# Cpk for Unilateral Tolerance

O

#### OmarEn

Hi Guys,

I have three situations trying to do a Cpk with unilateral tolerance. I hope you guys can give me some advice on this.

1. I want to conduct a CPK for a diameter that is 10.0mm +0.1 -0.0

2. I want to conduct a CPK for a diameter that is 10.0mm minimum (it does not have a maximum limit).

3. I want to conduct a CPK for a flatness of 0.3mm.
As you may know, flatness tolerance is an absolute value. It means that the spec is maximum 0.3mm since there is not a possibility to have a value less than 0 since 0 would be a perfect flatness.

I am trying to complete this in Minitab but I do not know if it is possible to calculate ability for processes with this kind of tolerance.

O

#### OmarEn

Hello Marc,

Yes, I had been looking for andwers in another existing discution. But my questions are a bit different.

#### Marc

##### Hunkered Down for the Duration with a Mask on...
Staff member
Hopefully someone here will help in the next day or two. GD&T isn't in my specialty domain.

#### Miner

##### Forum Moderator
Staff member
Hi Guys,

I have three situations trying to do a Cpk with unilateral tolerance. I hope you guys can give me some advice on this.

1. I want to conduct a CPK for a diameter that is 10.0mm +0.1 -0.0
In Minitab, enter 10.0 and 10.1 as the spec limits. Under Options, enter 10.0 as the Target. Cpk will be calculated using the 10.05 as the center of the spec, but Cpm will be added to the output and will use 10.0 as the target.

2. I want to conduct a CPK for a diameter that is 10.0mm minimum (it does not have a maximum limit).
Enter 10.0 as the Lower spec and leave the upper spec field blank.

3. I want to conduct a CPK for a flatness of 0.3mm.
As you may know, flatness tolerance is an absolute value. It means that the spec is maximum 0.3mm since there is not a possibility to have a value less than 0 since 0 would be a perfect flatness.

I am trying to complete this in Minitab but I do not know if it is possible to calculate ability for processes with this kind of tolerance.
Enter 0 as the Lower spec and check the box labeled Boundary. this tells Minitab that it is not possible to have values below zero. Enter 0.3 as the Upper spec.

Last edited:

#### bobdoering

Trusted Information Resource
First, note that AIAG PPAP 4th edition 2.2.11.5 (NOTE) states that Cpk and Ppk "assume normality and a two sided specification (target in the center). When this is not true, using this analysis may result in unreliable information."

I can attest that the statement is a fact. I can also attest that MANY people that request Cpk's have never read it and simply rubber stamp the requirement with zero statistical knowledge.

That being said...

1. I want to conduct a CPK for a diameter that is 10.0mm +0.1 -0.0.
Cpk does not care how the dimension is called out, it cares about the distribution and the distance of its mean to the closest specification. If the process variation is independent, random and normal, calculate Cpk with the 10.0 mm to 10.1 mm specification.

2. I want to conduct a CPK for a diameter that is 10.0mm minimum (it does not have a maximum limit).
If the process variation is independent, random and normal, simply calculate CpL. The distance to the specification is what you need to know.

3. I want to conduct a CPK for a flatness of 0.3mm.
Unless you have poor flatness control (very far away from 0) you have a non-normal distribution. See note above.

Rather than rehash the whole thing here on this example, check out this blog on the topic:
https://elsmar.com/Forums/blogs/bobdoering/309-unilateral-tolerance-capability-calculation.html

T

#### turinoch

Minitab can definitely handle all of those calculations. As a note, some distinguish Case 1 as an "asymmetric" tolerance and Cases 2 and 3 as truly "unilateral."

Case 1 often appears in machining especially where fits and clearances are concerned. As such, the nominal dimension is just a convention. Example: a pin is specced as diameter 10 -0.05 / -0.10 and a hole as 10 +0.1 / -0. The nominal 10 serves as a common reference point.

In cases 2 and 3, there is effectively no Cp index - only Cpk. More specifically, for a minimum spec (no max such as Case 2) there is only CpL. Likewise for Case 3 there is only CpU.

There is one slight difference - Case 3 has a theoretical boundary at 0 which can affect the results. Minitab has an option to specify a limit as a boundary which should be enabled in this case.

On a final note, some situations do occur where specifications such as 10 +0.1 / -0 actually convey a target (ideal) of 10 instead of the usual "halfway between the limits" interpretation. An example might be an assembly where the goal is "flush," but being slightly proud has more consequences (damage, interference) than being recessed (annoying). A good FMEA can help identify such cases. The CpM index takes the "target" into account and is especially relevant for those kinds of scenarios.

O

#### OmarEn

Now I have a more clear idea of how to deal with this.

Thanks a lot.

##### Registered
Minitab can definitely handle all of those calculations. As a note, some distinguish Case 1 as an "asymmetric" tolerance and Cases 2 and 3 as truly "unilateral."

Case 1 often appears in machining especially where fits and clearances are concerned. As such, the nominal dimension is just a convention. Example: a pin is specced as diameter 10 -0.05 / -0.10 and a hole as 10 +0.1 / -0. The nominal 10 serves as a common reference point.

In cases 2 and 3, there is effectively no Cp index - only Cpk. More specifically, for a minimum spec (no max such as Case 2) there is only CpL. Likewise for Case 3 there is only CpU.

There is one slight difference - Case 3 has a theoretical boundary at 0 which can affect the results. Minitab has an option to specify a limit as a boundary which should be enabled in this case.

On a final note, some situations do occur where specifications such as 10 +0.1 / -0 actually convey a target (ideal) of 10 instead of the usual "halfway between the limits" interpretation. An example might be an assembly where the goal is "flush," but being slightly proud has more consequences (damage, interference) than being recessed (annoying). A good FMEA can help identify such cases. The CpM index takes the "target" into account and is especially relevant for those kinds of scenarios.

In Mini Tab 18,
Under Stat >> Quality Tools >> Capability Analysis >> Normal
I could see the Boundary check box next the LSL & USL.
But I need the same option for Capability Six Pack as well. Unfortunately I couldn't see that there.

#### optomist1

##### A Sea of Statistics
Super Moderator
"3. I want to conduct a CPK for a flatness of 0.3mm.
As you may know, flatness tolerance is an absolute value. It means that the spec is maximum 0.3mm since there is not a possibility to have a value less than 0 since 0 would be a perfect flatness.

Re: Above a screen shot of what you are trying to share would help....below flatness tol zone definition
Flatness Control Tolerance Zone – is two parallel planes spaced apart by the Flatness Tolerance value. One plane of the Tolerance Zone is oriented by the high points of the surface. The remaining plane is parallel to the first plane and offset by the Flatness Tolerance Value.

G Should I calculate both Cp and Cpk for a Unilateral Tolerance? Statistical Analysis Tools, Techniques and SPC 8
L Calculating Cpk on a single sided (unilateral) tolerance Capability, Accuracy and Stability - Processes, Machines, etc. 28
Software Calculation Errors for Cp and Cpk With Unilateral Tolerances Capability, Accuracy and Stability - Processes, Machines, etc. 4
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
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
D Calculating Cpk on Non-Normal Data Distribution Capability, Accuracy and Stability - Processes, Machines, etc. 10
D Cpk relation to Reliability Capability, Accuracy and Stability - Processes, Machines, etc. 4
B Process Capability - Changing Limits to Improve Cpk or find Root Causes? Capability, Accuracy and Stability - Processes, Machines, etc. 6
Cpk vs Ppk to look at the Capability by Fixture Capability, Accuracy and Stability - Processes, Machines, etc. 4
Convincing Management Cpk without Stability is Meaningless Capability, Accuracy and Stability - Processes, Machines, etc. 7
C Hardness Testing - Low Cpk's using Minitab Misc. Quality Assurance and Business Systems Related Topics 10