# Is Cpm of any use?

Six Sigma – iSixSigma Forums Old Forums General Is Cpm of any use?

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• #31684

Ranjan
Participant

I have a process that is measured by its deviation from zero. I currently use the Cpm measure (with minitab) to get process capability. My current process deviates a maximum of less than one half of the tolerance width, but the corresponding Cpm value does not portray it to be very capable (values<1). I am confident that the process is well over what Cpm reports. Is there any other way to evaluate this kind of a process?

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#83705

Mikel
Member

Cpm is probably the best of all the capability metrics.
You are measuring deviation from zero – does that mean all of your readings are positive? If it does, this is a one sided spec and should be treated as such. Cpm would not be appropriate.

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#83706

Ranjan
Participant

As you asked, my readings are all diametral deviations derived from radial deviations from the nominal, and thus positive in nature. Would there be any other statistic other than Cpm?

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#83708

Mikel
Member

Yes, enter the spec as one sided as it only has a maximum dimension and use Cpk/Ppk.
If your nominal is anywhere near zero, this also will not be normally distributed, it will be skewed right.
Post your data if you want further help.

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#83729

Gabriel
Participant

Yes, it is usefull, but not widely used.
There is a nice article about Cpm (with a link to Cpk and Ppk) at http://www.pqsystems.com/cpk-ppk-cpm.htm
Cpm is like Cpk (or, more correctly, like Ppk) but you calculate the standard deviation from the TAGET, instead of from the AVERAGE (i.e. inside the square root you use (Xi-T)^2 instead of (Xi-Xbar)^2).
When the process is centered, Pp, Ppk and Cpm are the same (I am assuming that the center of the specification is the target, what is NOT allways the case)
Pp does not change when off-centering (it just compares specification against the variation arround the process average.
Ppk gets lower when off-center but does not take the target into account. It compares the distance between the average and the specification limit against the variation arround the process average.
Cpm gets lower when off-target. It compares the specification against the variation arround the target.
You can think of the variation arround the target as the varieton of the individuals arround the process average plus the distance between the process average and the target (just the concept, not mathematically correct).
For example, imagine that you have a process that you want to run at Ppk 1.5. That is that the process average is at 4.5 sigmas form the closest specification limit. If you improve the process variation (reduce sigma) you can move the average closer to the specification limit (to keep 4.5 sigmas) and the Ppk is the same. However, the Cpm would have worsened, because the average distance of the individuals from the target would have increased due to the “distance between the process averaage and the target” term.
We could say that Cpm is more “loss function” (aim to the target) focused, while Ppk is more “goal post” (meet the specification) focused.
Now, as Stan said, if “zero” is a phisycal lower limit (like in ovality, rughness, etc.), then Cpk or Ppk may be more suitable (using the upper specification limit). Even in that case, Cpm can give you extra information.
Let’s take ovality as an example. Let’s say that the specifiecation is 0.1 max. Just to simplify the example, let’s say that the ovality is normally distributed (which most probably will NOT be the case). Let’s say that you current process delivers an average ovality of 0.05 with a standard deviation of 0.02. That leads to a Ppk=0.83 and a Cpm=0.31.
Now let’s say taht you make a change in the process with which you can cut variation to 0.01, but the varage ovaliti goes to 0.07. Now you got a Ppk=1 and a Cpm=0.24. Leave the absolute vaues and think of the change.
The Cpk has improve because the “worst case” parts are “more in specification”. Average + 3S = 1.1 before and 1 after. You will have more parts inside the specification.
The Cpm worsens because, even with an improving contribution due the reduced variation, the worsening contribution due to the larger of-target increase has more weight. You want “zero” ovality, on average you had 0.5 before and you have 0.7 now. You will have more parts farther from the target.
So, you seem to have a god capability: “My current process deviates a maximum of less than one half of the tolerance width”. Maybe you should use the Cpk or Ppk to inform your customer about your ability to meet the specification and monitor the evolution of Cpm (regardless its absolute value) to direct your improvement efforts. When you improve Cpm you ALLWAYS improve Cpk.
From the link at the beginning of this post:
“Regardless of the target in relation to the specifications, the focus should always be on making the product to target with minimum variation. Cpm is the capability index that most accurately depicts this.”

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#83731

Mikel
Member

Well said

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