# Cpk for one sided dimension - GD&T true position

D

#### dave@utah

What is the formula (or concept) for calculating a Cpk on a "smaller is better" dimension. Specifically, I am trying to calc Cpk for a GD&T true position of .030. And would the same concept work for profiles, flatness, runout, etc.
Thanks
Dave

D

#### Don Winton

Go to Free Files Directory and download CPK.pdf. That should explain all you need.

Regards,

Don

Last edited by a moderator:

#### Marc

##### Fully vaccinated are you?
Some additional 'thought food':

>Luiz Alberto Rodrigues wrote in message
>Who know ?
>
>Why the minimum requirement for potential capability (unilateral
>specifications) is the ability to produce 99.865, not 99.73, percent
>conforming product ?

-----------------------

From: Kevin
Newsgroups: misc.industry.quality
Subject: Re: Capability
Date: Wed, 22 Mar 2000 06:41:06 GMT
Organization: AT&T Worldnet

Luiz,

I'm sorry Luiz, but I am as dumb founded as you are at this. Can any Statismajicians please explain? 99.73% is arrived through a normal bilateral distribution, given a +/- 3 sigma dist.. The part that is not inside the +/- 3 sigma is 0.27%. I can see were the 0.135% came from, its just that I cannot justify it. If I put the outside of the normal curve on zero, the smallest sigma value would still be 0.135% of the total range away, and the max sigame value would be at 99.865% away, but this would still leave 0.27% of the curve outside of the +/- 3 sigma range. Luiz, could you explain who told you this?

Thank you,

Kevin Terrill

-----------------------

From: BML
Newsgroups: misc.industry.quality
Subject: Re: Capability
Date: Wed, 22 Mar 2000 16:54:47 GMT
Organization: Deja.com - Before you buy.

The problem with the one-sided Cp/Cpk etc. is the fact that it does not take into account the other side. For example, you state that even for a unilateral measurment, 0.27% is still outside the +/- 3S limits.

That is true. However, since the measurement is unilateral, we're not concerned with one of the tails, so it doesn't count. (Remember hypothesis testing?) The tolerance is unilateral exactly because that other tail doesn't count, i.e. the part is good even if it is in that one tail. Therefore the only way you can have a bad part is if you are in the *other* tail, which has an area of 0.27/2 = 0.135. Kinda confusing, but that's the way it works.

Ben

--------------------

From: "John Duffus"
Newsgroups: misc.industry.quality
Subject: Re: Capability
Date: Wed, 22 Mar 2000 19:29:29 GMT
Organization: MetroNet Communications Group Inc.

Here's another way of looking at it. You are running a marginal process with a Cpk of one, i.e with .00135 fraction defective in each tail for a total of .0027.

The specification is then changed so that one tolerance limit is disregarded, So you can now say, good, now I only have .00135 fraction defective. You improved the fraction defective, not by having a better process but by relaxing the tolerance.

If you start from an objective of a certain fraction defective, you could argue that you should have a lower Cpk for a one-sided tolerance, but if you put all your fraction defective in one tail you have an increased sensitivity of the fraction defective to shifts in the process average. In any event fraction defective depends on an assumption of a normally distributed population making the calculations only very approximate in most cases.

John Duffus

#### Marc

##### Fully vaccinated are you?
misc.industry.quality
Re: Capability

The whole argument about unilateral characteristics and their meaning in reality is often wrongly interpreted in industry.

Firstly, for a process with a natural boundary (such as flatness) of zero and a upper tolerance the model distribution when the system is tuned to peak performance (centred) and has no external variation is - Rayleigh Distribution.

However, this very seldom happens in reality. The secret of successful capability studies are to ignore what distribution model it should be {afterall, the process doesn't care what you 'think' it is} and concentrate on modelling the actual data. This model can then be used to get more realistic capability assessments of the process.

In order to do this you need a statistical analysis software that can do this. I recommend the package I use - qs-STAT by Q-DAS.
www.q-das.com

I have used this many times to the advantage of machine tool builders to rationalize just situations.

M

#### Mary - QA Manager

I realize this post is 15 years old, but was wondering if anyone had an up to date answer. I am having the same issue with true position, and profiles. Is there a formula I can use in excel for the Cpk?

Mary

#### bobdoering

##### Stop X-bar/R Madness!!
Trusted Information Resource
I realize this post is 15 years old, but was wondering if anyone had an up to date answer. I am having the same issue with true position, and profiles. Is there a formula I can use in excel for the Cpk?

Mary

There really is no such thing as a Cpk for a unilateral dimension. The point of Cpk is to determine if the mean is centered within the tolerance. There is no center to a single tolerance. For form features - such as roundness - you do NOT want to be centered as a target - target is zero. "Half Cpks" do not answer the centered question - but a totally different question of distance to tolerance. Moreover, they are generally incorrectly calculated assuming a normal distribution, and typically are non-normal (such as beta distributions). In the AIAG PPAP book there is a specific paragraph for non-normal and unilateral tolerance that specifies Cpk calculations will be erroneous. Most people don't read that paragraph...skip right over it.

G

#### GoKats78

I developed this a few years back..it might not be perfect but it works for our purposes

it is password protected (and contains macros)....password is forms

#### Attachments

• QA000075.xls
402.5 KB · Views: 650

#### bobdoering

##### Stop X-bar/R Madness!!
Trusted Information Resource
I developed this a few years back..it might not be perfect but it works for our purposes

it is password protected (and contains macros)....password is forms

This tool is great for bilateral, normally distributed variables. For unliateral tolerances, I recommend Distribution Analyzer at variation.com. More than likely the distribution is non-normal. This will determine the best fit distribution model, and calculate capability and probability based on the best model - not a "half Cpk" = which is statistically unsubstantiated.

#### Bev D

##### Heretical Statistician
Super Moderator
ah but all capability indices are mathematical voo-doo masquerading as statistics.

G

#### GoKats78

This tool is great for bilateral, normally distributed variables. .

Not sure what you mean...I am not a stats guy...but the formulas I have listed on the one-sided tolerance tabs are, what I found though doing digging through reference documents and multiple articles, correct for single sided tolerances. If they aren't, I will correct them!