# Difference between Cpk and Ppk

#### Filipa

##### Registered
I have a question regarding the process stability assessment.
The difference between Cpk and Ppk can tell us whether the process is in control or out of control. When these two indicators are equal, it means that the short-term and long-term standard deviations are close, that is, there are no special causes acting on the process, so the process is in control. However, the greater my capacity (the smaller the standard deviation), and maintaining the difference between the long-term and short-term standard deviation, the greater the difference between Ppk and Cpk. In other words, I will tend to say that the process is out of control. But in reality the difference in standard deviation is the same as in the past, when the variation values were greater. Can we use this metric to evaluate the difference between Ppk and Cpk to check if the process is in control?

If you could help me, I would really appreciate it. What are your opinions?

#### Miner

##### Forum Moderator
Your argument would be better if you were to use Cp and Pp. The reason being that Cpk/Ppk include centering. Ppk could be greater than Cpk because the process had less variation (was in control) but at a greater distance from nominal.

Regardless, using the capability metrics to assess control would be a very rough and crude way to assess control, particularly given the uncertainty around these metrics. Most people take the point estimates of Cp/Cpk/Pp/Ppk as values with zero uncertainty, but that is far from reality. There was uncertainty in the sample mean and uncertainty in the sample standard deviation, both of which result in even greater uncertainty in the calculated index. You are better off evaluating the control chart using the rules most appropriate for your process.

#### Bev D

##### Heretical Statistician
Super Moderator
At best you have put the cart (Cpk/Ppk) before the horse (control charts). At worst your cart has no wheels and your horse is no where in sight…

You absolutely cannot use Cp/Pp or Cpk, Ppk to determine the state of statistical control. While there may be some mathematical relationship it is merely coincidental based on a theoretical foundation of homogeneity which simply doesn’t always exist in the real world.

Control charts with a true rational subgrouping scheme are the only way to establish statistical control. PERIOD. Full Stop.

A non-homogenous process will have very divergent Cp/Cpk and Pp/Ppk values because the subgrouping scheme is not rational (traditional and widely used subgrouping in Cp/Pp world is to use piece to piece as the subgrouping scheme). A naturally non-homogenous process will require a subgrouping scheme that is not piece to piece. And that process may also be completely stable and predictable. I know this because of my deep research into this topic and more importantly my 40+ years of studying and improving literally thousands of processes from a very wide and diverse universe of processes - most of which were non-homogenous.

The calculated Cp/Cpk and Pp/Ppk indices ‘might’ be useful IF:
(1) The sample size is sufficiently large to estimate the standard deviations
(2) The subgroups are spread out enough to be representative of the true process variation
(3) The indices are NOT used to determine the ‘defect rate’ which is always based on some theoretical distribution which always overestimates the extreme values.

Process capability indices have been debunked and gutted many times but lazy people love them because they reduce variation to a single number and replace thinking with rote mathematical calculations that can be performed by a computer…please don’t be one of those people.

#### Filipa

##### Registered
Your argument would be better if you were to use Cp and Pp. The reason being that Cpk/Ppk include centering. Ppk could be greater than Cpk because the process had less variation (was in control) but at a greater distance from nominal.

Regardless, using the capability metrics to assess control would be a very rough and crude way to assess control, particularly given the uncertainty around these metrics. Most people take the point estimates of Cp/Cpk/Pp/Ppk as values with zero uncertainty, but that is far from reality. There was uncertainty in the sample mean and uncertainty in the sample standard deviation, both of which result in even greater uncertainty in the calculated index. You are better off evaluating the control chart using the rules most appropriate for your process.
I understood what you said. There is always a certain uncertainty associated with it. Thanks!
If using the difference between Cp and Pp it is the same thing, right?
I wanted to "automate" how to tell if the process is in control or out of control. It seems impracticable to go by these indicators, so can I go by the probability rule of the control charts? That is, for a process to be in control (within 6 sgima) the probability is 99.73%. Therefore, in 1000 subgroups I can only have 3 points out of control (cases of out of control - trends, outside the 3 sigma...)

#### Bev D

##### Heretical Statistician
Super Moderator
You need to research your topics a bit more...you are referencing a lot of misinformation about both process capability and control charts. This is not your fault - there is a lot of misinformation out there...

Here is a reading list (most are free on the internet):

Sullivan, L. P., “Reducing Variability: A New Approach to Quality”, Quality Progress, July 1984 and “Letters” Quality Progress, April, 1985 https://asq.org/quality-progress/ar...o-quality?id=a9e0a3a5f34f48f4b5604841de41865d (free for ASQ members) This is the seminal article on process capability that is useful and makes NO estimation of defect rate...

Gunter, Berton H., “The Use and Abuse of Cpk”, Statistics Corner, Quality Progress, Part 1 January 1989, Part 2 March 1989, Part 3 May 1989, Part 4 July 1989 https://asq.org/quality-progress/ar...-parts-14?id=4a37bc559698426f8543d26330fa5176 (free for ASQ members)

Pignatiell, Joseph J. Jr., Ramberg, John S., “Capability Indices: Just Say “NO!””, ASQC Quality Congress Transactions – Boston, 1993

Leonard, James, “I Ain’t Gonna Teach It”, Process Improvement Blog, 2013 "I ain't gonna teach it!" - Jim Leonard - Process Improvement

Nelson, Peter R., Editorial, Journal of Quality Technology, Vol. 24, No. 4., October, 1992 Issue devoted to Process Capability Indices

Wheeler, Donald J., “Myths About Shewhart’s Control Charts”, SPC Tool Kit column, Quality Digest, September, 1996 https://www.qualitydigest.com/sep96/spctool.html

Wheeler, Donald, J., “Foundations of Shewhart’s Charts”, SPC Tool Kit column, Quality Digest, October, 1996 https://www.qualitydigest.com/oct96/spctool.html

Wheeler, Donald J., “The Empirical Rule”, Quality Digest, March 2018 (broken link removed)

Wheeler, Donald, “The Right and Wrong Ways of Computing Limits”, Quality Digest, January 2010 The Right and Wrong Ways of Computing Limits

Wheeler, Donald, “Good Limits from Bad Data I”, Quality Digest, March 1997 SPCTool

Wheeler, Donald, “Good Limits from Bad Data II”, Quality Digest, April 1997 SPCTool

Wheeler, Donald, “The Empirical Rule of Distributions”, Quality Digest, March, 2018 (broken link removed)

McGue, Frank; Ermer, Donald S., “Rational Samples – Not Random Samples”, Quality Magazine, December 1988

Wheeler, Donald, “What is a Rational Subgroup?”, Quality Digest, October 1997 SPCTool

Wheeler, Donald, “Rational Subgrouping”, Quality Digest, June 2015 (broken link removed)

Wheeler, Donald, “Rational Sampling”, Quality Digest, July 2015 Rational Sampling

Wheeler, Donald, “The Three-Way Chart”, Quality Digest, March 2017
The Three-Way Chart

Wheeler, Donald J., Neave, Henry R., “Shewhart and the Probability Approach”, Quality Digest, November 2015 (broken link removed)

#### Miner

##### Forum Moderator
I wanted to "automate" how to tell if the process is in control or out of control. It seems impracticable to go by these indicators, so can I go by the probability rule of the control charts? That is, for a process to be in control (within 6 sgima) the probability is 99.73%. Therefore, in 1000 subgroups I can only have 3 points out of control (cases of out of control - trends, outside the 3 sigma...)
Unfortunately, this is not a good approach either. Shewhart never based his control charts on fitting a specific distribution and on probability theory. He simply used an empirical approach and arrived at 3 standard deviations solely because it seemed to strike an economical balance between the cost of missing a process change and the cost of chasing down a false alarm. Other latecomers, not understanding this, saw 3 standard deviations and immediately piled all of the probability theory on top. The theory is not what makes SPC work.

Additionally, each process is unique and subject to unique ways of going out of control. Some will shift abruptly when you change a batch of raw material. Others will trend slowly out of control. Yet others will exhibit small shifts followed by long runs due to the automated control mechanism. Sometimes, if the process is highly capable, the economic decision might be to live with these minor idiosyncrasies in an otherwise well-behaved process.

#### Bev D

##### Heretical Statistician
Super Moderator
I had similar beliefs and inclinations when I graduated and started out as a quality engineer. I was so excited to calculate defect rates using the Normal distribution and Xbar R charts adn fishbone diagrams to help me solve problems and maintain process control just like in the Quality Journals of the day said I could. And the best part was I wouldn’t even have to leave my desk, gown up and head out to the manufacturing floor. BOY WAS I WRONG. Rule 1 - get out on the floor and see for yourself what is actually happening. Rule 2 - GRAPH your data Rule 3 - Use your scientific and practical knowledge to understand what the data is telling you, in other words: THINK. Rule 4 - don’t go it alone. You need someone to coach you and to bounce ideas off. I found a book by Ellis Ott. It changed the course of my career and gave me a healthy level of skepticism and the foundation for understanding variation.