# Process limits calculation

Six Sigma – iSixSigma Forums Old Forums General Process limits calculation

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• #51187

Coko
Participant

Our customer is giving us the demand:

Cpk = 2
Lower tolerance limit = 105
Upper tolerance limit = 155

How can we define the process limits which we should respect to achieve Cpk 2? We have no parts that can be measured yet. But we need to know the process limits before we will start to produce.

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#177057

KC
Participant

Using a basic Cpk calculation and assuming that you have a process that’s “in control” and have the ability to adjust the process to run at the center of the spec limits, the aim should be at 130 and the standard deviation must be 4.15 or less.

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#177075

Participant

Yeah, you need to know your process capability. I
think what you should worry about are control
limits. Is that what you mean by “process limits”? I mean what are you going to do–run all the time
and sort the products that are above 145 and
through them out? KC is correct. aim for the
middle and maintain control. That is all there is
to it.

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#177088

Coko
Participant

Thank you both KC and Michael.
The process will be as you mentioned. There is a 100% control station measuring the value. I want to hold all the parts which would be out of control limits in order to respect Cpk 2. If I consider to adjust the process on the center line 130 and sigma 4,15, than I have to define the control limits at 117,55 and 142,45? Do you maybe know some simple software of excel file than can be used for such purposes?
I would expect that the control limits would be much to narrow than the above calculated to achieve Cpk 2. Why is it so?
Thank you all very much again.

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#177090

Participant

Hello Coko,I am not sure you understand the concept of control
limits. They are for averages. They are not
directly related to individual parts. a CpK of 2
does not mean that all parts will be within the
this is a basic concept of statistical process
control.In which country do you reside?

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#177107

yesitisme
Member

KC is right, your avegarge will be 130 and the control limits should be:
UCL= 130+3*4.15
LCL= 130-3*4.15

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#177120

Ron
Member

A Cp of 2 implies that your process variation is twice as small as your specification limits.
You should be able to calculate your current process Cp and Cpk to see how much variation exists within your process that you intent to run the subject product on.
If you have very small variaiton you should be okay.  Since you did not specify the type of process you will be running it is difficult to give you a more specific answer.

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#177137

Brian M
Participant

Your control limits should be narrower.Figuring this backwards from the end (Cpk) to the beginning (X Bar R chart) you can use your tolerance and desired Cpk to set up a chart to get you going, with the understanding that you will need to recalculate everything once the real data begins to come in.All of these numbers are based on a sample size of 3Cpk = Tol/(6*sigma^) Sigma^ is the estimated sigma based on the average range from your control chart (sigma^ = Rbar/D2). So by doing a little juggling you can figure sigma^ (4.16) and average range (7.05).Once you know those values you can calculate your control limits for the Xbar chart. Xbar UCL = Xdouble bar + Rbar*A2 (137.2). Xbar LCL = Xdouble bar – Rbar*A2 (122.8)Your control limits for the range chart will be: UCL = Rbar*D4 (18.1) and LCL = Rbar*D3 (0).Once again, this s all just to have some place to start to see if you are in the ballpark. Once you’ve collected enough data, recalculate everything.I think thats all correct.Have fun. Brian M

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#177140

Mikel
Member

Wy do you assume a sample size of 3?

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#177141

Brian M
Participant

Just for the sake of having something to calculate… which is why I said I was using that sample size. If he is using a different sample size, he’ll need to look up the factors himself ;)

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#177195

Brian M
Participant

Correction… Cp = Tol/(6*sigma^) NOT Cpk = Tol/(6*sigma^)

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#177198

Mike Carnell
Participant

Brian M,Is this Brian from London?

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#177220

Chris Seider
Participant

Michael,
Why say control charts are for averages only?  What about I-MR charts?……they are for individuals!  Maybe Coko has no rational subgroups.

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#177221

Participant

Hello Ron, Here the is way I see it. (Not always right but
seldom completely wrong.)Well, he has process capability to base his control
chart on. Rational subgrouping is not a
requirement. We are looking at variation within the
subgroup and the variation between subgroups.Individuals charts are ok….but, you can’t tell
the difference between the “between” and “within”
variation. They are not sensitive to process
changes. I don’t recommend them for this reason.
There is nothing wrong with using them as an
inspection record, but not for process control.

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#177223

Chris Seider
Participant

Michael,
Agreed…..however, there are more than a few cases where individual are the most appropriate thing to chart with SPC….
I would hesitate to tell someone to “create subgroups” if no rational basis existed for the subgroup.  If no rational subgroups exist, I would hesitate to look for within variation.  If no rational subgroup existed, then what would be the response plan if within variation went out of control?

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#177225

Participant

My response would be to immediately look for loose
fixturing or dull tools, anything that would vary
between one part and the next.

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#177233

Brian M
Participant

Nope, New Jersey

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#177243

Brian M
Participant

Wrong

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#177248

Mikel
Member

Hey, I think this is infringement.

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#177250

Brian M
Participant

I never noticed a TM in your posts ;) lol

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