# Cumulative Count of Conforming Control Chart (CCC) - Calculating UCL and LCL

J

#### jeffrey_Chang

Hi,
Does anyone ever has any experience with this particular type of control chart, Count of Conforming Control Chart, or commonly known as CCC chart?
How do we calculate the UCL and LCL?
I've tried to do a search in the web and the forum but not much of useful information found.
thks.
jeffrey.

#### Howard Atkins

Staff member
Re: Cumulative Count of Conforming Control Chart (CCC)

Hi,
Does anyone ever has any experience with this particular type of control chart, Count of Conforming Control Chart, or commonly known as CCC chart?
How do we calculate the UCL and LCL?
I've tried to do a search in the web and the forum but not much of useful information found.
thks.
jeffrey.
Welcome

I found this http://www.eng.nus.edu.sg/EResnews/9602/feb96p11b.html with google. Does it help?

J

#### jeffrey_Chang

Re: Cumulative Count of Conforming Control Chart (CCC)

Hi Howard,
I came across this article also during my search on this topic but I'm still very lost as to how the UCL and LCL can be calculated after reading it....
thks.
jeffrey.

#### harry

Super Moderator
Re: Cumulative Count of Conforming Control Chart (CCC)

Do you have this paper, Jeff.

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J

#### jeffrey_Chang

Re: Cumulative Count of Conforming Control Chart (CCC)

Hi Harry,
No, I don't have this paper. The article you attached did give me a clearer insight into how the UCL and LCL can be calculated and now there I know it is some form of a geometric chart, I can proceed to do more research from here.
Nonetheless, is there anyone out there that have implemented this chart in their processes. If so, mind sharing it here.
thks.
jeffrey.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
I use this chart quite a lot actually. It is best used for very low defect rates. I also use it for accident rates which are also fairly rare.

The most common charts for counts of defects require a fairly high defect rate otherwise you only have a series of zeros followed by an occasional 1 defect. The control limit is therefore less than 1 and so any occurrence is plotted as an out of control point...not very insightful.

The CCC chart (are you at Intel by the way? Its' commonly called that there) overcomes this by using the geometric distribution and plotting the count of SUCCESSFUL units between a defect.

The formulas are:

calculate the average number of units - or runs - between defects.

then the center line for the chart is 0.7*Avg successful # runs

the UCL = avg runs*natural log(alpha/2) alpha is 1-confidence. for 2 sigma limits, alpha = .05, etc.

the LCL = avg runs*(alpha/2)

An out-of-control condition exists when:
1 point falls below the LCL (above the limit is an improved condition)
5 points fall consecutively below the Center Line (5 in a row above the center line is an improved condition)

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Last edited:
J

#### jeffrey_Chang

Hi Bev,
The explanation you have given is excellent. It has finally clear my doubts pertaining to this topic. Anyway, I'm not from Intel but one of my customer AMD required us to use this particular chart without given much detail to it.
Thanks for clarifying my doubts.
rgds.
jeffrey.

D

#### drousz

so sorry to bring this old topic back...
An out-of-control condition exists when:
1 point falls below the LCL (above the limit is an improved condition)
5 points fall consecutively below the Center Line (below the center line is an improved condition)
hi bev,
i thought "above the center line is an improved condition"
i'm new to CCC thing, but ur line make me a bit confused

thanks
Andi

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
yes - good catch. that was a typo on my part. high points are good (more good events befroe a bad event, low points are bad (fewer good events before a bad event). I have edited my original post to correct it.

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