# How much does Cpk > 1.33 represent in precentage of good pieces?

T

#### tattva

Cpk

Hi all!

Could someone help me with the following:

How much does CPK>1.33 represent in precentage of good pieces? Is there a matrix where I can find these values at Cpk>1; Cpk>1.67; Cpk<1; Cpk=0?

#### howste

##### Thaumaturge
Super Moderator
I've only got a minute before I've got to go, so I'll just get you started...

First, in order for the statistics to be meaningful, you need to have a normal process that is in control. Now, the percentage can actually be different depending on if the distribution is centered or not. A perfectly centered process with Cpk = 1 will have twice as much (theoretical) nonconforming product as one with a Cpk = 1 that is not close to being centered.

What you need to get the percentages is the Z value(s) and a "standard normal" table to look up the results. When you look at the formulas you find that basically Z = 3xCpk.

I'm attaching a standard normal table - hopefully you can figure it out from here. If not I'll be back later...

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#### howste

##### Thaumaturge
Super Moderator
Great link, Howard. I was trying to explain how a watch works, when all Tattva asked for was the time...

#### Darius

##### Quite Involved in Discussions
Howard, it's a great link, tanks for the tip

For the ppm to Cpk question, both articles, Capability and Six Sigma look like a check mate (no more can be told).

From Six Sigma article (in Howard's link)

Cpk =0.8406+(29.37-LN(ppm)*2.221)^0.5

or

ppm = EXP(-((Cpk-0.8406)^2-29.37)/2.221)

But keep on mind what Don Wheeler said in te point 8.4 from Advanced Topics in Statistical Process Control, 1995.
"It's impossible to convert a capability ratio into a fraction of nonconforming product without using some probability dsitribution in the convertion... of course
, the traditional assumption is that the data are normally distributed.... in most cases the uncertainty in the fraction nonconforming will be greater than the refinement offered by such convertion"

S

#### Sam

tattva said:
Hi all!

Could someone help me with the following:

How much does CPK>1.33 represent in precentage of good pieces? Is there a matrix where I can find these values at Cpk>1; Cpk>1.67; Cpk<1; Cpk=0?

I'm going to step out on a limb and say that Cpk, in and of itself, will not tell you how many good parts you have. Cpk only measures process centering.

Case in point; I have a process that has a Cpk= .8 , Cp = 1.66, Zmin = 2.386, Spec avg = .125, Process avg = .1197
There are zero nonconforming parts. All data entered was within spec.

Using the Z-value would show a "potential" for approx. .85% nonconforming.
When I want to relate percent defective to number of parts I use PPM.

#### howste

##### Thaumaturge
Super Moderator
Sam said:
I'm going to step out on a limb and say that Cpk, in and of itself, will not tell you how many good parts you have. Cpk only measures process centering.

Case in point; I have a process that has a Cpk= .8 , Cp = 1.66, Zmin = 2.386, Spec avg = .125, Process avg = .1197
There are zero nonconforming parts. All data entered was within spec.

Using the Z-value would show a "potential" for approx. .85% nonconforming.
When I want to relate percent defective to number of parts I use PPM.
The usefulness of statistics comes from measuring samples and then making inferences about the population. My question is (assuming the process is normal and in control), did you measure every part in the population? If not, then I would guess you really do have nonconforming product, you just didn't happen to find it in the samples you took.

S

#### Sam

howste said:
The usefulness of statistics comes from measuring samples and then making inferences about the population. My question is (assuming the process is normal and in control), did you measure every part in the population? If not, then I would guess you really do have nonconforming product, you just didn't happen to find it in the samples you took.

I think that's what I inferred in my response when I said the reaults of the Z-value provided the "potential" nonconformances.
In response to Tattvas' question "can Cpk be related to Nonconformances"? I said no, and I stick wth that.

#### howste

##### Thaumaturge
Super Moderator
Sam, I very much respect your opinion, as IMO you've proven yourself to be very knowledgeable here at the Cove. I'm just trying to figure out what you're getting at. Here's what I've finally decided...

Your point: You don't know exactly how much defective product you have based on Cpk
My point: You can get a pretty good estimate if you do it right

Does that sound pretty close?

S

#### Sam

howste said:
Sam, I very much respect your opinion, as IMO you've proven yourself to be very knowledgeable here at the Cove. I'm just trying to figure out what you're getting at. Here's what I've finally decided...

Your point: You don't know exactly how much defective product you have based on Cpk
My point: You can get a pretty good estimate if you do it right

Does that sound pretty close?
That sounds close enough to me.

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