# Cumulative Count Control Chart

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• #30355

Raymond
Participant

I will be very appreciated if anybody could tell me how to calculate the Cumulative Count Control Chart(CCC Chart)control limit & its center line, because I do not know how to define the parameter Alpha in its formula of control limit.
Best Regards…..

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#78976

James A
Participant

Raymond – I’ve never yet used one of these, but have been able to track down the following references which may be of help (or they may not)  “Implementing Six Sigma” by Forrest W. Breyfogle III has a large-ish section on CUSUM charts.  MiniTab’s Help section also goes into some detail (with worked examples) if you have access to a copy of that.
As I understand it your centre line should be a zero value, i.e. you are looking at the cumulative sums of the deviation of your samples from a target value.  No deviation from target, no problem, hence value = 0.
UCL and LCL are +/- 3 sigma from this 0 value, and the sigma is estimated from MRbar/d2 (as per usual guesstimates of sigma) so you will need some historical (hysterical??) data to start with to get a current sigma value to work with.  The moving range is of length 2, since consecutive values have the greatest chance of being alike.
None of the formulae I’ve looked at refer to ‘alpha’ but I’m guessing here that it may refer to an acceptable quality level – so is there an acceptable reject level as well in your formula? If this alpha is the case, then you are probably using the chart to determine incoming parts quality.
Now I’ve stuck my neck on the block, is anyone else out there prepared to offer any further constructive comment to help Raymond out on CUSUM charts??
James A

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#78979

Ben Royal
Participant

Both the Grant and the Montgomery texts on statistical quality control cover CUSUM charts in depth. Difficult to completely cover given limited space available here.

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#78990

QAS Reporter
Participant

in addition to mini-tab, we’ve been using hertzler software purportedly developed with motorola in the early 1980’s to help collect and calc cusum and all the other sigma, defect management and spc related stats… the on-line help files have detailed explanations of how its done (http://www.hertzler.com)

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#134007

YTC
Member

I posted this reply because I too was looking for advice on CCC chart. I think this is not the same as Cusum chart, so for the benefit for others who may chanced upon this, I hope this will lead them to the answers.
I believe Raymond meant Cumulative Count of Conformity chart.
CL=0.7/(p-bar)
LCL=(alpha/2)/(p-bar)
UCL=-ln[(alpha/2)/(p-bar)]
p-bar, estimate of defective proportion, alpha -producer risk
Use typically when p-chart is not applicable because n*p <5.
I do not have the reference but was told it can be found in “Statistical Quality Control” 7th Edition by Eugene Lodewick Grant, Richard S. Leavenworth. Publisher McGraw Hill, 1996.

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#134008

TYC
Member

Ooops! Make a boo boo. I assume it can be found in the SQC text since that was the reference given for the SQC course that I attended. But it turned out that this might be from published paper by the instructors. Check this out:
http://www.ise.nus.edu.sg/research_groups/quaeng/journal-papers.html

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