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Specific Capability case - Target Value is same as the Lower Limit



Dear All,

I would like to have your support/opinions about a special topic again.
I was analyzing some capability studies and encountered a case that I never encountered before.
The target value (in this case 7.2) was the same as the lower limit. So the drawing specification was saying 7.2 +0.3 -0. Off course, when you want to calculate a Cpk, this will be too low since the supplier is not aiming on the middle of the tolerance, what is also requested on the drawing.
Apart from that you can also say that the data is normally distributed with following parameters:
n = 50
Average = 7.28
Median = 7.29
Mode = 7.29
Skewness = 0.1723
Standard Deviation = 0.02997
Max = 7.36
Min = 7.21
Cpk = 0.91

Could you guys help me out drawing some conclusions concerning the capability? Do I need to use other formulas, other tolerances??
Thank you in advance!
Elsmar Forum Sponsor


One question. Is 7.2 a physical boundary? Can any part measure less than 7.2? If so then I hope you are using Minitab where you can click on the box for a boundary condition and obtain a much better Cpk.


Thank you for the reply!

It is possible that a part measures less than 7.2. At the moments I am not using minitab. Do you know the formula's/assumptions that are behind this "Boundary condition" + maybe the theory?

Jim Wynne

Staff member
First, I'm not sure why you're describing 7.2 as the "target" value. It's the nominal value, which may or may not be the target. In most cases, depending on the manufacturing process, some point between the upper and lower tolerance limits will be chosen as the target.

There has been a lot of discussion in the Cove regarding capability studied for unilateral tolerances. Cpk assumes a bilateral, equilateral tolerance spread and is inappropriate for unilateral tolerances. Start with a few of the threads listed towards the bottom of this page, and also search for unilateral and/or one-sided tolerance posts and you'll find a lot of information. Let us know if you have specific questions after that.


As usual, you have to realise that Cpk is a tool, and its only as much use as what its used for. It is NOT a means to an end.

What exactly are you trying to do? If the process can make a part <7,2 then you want to set it up so that the risk of it doing so is minimised. As Cpk generally assumes normal distribution, if you cant easily do the boundary calculat6ion, an easy fix is to shift the nominal to 7,35 and run the process on 7,35 +/- 0,15.

That isn't exactly what the designer wanted, but in practice, if there is no physical boundary to prevent the parts going below 7,2 and the process is normally distributed, that is actually what the parts will have to be to stay in tolerance.

EDIT: Im not here often enough to pick up all the discussions, but: Wot Jim said.

Steve Prevette

Deming Disciple
Staff member
Super Moderator
If I take your question literally, that the "specification" for the product matches the current Lower Control Limit, then what you need to do now has nothing to do with statistics, but everything to do with the production process. The parameters controlling the process need to be adjusted!

Looks like it is a fairly precise process right now (quite low variation) but is not accurate. Do whatever is needed to lower the center of the produced materials from 7.28 to 7.21.

Again, this is a "literal" answer, assuming that the data values and specification are given correctly.

Bev D

Heretical Statistician
Staff member
Super Moderator
can you post your raw data?
its so much better to look a the data rather than react to a number or set of summary statistics.

My other comment at this time is that teh designer had a reason for specifying a lower limit and taget/nominal value. It is probably more important to match that requirement as well as possible rather than try to get a 'good' Cpk. thsi can be discussed with your SQE - Cpk is often a cookie cutter requirement that can be waived given logic and science...


By the same token, often designers don't really understand that suppliers get asked to show process capability and how that is affected by a one-sided tolerance. I have worked with many a designer that admitted, "Its easier to model the part at the size limit than at the nominal" or even "I just picked that tolerance because that's what was on the last print".

I suggest you involve both your customer SQE and your customer Designer in discussions. It is very possible that they can change the print to 7.35 +/- 0.15

TWA - not the airline

Trusted Information Resource
You first need to understand where that spec comes from. It could be that the designer initially designed a device (e.g. in 3D) without having tolerances in mind, so two parts that need to fit into each other were designed on a perfect fit. Once the design was ready and the single (often 2D) parts drawings for the specs were derived, the nominal was kept but then the male part was specced to be +0/-x while the female part was specced +x/-0, i.e. each part gets one half of the tolerance but without adapting the nominals. That way they can use the 3D model to derive the 2D drawings without changing anything, which saves them time.

If, one the other hand, the nominal is really the target, i.e. the part fulfills its function best, if it is as close to the nominal as possible but never below it, then that's a totally different story.

As your process is very stable compared to the tolerance band, you should take your data to your customer and together decide on your target...
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Stop X-bar/R Madness!!
Trusted Information Resource
Also remember, the process doesn't care what the designer "wants"[/I] - it only knows its own distribution of variation from the results of its "total variance equation". If it is normal, it will need to be centered. If it is not normal, it needs to be calculated based on the appropriate distribution or transformed as a last resort.

And remember, the point of Cpk is to determine if the distribution is centered within the tolerance. Get it?? See the problem here?? It is a point often lost on rubber stamping capability index normalcentrics. So, either use Cp, or seek to center the distribution to best meet the specification.

Bottom line: a single number does very, very little to either describe or predict a process' ability to make parts to specification.

Personally, I wouldn't change the print if it is truly the intent to describe the relation of the dimension to the function of the part (CAREFUL: this is often NOT the case in metric prints!) But, I would not treat it as the target for Cpk calculations - it is inappropriate for all the reasons above.
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