What is the 'k' in Cpk?

[Ibrahm]

I know the meaning of Cpk but curious about what k stands for. Anybody knows ?

[Jennifer Kirley]

Originally Posted by Ibrahm

I know the meaning of Cpk but curious about what k stands for. Anybody knows ?

Here is the fastest, best explanation I could find for you. While it doesn't obviously say "Here is what k means", I thought it described the subject pretty well:

http://www.isixsigma.com/library/con...0806a.asp#defs

[Al Dyer]

E=MCsquared

Energy = mass x speed

Why is acceleration/speed designated as "C"?

Gotta call it something!!!!!

Cindy !!!

[Atul Khandekar]

Here's a discussion from the site Jennifer referred:
http://www.isixsigma.com/library/content/c030304a.asp

[Marc]

A quick summary from Atul's link:

The "k" in Cpk is not for Victor Kane, although it would be a fitting tribute to his work in this field. The origins of k actually go back to the 1970s in Japan. The Japanese are credited with developing the the Cp, Cpl, Cpu, Cpk, and k indexes of process capability.

So what is k? It is an index of process centering, defined as follows, where M is the middle of the tolerance, mu is the process average, USL is the upper spec limit, and LSL is the lower spec limit:

k = |M - mu| / [(USL - LSL) / 2]

k is then used as follows to compute Cpk.

Cpk = Cp (1 - k)

When the process average is centered at the middle of the tolerance, M = mu, and therefore, M - mu = 0. With k = 0, Cpk will equal Cp.

Cpk = Cp (1 - 0) = Cp

If the process average is centered anywhere else, then the absolute value of the quantity M - mu is greater than zero, making k also greater than 0. Suppose k is 0.30 for a process. Then the Cpk index for this process is only 70% of the Cp index.

Cpk =Cp (1 - 0.30) = 0.70Cp

So in one way, k measures how much potential capability is lost due to poor centering. In the above example, Cpk could be increased by 30% if we could center mu at M.

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You really started my day off with a good laugh. Vic and I worked together for many years. He would enjoy this one! He had nothing to do with defining the k in Cpk. Although his paper on Capability Indices is excellent, the index has been around for many decades. It can be found in some AT & T material from the 50's and 60's. I do not know where it originated. However, the definition of Cpk is frequently defined as:

Cpk = min 1/3(Zsub L, Z sub U)or min 1/3(lsl-xbar/sigma, usl-xbar/sigma)

The z-statistic is defined as (x-xbar)/sigma. This quantity used to be defined as the k-statistic in the 40's-50's, later to be changed to z. Hence, the Cpk. Maybe, we should change it to Cpz?

As for the Argentine Ford Material, it was originally written by Pete Jessup at Ford in North America, specifically Dearborn, Mich. Pete compiled existing material for the SPC manual. He did not define Cpk either. It is an index much older than either Vic or Pete.

Eileen Beachell, Quality Disciplines

[Bill Pflanz]

I read this posting mainly out of curiosity since I also have always used Cpk but do not remember how it was started. Maybe I can look through my files and see if I have anything else to contribute.

The interesting part is that the use of the term is obviously related to the sampling and other statistical tools developed during the 1940's and 50's. That is not totally surprising since many of the modern techniques and standards can be traced back to the military and World War II. I also noticed the reference to AT&T which can trace its history to Western Electric and the work done by Shewhart, Juran and other quality gurus.

Bill Pflanz

[Jim Howe]

Originally Posted by Bill Pflanz

I read this posting mainly out of curiosity since I also have always used Cpk but do not remember how it was started. Maybe I can look through my files and see if I have anything else to contribute.

The interesting part is that the use of the term is obviously related to the sampling and other statistical tools developed during the 1940's and 50's. That is not totally surprising since many of the modern techniques and standards can be traced back to the military and World War II. I also noticed the reference to AT&T which can trace its history to Western Electric and the work done by Shewhart, Juran and other quality gurus.

Bill Pflanz

I was also curious! let me state that in all the math courses I ever took the letter "k" was always used to designate a constant. Could it be that it is this simple "a constant"?

[Marc]

Originally Posted by Jim Howe

I was also curious! let me state that in all the math courses I ever took the letter "k" was always used to designate a constant. Could it be that it is this simple "a constant"?

You know, now that you mention it I think I remember that as well from math courses years ago. For whatever reason k was always a derived constant. It always came from somewhere but when you asked where from the response was something like "We'll be getting to that, but for now all you need to know is this list of k's to solve the problems I'm giving you" or "It's beyond the scope of this course" or similar reply.