# Capability index for one-sided specification? Cpk(max) = (USL-Xbar)/3*s ??

C

#### Chris_UK

Does anybody know if there is a capability index I can use for a one-sided specification. ie +0.5mm -0mm. The distribution is normal.

D

#### Don Winton

Cpk(max) = (USL-Xbar)/3*s

Regards,

dWizard

------------------
I was better but I got over it.

F

#### freeda

Chris,
I have a Word document that shows you the non-standard capabilities. If you will send me your e-mail address, I will send it to you. The formulas are a little hard to understand when you write them out here in the forum.

C

#### Chris_uk

Freeda
I tried to mail you my address but the message was returned as undeliverable.
You can mail me at
[email protected]

Cheers
Chris

M

#### MarkR

Chris,

I don't think your example of +0.5 -0 illustrates a single sided tolerance. It is still bi-lateral, just not symmetrical. If you can make parts that are too big (over +.5) AND parts that are too small (under the -0) then it is bi-lateral.

A better example of single sided tolerance is flatness. If parts must be held flat within 0.030, then 0.030 is the upper spec and there is no lower spec (zero isn't the lower spec, it's the target). This is the situation where Cp doesn't apply and only the upper Cpk equation is used.

I think you still need to calculate Cp and both Cpk values to check for the possibility of making parts that are too big and too small. The only exception I can think of is if you have some natural limit on the process that simply can't be exceeded.

V

#### V. Manea

Hello there,

I too seem to find that some confusion exists with regards to one-sided tolerances. My example of one-sided will be most of the regular GD&T callouts. For example, true position of a hole. Defined as the diameter of a circle whithin which the centre of the hole must fall. So in most cases we see a 1.0mm diameter true posistion. Zero will be the target, 1.0 will be the USL, so how do we evaluate the process?
One option will be to calculate the Cp as 1.0/6-sigma.
Then calculate Cpk based on USL-proccess average/3-sigma.

Any other ideas?

Victor M.

K

#### Ken K.

You're correct.

Using

Cpk = CPU = (USL - mean) / 3s

for a one-sided upper limit and

Cpk = CPL = (LSL - mean) / 3s

for a one-sided lower limit is standard AIAG SPC methodology.

If you were using MINITAB statistical software, you would also have the option of identifying a limit as being a "Boundary", which means that the product/process physically cannot exceed the boundary value.

In this case the data are treated as if there was a one-side spec limit (the bound is not considered a spec limit), AND the area beyond the boundary value is excluded from any PPM defective calculations.

J

In response to the original question, "Does anybody know if there is a capability index I can use for a one-sided specification. ie +0.5mm -0mm. The distribution is normal."

This is not a one sided tolerance.

A one sided tolerance has a natural limit. For instance, run-out will never be less than zero.

If you have a Ø5.00 hole with a +0.5mm -0mm tolerance, you treat it as Ø5.25 ± 0.25mm and use the normal calculation methdods for a bilateral tolerance. It is still a unilateral tolerance because it does not have a natural limit.

The intent of this type of tolerance is to indicate that the low limit is more critical than the high limit.

A high cpk using USL-Mean/3s would actually mean you are producing the part toward the risky side of the tolerance.

I believe you can find information on + or - only tolerances in one of the newer GD&T handbooks.

[This message has been edited by jadubar (edited 23 June 2001).]

J

#### jspatiala

One sided tolerence is when the specs are stated as say 0.9 max or 0.25 min. & in such cases we can calculate CPk(max) or Cpk(min) depending upon the type of tolerence i.e max or min.

#### bobdoering

Trusted Information Resource
You're correct.

Using

Cpk = CPU = (USL - mean) / 3s

for a one-sided upper limit and

Cpk = CPL = (LSL - mean) / 3s

for a one-sided lower limit is standard AIAG SPC methodology.
Yes, I have seen this mentioned in the AIAG manuals, but it is really kind of back yard hack (I admit, I used to do it before I learned better.) It assumes you have half of a normal distribution, which is typically not true. For a better approach, I use Distribution Analyzer software, which runs the data through a large number of distributions and determines the best fit. It then does a transformation and calculates capability. That gets you much closer to the correct analysis. It will also plot the correct curve over your histogram, and give you a list of outliers. Very nice.

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