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...
Thanks to howste for your informative Post and/or Attachment!
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.
Quote:
"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"
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?
Thanks in advance!
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.
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.
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.
Cpk
Linear Mode
