# Estimate Control Limit from Cp or Cpk

Six Sigma – iSixSigma Forums Old Forums General Estimate Control Limit from Cp or Cpk

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• #28429

Kenny
Participant

Assumption  Spec tolerance(USL-LSL) is fixed.  Cp = 1.67
From, Cp=1.67, we get the std_dev.  Where std_dev = RBar/d2.Thus we can get RBar.
From A2*RBar,  we get the control limit.
My purpose is to calc the economic control limit.
I’m not sure if this estimation is correct.  Pls help me.Thanks in advance.

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#70808

Mike Carnell
Participant

I do not understand what you are tying to do. If you have the data to do all the calculations you have done so far what is the question?

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#70809

Ravi Khare
Participant

Control Limits will tell you the natural limits of variation. The parameters A2 as well as d2 depend upon the subgroup size. A control chart simply tells you whether a process is stable in centering and maintains a steady variation along the time scale. It is thus only a stability monitoring tool.
A Control chart being usually plotted on means of subgroups is a better tool to detect systematic drifts from random variations. The Control Limits of a process with high variation will be set wide, and those of a low variation process will be set tight. They do not realy indicate any economic limit, neither can they be used as a measure of Quality.
Ravi Khare
http://www.symphonytech.com

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#70824

Mike Carnell
Participant

If this question is really just how to calculate the control limit you should save yourself a lot of trouble and read “Statistical Quality Control” by grant and Levenworth.

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#70828

Dave Strouse
Participant

Ravi-
Walter Shewhart wrote “Economic Control of Msanufactured Product” to show a way to calcuolate economic limits for control of a process.
His intent was to show how to balance the two primary risks in manufacturing, i.e. the Alpha nad Beta risks. His conclusion was that 3 sigma limits established using the methodology and fators he pioneered would be the economic choice.
And so the majority of us agree with this today. Why do you now say that these 3 sigma limits calculated in that manner are not the economic limits? How would you set limits that economically tell us when to adjust the process and when to leave it alone?
As for the original post, I see nothing wrong with the suggstion as long as the Cpk study was correctly done, using rstional subgrouping, it should give a very good estimate of the within subgroup variation that is used to calculate control chart limits. It is what one wopuld do anyway in a phase one study.

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#70834

Ravi Khare
Participant

Dave
I agree with you.
I too believe that the purpose of control limits is to tell you when to leave the process alone and when to adjust it.
Putting it this way, you would indeed economize on unnecessary adjustments ( actually overadjustments which would pull the process centre to the other side).
Thanks for the clarity.
Ravi

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#70924

Kenny
Participant

Sorry if my question confuse you all.
What i want to say is that,    1) at initial stage, without collect any data, i fix Cp and the spec torelance, i calc the Std_Dev.   2) i calc RBar from Std_Dev.  (RBar=d2*Std_Dev)   3) and i calc A2*RBar from RBar.
So, can i use “this” A2*RBar as economic control limit at initial stage ?Or Is there any method to estimate control limit at *any* stage ?
Kenny

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#70932

Erik L
Participant

Kenny,
Your methodology mathematically looks correct.  However, what subgrouping are you basing the constants on?  Is the process that generated this Cp data in control?  If it isn’t, you could come out with a highly inflated estimate of the standard deviation which could have detrimental effects on the utility of the control charts.  If you’re looking at a quick ‘stab’ at the process, I’d recommend gathering data and plotting an IX-MR chart.  It’s fast and you can start getting ballpark figures after about 5 points.  This would be a good first approximation and would at least draw a line in the sand.  I’d progress with the analysis, perform process mapping, and understand the process better so that you can come back at a later time and perform the analysis with rational subgrouping.

Regards,
Erik

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#70936

TomF
Member

Hi Kenny,
From my understanding of your question, it appears as though you are “putting the cart before the horse.”  It seems to me that you are using statistical principles to develop a somewhat arbitary limit to compare a sample to initiate a change.  Control limits should be set based upon past history, not a goal.
As previous posts have mentioned, Cp and Cpk are the result of  functions.  You cannot arbitrarily set Cp or Cpk unless you are willing to change the specification to get your desired Cp or Cpk.
It is important to realize that the process should be stable (in other words in statistical control) before you calculate Cp or Cpk.  Without the statistical control, Cp and Cpk can vary randomly and change significantly over time.
The purpose of control limits is to understand when the process has changed by comparing a sample to a range of natural variation.  When you have exceeded the natural variation limits, you conduct an investigation and eliminate any special causes of variation.
What you have described seems to be another arbitary limit.  These arbitary limits will give you false signals and defeat the purpose of control charts because you may conduct investigations when nothing has changed.
I would recommend that you collect data to develop control limits to make the process stable.  Once you can reduce your variation and establish stability, calculate the Cp and Cpk.  If this doesn’t meet your goal, conduct simple experiments to see the influence of these factors on reducing the variation.
While control charts are to improve your process, I will mention that “modified” control charts exist.  The purpose of “modified” control charts is to make a decision of whether a lot is acceptable.  These charts compare a sample to accept and reject limits.
Sorry for the length of this posting.  I hope it helps you and others.
Sincerely, TomF.

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