Calculating Cpk on a single sided tolerance

Okay I have a diameter that is .250” +0.010” (note there is no minus), how do I calculate Cpk? And is it possible to calculate Cp as I think it is not based on the Cp equation (USL – LSL / 6 standard deviations). In this instance there is only size – plus, and not size plus and minus.
Also, is there an excel formula for the Cpk calculation (if poss)


Best Regards

Lee01

The issue of Cp and Cpk has been debated a great deal recently. Do a search for more info.

If the spec.is .250" - .260", consider the possibility of using a spec. of .255' +/- .005" for your spec. in calculating Cpk.

Lee,

In case you have a one sided tolerance (let's say upper tolerance only), the Cpk is evaluated as Cpk upper. Cp is not defined in such cases.

However from what you have written, it does look as though you really have a two sided tolerance. The tolerance is expressed on the plus side only as a convention (like in a hole basic system). Would it be acceptable for instance, if your diameter went below 0.250" ? It could even go to zero if you don't really specify a lower tolerance and the hole or the shaft under consideration would completely vanish.
A two sided Cp/Cpk formula would apply here.

One sided tolerances are typically found in parameters like surface roughness, breaking strength, and form tolerances like straightness, flatness, roundness and cylindricity.

Hope this helps.

Ravi

As Mike said "The issue of Cp and Cpk has been debated a great deal recently. Do a search for more info."

In

http://Elsmar.com/Forums/showthread.php?t=6410

I posted, that Cpm, or Cpmk are in my opinion better capability index than Cp, Cpk for one sided spec.

The problem that I saw in Cpkl or Cpku for one sided spec is that they don't take the target in account, and "Quality is to the target with the minimum variation".
:smokin:

Ravi,

This is a single sided tolerance as the size described is 0.250 + 0.010. This means that obviously it cannot be below the .250 size.

I have been told that there is an equation that takes into consideration the Skewness and Kurtosis to give a value, this value is then used to calculate Cpk.


Help please

Lee01

Lee,

1. If the size cannot go above 0.260 (0.250 + 0.010), the Upper Spec Limit = 0.260

2. If the size cannot go below 0.250 (as referred by you above), the Lower Spec Limit = 0.250

Any parameter that has both, USL & LSL is to be treated as a two sided tolerance.

To determine Kurtosis and skewness, you will have to look at the histogram. Kurtosis describes the peakedness of the distribution. Skewness describes whether the distribution is lopsided.

If you have to determine the process capability using a Non Normal distribution there are methods to transform the data. You could look up Pearson and Johnson families of distributions for this.

Ravi

Lee, I think the confusion you're running into is between a single-sided tolerance which has only one direction that it can go, such as speed (i.e. you can never go slower than 0), and a unilateral tolerance, or unevenly distributed tolerance in which you may want the result to be closer to one end than the other, but is still possible to go out of spec on both ends.
To say that the hole size cannot go below .250 is more of a technicality. It can go below .250, but it should not due to design requirements, thus it is a two-sided tolerance with uneven distribution of the tolerance limits.


Ravi,

This is a single sided tolerance as the size described is 0.250 + 0.010. This means that obviously it cannot be below the .250 size.

I have been told that there is an equation that takes into consideration the Skewness and Kurtosis to give a value, this value is then used to calculate Cpk.


Help please

Lee01

Also see:

http://Elsmar.com/Forums/showthread.php?t=1068
http://Elsmar.com/Forums/showthread.php?t=1087

Single sided gauges,

We have had these in the form of hole position using GD&T (a diametric gauge) Where it can deviate from its nominal in any 360 degree direction.

In a similar manner that perhaps a call centre will respond to a qaury, it can only answer it in from the time it gets the call, not before.

We use the Cp to monitor the process, and Cpu (Cp upper) for the process in relation to the desired tolerances

Thomas

Calculating Cpk on a single sided tolerance

Okay I have a diameter that is .250” +0.010” (note there is no minus), how do I calculate Cpk? And is it possible to calculate Cp as I think it is not based on the Cp equation (USL – LSL / 6 standard deviations). In this instance there is only size – plus, and not size plus and minus.
Also, is there an excel formula for the Cpk calculation (if poss)


Best Regards

Lee01

Its very simple, conver the .250 diameter to 0.255" ± 0.005" and take SPC for that parameter, U can get the Cp and Cpk

Its very simple, conver the .250 diameter to 0.255" ± 0.005" and take SPC for that parameter, U can get the Cp and Cpk
What if 0.250 is the true target (the best value)?

Its very simple, conver the .250 diameter to 0.255" ± 0.005" and take SPC for that parameter, U can get the Cp and Cpk

just calculate the upper Cpk value and use it for your Cp value (a relativley useless index anyway)

If you know the target you can use it as teh bominal.

the upper Cpk value is much different depending on where the average and the high tail actuallly are and trying to default to the middle value is not a value add approach for understanding your variation - it only makes "checking the box" of having to calculate a Cp easier...

just calculate the upper Cpk value and use it for your Cp value (a relativley useless index anyway)

If you know the target you can use it as teh bominal.

the upper Cpk value is much different depending on where the average and the high tail actuallly are and trying to default to the middle value is not a value add approach for understanding your variation - it only makes "checking the box" of having to calculate a Cp easier...

Nominal does not matter to a Cpk calculation. It does not matter whether your specification is .250+0.010, .260+0/-0.010, or .255±0.005. The specification limits are exactly the same: .250 to .260.

Unless the diameter is specified such as .260 MAX, or .250 MIN, where the design requirements allow unlimited variation in one direction, it is not a single sided tolerance, and your process spread MUST be evaluated against lower and upper specifications.

The only true single sided specifications are those with natural boundary limits that are not possible to go beyond. Flat can be no flatter than perfectly flat, speed can go no slower than stopped, true position can be no more true than perfectly on target.

Diameters do not have a natural boundary that prevents them from being smaller or larger than desired, and it does not matter if you target the lower or upper specification or some point in between - the specifications are the same and you can go beyond them in either direction.

yes - brain fart on my part. thanks!

Lee,

If you have to determine the process capability using a Non Normal distribution there are methods to transform the data. You could look up Pearson and Johnson families of distributions for this.

Ravi

Thank you for you considerate information,would you mind elaborating on what's the perrson distribution ?
Here I can share my case for you ,wo do SPC with QDAS software and the pearson distribution will be applied automatically when meet the unilateral tolerance such as roundness,straightness.

But I never get a understanding about the pearson .so we are looking support from you .

Thank you for you considerate information,would you mind elaborating on what's the Pearson distribution ?
Here I can share my case for you ,wo do SPC with QDAS software and the pearson distribution will be applied automatically when meet the unilateral tolerance such as roundness, straightness.

But I never get a understanding about the Pearson, so we are looking support from you.

Hello Larry. Welcome to The Cove Forums! :bigwave: :bigwave:

Would this (http://en.wikipedia.org/wiki/Pearson_distribution) help?

Or this (http://www.google.com/search?hl=en&q=capability+using+pearson+distribution&btnG=Search)?

Stijloor.

I guess my question is who is asking you to calculate Cpk for a unilateral tolerance? Automotive does not require that, per the AIAG PPAP manual.

AIAG PPAP 4th Edition
2.2.11.5 Processes with One-Sided Specifications or Non-Normal Distributions

NOTE: The above mentioned acceptance criteria (2.2.11.3) assume normality and a two-sided specification (target in the center).

When this is not true, using this analysis may result in unreliable information.

These alternate acceptance criteria could require a different type of index or some method of transformation of the data. The focus should be on understanding reasons for the non-normality (e.g. is it stable over time?) and managing variation.

I love that part of the 4th ed PPAP book...:cool:

I guess my question is who is asking you to calculate Cpk for a unilateral tolerance? Automotive does not require that, per the AIAG PPAP manual.

AIAG PPAP 4th Edition
2.2.11.5 Processes with One-Sided Specifications or Non-Normal Distributions

NOTE: The above mentioned acceptance criteria (2.2.11.3) assume normality and a two-sided specification (target in the center).

When this is not true, using this analysis may result in unreliable information.

These alternate acceptance criteria could require a different type of index or some method of transformation of the data. The focus should be on understanding reasons for the non-normality (e.g. is it stable over time?) and managing variation.

I love that part of the 4th ed PPAP book...:cool:

Bob,

I am glad you do! See, it's not all that bad. :D

Stijloor.

A very good discussion going on here. Let me add some more fuel to the fire. How will be the calculations for +/+ or -/- tolerances. Though being unilateral, there are upper and lower limits (on the same side of course).

Umang

A very good discussion going on here. Let me add some more fuel to the fire. How will be the calculations for +/+ or -/- tolerances. Though being unilateral, there are upper and lower limits (on the same side of course).

Umang

I don't really classify those as truly unilateral - in my mind unilateral is a min or max type of tolerance. In metric tolerancing you find +/+ and -/- tolerancing, and often it does not hold the meaning that it may in english. They just like even numbers. In any event, if it is a length or a diameter being machined, it does not matter what the print says, the behavior will be uniform (non-normal) if controlled correctly. Treat the upper and lower specs as just that, and control within 75% of them.

Remember that just because you can draw it, doesn't mean you can make it or measure it.

Hello all,

I think original question is still open
you can get a Cpk from one sided tolerance, but not a Cp.
what does this Cpk represent? can it tell us btw two processes which one perform better?

pls clarify I have a similar situation to handle and my customer requires a cpk

Regards

I am glad you do! See, it's not all that bad.

Well....until you get to the SPC book, then they contradict themselves (see below). Sheesh.

Hello all,

I think original question is still open
you can get a Cpk from one sided tolerance, but not a Cp.
what does this Cpk represent? can it tell us btw two processes which one perform better?

pls clarify I have a similar situation to handle and my customer requires a cpk

Regards

Sounds like your customer wants a rubber stamp answer to a rubber stamp question - in which you can find the answer on page 137 of AIAG SPC Second Edition. They state that "If the product characteristic has a physical limit a Cp could be calculated using the physical limit (0.0) as a surrogate lower limit. But this number will not have the same relationship to Cpk as it does in the bilateral case." Most rubber stamp customers will accept this, but it really is a back yard estimate of capability assuming half of a normal distribution. To get a better idea, one should find the true distribution using software such as "Distribution Analyzer".

edoedo

I stated before in this tread, the best solution I could Think of, is Taguchi Loss function or If you want something Cp alike : Cpmk.

There has been lot of discusions about Cpk, just browse across this site and you will find out.

Cpk is a mean to evaluate a process variable capability giving a penalty for not being on the middle of the specs. For one sided spec you IMHO shouldn't calculate Cpk (unless no other option is available), because it don't take the target in account, just the variation and distance of the available spec, so less variation the better index eventho the mean could be farther from the target (not being always to be farther from the spec).:2cents: