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

D

#### [email protected]

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

#### Marc

##### Hunkered Down for the Duration with a Mask on...
Staff member

>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 ?

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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

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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

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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

##### Hunkered Down for the Duration with a Mask on...
Staff member
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

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

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#### bobdoering

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

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
Staff member
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!

S Determining Cpk on a single sided tolerance dimension Capability, Accuracy and Stability - Processes, Machines, etc. 3
B Does anyone have links to one sided CPK files? Excel .xls Spreadsheet Templates and Tools 2
A Cp, Cpk for One Sided Specification Statistical Analysis Tools, Techniques and SPC 2
T Calcuating a one sided (LSL) Cpk for Proccess Capability Capability, Accuracy and Stability - Processes, Machines, etc. 17
F Ppk/Cpk value with 1-sided specification - Only given a lower specification Statistical Analysis Tools, Techniques and SPC 1
B Cp, Cpk, Sp, Spk for a one-sided minimum specification Capability, Accuracy and Stability - Processes, Machines, etc. 2
L Calculating Cpk on a single sided (unilateral) tolerance Capability, Accuracy and Stability - Processes, Machines, etc. 28
C Capability index for one-sided specification? Cpk(max) = (USL-Xbar)/3*s ?? Capability, Accuracy and Stability - Processes, Machines, etc. 13
LTPD, AQL, Ppk and Cpk validation sampling plan table Inspection, Prints (Drawings), Testing, Sampling and Related Topics 0
Cp and Cpk for straightness and parallelism Capability, Accuracy and Stability - Processes, Machines, etc. 8
Capability - CPk comparison values Capability, Accuracy and Stability - Processes, Machines, etc. 12
Tolerance definition based on expected Cp/cpk Reliability Analysis - Predictions, Testing and Standards 14
Analysis variation among the lots during cpk calculation. Design and Development of Products and Processes 1
Recommendation for user friendly Gaga R&R and Cpk software Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 10
How to set up Continuous CpK monitoring of an injection mold process Reliability Analysis - Predictions, Testing and Standards 7
Interpretation with regards to Ppk > Cpk Capability, Accuracy and Stability - Processes, Machines, etc. 14
Cpk Calculation - I analyse a double seam cans Manufacturing and Related Processes 15
Cp / Cpk on position using multiple MMC bonuses Capability, Accuracy and Stability - Processes, Machines, etc. 2
Can we use pin gauges to measure an accurate Cpk ? Capability, Accuracy and Stability - Processes, Machines, etc. 9
Final process capability results - What I am supposed to present? Cp and CpK? APQP and PPAP 11
CpK on a manufactured assembly? Reliability Analysis - Predictions, Testing and Standards 7
How is the Cmk and Cpk calculated? Statistical Analysis Tools, Techniques and SPC 0
O Cpk for Unilateral Tolerance Capability, Accuracy and Stability - Processes, Machines, etc. 9
How to calculate CPK with n = 1 Manufacturing and Related Processes 2
O CPK with a P value less than 0.005 Manufacturing and Related Processes 8
Short Term vs. Long Term SPC Study - Where is Cp and Cpk Defined Statistical Analysis Tools, Techniques and SPC 8
A Cpk Formula seems off, need help!? Capability, Accuracy and Stability - Processes, Machines, etc. 11
D Cp/Cpk on Gages for MSA (vs. Cg/Cgk) Capability, Accuracy and Stability - Processes, Machines, etc. 21
E Questions regarding Cpk Calculation - Should we be using LSL/USL or LCL/UCL? Capability, Accuracy and Stability - Processes, Machines, etc. 5
B Maximum Material Condition with Bonus - Determine Cpk for this one kpc Measurement Uncertainty (MU) 2
Cpk Setting Tolerance - Cart before the Horse? (Wifi Routers) Capability, Accuracy and Stability - Processes, Machines, etc. 3
Calculating LCL, UCL, Cp, and Cpk in an Excel Spreadsheet Statistical Analysis Tools, Techniques and SPC 3
Cpk on Position w/ MMC on Location and Size Capability, Accuracy and Stability - Processes, Machines, etc. 3
SPC Production - Getting Cpk and Ppk Statistical Analysis Tools, Techniques and SPC 8
S Track Cpk trend Statistical Analysis Tools, Techniques and SPC 5
M Cp & Cpk about a diameter measured with min.,max. and average values. Capability, Accuracy and Stability - Processes, Machines, etc. 13
P Non-normal Data Cpk Statistical Analysis Tools, Techniques and SPC 5
Cpk for Solder Paste Height Statistical Analysis Tools, Techniques and SPC 5
As a part of validation, should i include the acceptance criteria of CPk index >1.33? Qualification and Validation (including 21 CFR Part 11) 4
T Cpk for 0 as Ideal Value Statistical Analysis Tools, Techniques and SPC 1
P Profile Tolerance and CPK Manufacturing and Related Processes 3
V When to use Cp Cpk and Pp Ppk Capability, Accuracy and Stability - Processes, Machines, etc. 4
M Calculating Cpk when sample size equals to 1 Capability, Accuracy and Stability - Processes, Machines, etc. 12
CpK in Minitab when 0.0 is the lower spec limit Statistical Analysis Tools, Techniques and SPC 7
Best way to Chart an On-Going CPK Requirement Capability, Accuracy and Stability - Processes, Machines, etc. 4
U Cpk for Contaminant Mass - Washing Parts Capability, Accuracy and Stability - Processes, Machines, etc. 6
Help with Cpk procedure Capability, Accuracy and Stability - Processes, Machines, etc. 3
J Calculation of σ within subgroups for Cpk in Minitab Using Minitab Software 1
S Value of Ppk or Cpk when targeting thinner material Statistical Analysis Tools, Techniques and SPC 4
B How to validate Microsoft Excel Spreadsheet Calculations for the Cpk value Capability, Accuracy and Stability - Processes, Machines, etc. 9