does answer your question indirectly. It states that the Cp/Cpk indices use Inherent Variation and the Pp/Ppk use Total Process Variation. If you go to the glossary and look up Variation, these terms are defined.

#### AMIT BALLAL

Super Moderator
Thanks a lot Bev D and Miner.

Elsmar has always been very helpful throughout my career right from when I started my career in QMS years back.

In these years I have learnt a lot and also tried to contribute in this forum wherever possible.

I would like to take this opportunity to ask your secrets behind all this wisdom and knowledge. If you can share some tips or books, it would be really a big help and I'll always be thankful.

Thanks,
Amit

#### AMIT BALLAL

Super Moderator
Part of the confusion was that in the early 1980's, Ford Motor Company used the reverse nomenclature, stating Ppk was for process POTENTIAL and Cpk was for process CAPABILITY. After a few years, they reversed it to what is currently used today.

The current AIAG SPC manual defines Ppk as the PERFORMANCE index.

The AIAG SPC manual does answer your question indirectly. It states that the Cp/Cpk indices use Inherent Variation and the Pp/Ppk use Total Process Variation. If you go to the glossary and look up Variation, these terms are defined.

Thanks a lot Miner! I found it on Page no.131 and 203 of AIAG SPC Manual 2nd edition.

Thanks,
Amit

#### Miner

##### Forum Moderator
I would like to take this opportunity to ask your secrets behind all this wisdom and knowledge. If you can share some tips or books, it would be really a big help and I'll always be thankful.

It is mostly a broad experience in a number of different industries, and even more facilities, products, and processes.

Some tips:
• Never pass up an opportunity to take training
• Research the latest developments continually
• Look for best practices and adapt them as needed for your particular situation
• Look for multiple options and synthesize something new using the best features of each
• Don't just point out a problem. Be part of the solution.
• Don't hold out for the perfect solution. Take a partial victory now and come back later for additional improvement.
• Look outside your industry. Many things are already happening somewhere else and may directly apply in your industry.
• Resist implementing something that while good is not necessary at the present time. For example, I was asked why I did not implement SPC in a machining department. My response was we have zero problems coming from machining. All of our problems come from assembly. That is where our attention needs to be focused. SPC is a good thing, but wasn't going to help us where we needed improvement.

#### AMIT BALLAL

Super Moderator
It is mostly a broad experience in a number of different industries, and even more facilities, products, and processes.

Some tips:
• Never pass up an opportunity to take training
• Research the latest developments continually
• Look for best practices and adapt them as needed for your particular situation
• Look for multiple options and synthesize something new using the best features of each
• Don't just point out a problem. Be part of the solution.
• Don't hold out for the perfect solution. Take a partial victory now and come back later for additional improvement.
• Look outside your industry. Many things are already happening somewhere else and may directly apply in your industry.
• Resist implementing something that while good is not necessary at the present time. For example, I was asked why I did not implement SPC in a machining department. My response was we have zero problems coming from machining. All of our problems come from assembly. That is where our attention needs to be focused. SPC is a good thing, but wasn't going to help us where we needed improvement.

Thanks a lot Miner for the amazing tips. It will be extremely helpful.

Thanks,
Amit

#### Bev D

##### Heretical Statistician
Super Moderator
Miner has a great list.

I would add that three are two fundamental drivers to 'our secret':
1. never-ending curiosity. don't accept things at face value. do your own research and study to truly understand WHAT, HOW and WHY things work. One of the difficulties quality professionals have is that the bulk of the literature (and the Customer 'Quality Manuals") bought into so many flawed approaches that the really informative articles and books are difficult to find. If you don't have an ASQ membership I recommend it as their vast library of articles and conference transactions are available for a nominal fee of \$5. \$10 if you are not a member.

2. Age. Unfortunately it takes time to gain the breadth and depth of experience necessary.

Below is a list of articles that I would recommend to start your studies (or any one who is interested in Quality Engineering)

Process Capability
“Reducing Variability: A New Approach to Quality”, by L. P. Sullivan, Quality Progress, July 1984 and “Letters” Quality Progress, April, 1985

“The Use and Abuse of Cpk”, Statistics Corner, by Bert Gunter, Quality Progress, Part 1 January 1989, Part 2 March 1989, Part 3 May 1989, Part 4 July 1989

“Capability Indices: Just Say “NO!””, by Joseph Pignatiell and John Ramberg, ASQC Quality Congress Transactions – Boston, 1993

I Ain’t Gonna Teach It”, by James Leonard, Process Improvement Blog, 2013

Basic Stats
“(broken link removed)”, W. Edwards Deming, American Statistician, November 1975, Vol. 29, No. 4, pp. 146-152

“(broken link removed)”, W. Edwards Deming, The Journal of the American Statistical Association, Vol. 48, 1953, pp. 244-255

Render unto Enumerative Studies…”, Rip Stauffer, Quality Digest, July 2013

Teaching Statistics that Help not Hinder Management”, David Schwinn, Quality Digest, September 2012

Why We Keep Having Hundred Year Floods”, Donald Wheeler, Quality Digest, June 2013

"The Secret Foundation of Statistical Analysis”, Donald Wheeler, Quality Digest, December 2015

Structured Problem Solving
“The Technique of Experimenting in the Factory”, Leonard Seder, Industrial Quality Control, March 1948

A Painless Look at Using Statistical Techniques to Find the Root Cause of a Problem

“Locating Sources of Variability in a Process”, W. J. Youden, Industrial and Engineering Chemistry, September, 1951, Vol 43, No.9, pp. 2059-2062

“A New Science of Trouble Shooting”, Leonard Seder, Industrial and Engineering Chemistry, September 1951, Vol. 43, No. 9

“Three Good Questions (and One Not So Good), John Allen, The New Science of Fixing Things, 2006, www.tnsft.com

“Diagnosis With Diagrams – Part I”, Leonard Seder, Industrial Quality Control, January 1950, pp. 11-19

“Diagnosis With Diagrams – Part II”, Leonard Seder, Industrial Quality Control, March 1950, pp. 7-11

“The Multi-Vari Chart: An Underutilized Quality Tool”, Robert D Zaciewski and Lou Nemeth, Quality Progress, October 1995, pp. 81-83

“Strategies for Variability Reduction”, Stefan Steiner and Jock MacKay, Quality Engineering, Volume 10, Issue 1, September 1997 , pp 125-136

#### AMIT BALLAL

Super Moderator
Miner has a great list.

I would add that three are two fundamental drivers to 'our secret':
1. never-ending curiosity. don't accept things at face value. do your own research and study to truly understand WHAT, HOW and WHY things work. One of the difficulties quality professionals have is that the bulk of the literature (and the Customer 'Quality Manuals") bought into so many flawed approaches that the really informative articles and books are difficult to find. If you don't have an ASQ membership I recommend it as their vast library of articles and conference transactions are available for a nominal fee of \$5. \$10 if you are not a member.

2. Age. Unfortunately it takes time to gain the breadth and depth of experience necessary.

Below is a list of articles that I would recommend to start your studies (or any one who is interested in Quality Engineering)

Process Capability
“Reducing Variability: A New Approach to Quality”, by L. P. Sullivan, Quality Progress, July 1984 and “Letters” Quality Progress, April, 1985

“The Use and Abuse of Cpk”, Statistics Corner, by Bert Gunter, Quality Progress, Part 1 January 1989, Part 2 March 1989, Part 3 May 1989, Part 4 July 1989

“Capability Indices: Just Say “NO!””, by Joseph Pignatiell and John Ramberg, ASQC Quality Congress Transactions – Boston, 1993

I Ain’t Gonna Teach It”, by James Leonard, Process Improvement Blog, 2013

Basic Stats
“(broken link removed)”, W. Edwards Deming, American Statistician, November 1975, Vol. 29, No. 4, pp. 146-152

“(broken link removed)”, W. Edwards Deming, The Journal of the American Statistical Association, Vol. 48, 1953, pp. 244-255

Render unto Enumerative Studies…”, Rip Stauffer, Quality Digest, July 2013

Teaching Statistics that Help not Hinder Management”, David Schwinn, Quality Digest, September 2012

Why We Keep Having Hundred Year Floods”, Donald Wheeler, Quality Digest, June 2013

"The Secret Foundation of Statistical Analysis”, Donald Wheeler, Quality Digest, December 2015

Structured Problem Solving
“The Technique of Experimenting in the Factory”, Leonard Seder, Industrial Quality Control, March 1948

A Painless Look at Using Statistical Techniques to Find the Root Cause of a Problem

“Locating Sources of Variability in a Process”, W. J. Youden, Industrial and Engineering Chemistry, September, 1951, Vol 43, No.9, pp. 2059-2062

“A New Science of Trouble Shooting”, Leonard Seder, Industrial and Engineering Chemistry, September 1951, Vol. 43, No. 9

“Three Good Questions (and One Not So Good), John Allen, The New Science of Fixing Things, 2006, www.tnsft.com

“Diagnosis With Diagrams – Part I”, Leonard Seder, Industrial Quality Control, January 1950, pp. 11-19

“Diagnosis With Diagrams – Part II”, Leonard Seder, Industrial Quality Control, March 1950, pp. 7-11

“The Multi-Vari Chart: An Underutilized Quality Tool”, Robert D Zaciewski and Lou Nemeth, Quality Progress, October 1995, pp. 81-83

“Strategies for Variability Reduction”, Stefan Steiner and Jock MacKay, Quality Engineering, Volume 10, Issue 1, September 1997 , pp 125-136

Thanks a lot Bev D for excellent tips and showing the path. This will really help. Thank you both for sharing.
Thanks word is small as compared to the help, but don't how to thank you for this. May be learning by following the path you've shown and contributing to the forum is one I can think of right now.

Thanks,
Amit

Last edited:

Replies
20
Views
3K
J
Replies
34
Views
7K
V
Replies
1
Views
5K
michajel86
M