What Is Cpk?

Hi Scott,

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.

Hope this helps.

k = katayori or kitayuri  I'm not sure and it means the shift of process

It should be "katayori" which means deviation, inclination or offset in my Japanese --> English Dictionary

I have a booklet from Ford Motor Argentina "Control Continuo de Proceso" (i.e. Ongoing Process Control). It is dated 1983, it looks very much (both in content and in format) as the current SPC by AIAG, and I don't think it was "invented" by Ford Motor Argentina. It is probably based on a previous English version from Ford Motor Co. As a curiosity, this material does not even mention Cp, but it states "Cpk=MIN(USL-Xbarbar;Xbarbar-LSL)/3"

I am sure that Cpk is even much older than that, but this objective evidence is enough to prove that your theory is wrong.

Sorry, this does not answer your question.

Scott,

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

Thanks moly.  That makes sense...  After Ross's message, that is where I would have headed on my own.  Thanks for the help.

This may be a long shot, but in Mil Std 414, Inspection Sampling with varible data, you calculate the Qu and Ql and compare it to a k value.  Mil Std 414 was replaced by ANSI/ASQ Z1.9

jabavock and moly figured it out for me.  Thanks all.

thank you Ross and Eileen, your answers really help, however what are the best values for cpk and cp? pls help. Do they need to be at center?

If the item or the process is still in the design stage, target Cpk or Ppk must be 1.67 while for stable processes, it's 1.33.

There is a tendency that the data sampled is not in the center due to some variations/drifts and depending on the distance of the drift, this will further lessen the Cpk and will have larger defects

Hi Romel,

Can i get in touch with you on your e-mail ID, need to understand how do we calculate CPk for process in design stage?

Pradeep Sharma

It's the same except that for design stage, Ppk or preliminary process capability is the term used and the target is 1.67. Also, the sample size may not be as big for the design stage and let the design team decide on this.

Hi all, I just a beginner in this spc, but i feel it is very interesting to explore a new things, wish you can help me.

Te envio la informacion de porque es la K en CPK.

saludos.

After reading all the responses, nobody has been able to explain what K means. Why K instead of S or W????

Why we look at Japanese words to find the answer to this question?

The answer may simply be that somebody selected K to describe the offset location of the mean. Plain and simple/

Thoughts please.

Jose

Why do you care.................