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Mar 10, 2015 1:10 PM
(12366 views)

With reference to the table attached:

I have about 30 observations. The values have a std deviation of 0.534121.

The average is: 73.93235.

Now if I want to calculate the control limits based on the thumb rule of ± 3 sigma, the limits come out to: 72.3 LCL and 75.5 UCL.

However if I plot a control chart with the table in the attachment, the UCL and LCL are calculated to be: 72.852 to 75.01.

I am unable to understand the reason for this difference.

Can some one explain ?

I tried to work this out and figured out the JMP is usung ± 2 sigma to calculate the limits and also the value of sigma it esimates for this purpose is different from the values I cacluated abouve. I am unable to understand this.

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Mar 10, 2015 1:41 PM
(19048 views)

Solution

You are correct when you say "thumb rule" of 3 sigma since in actuality the IR control chart (subgroup size 1) uses the moving range for the calculation.

The formula for the limits are as follows

UCL = mean + 2.66 (0.406) = 73.93 + 1.08 = 75.01

LCL = mean -2.66 (0.406) = 73.93-1.08 = 72.85

The 0.406 is the calculated mean of the moving range in your data.

I have attached the file with the moving range column added.

I highly recommend Donald Wheeler's book on Statistical Process Control.

14 REPLIES

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Mar 10, 2015 1:32 PM
(9524 views)

This is a common question and is answered in the JMP course on Statistical Process Control. I assume you are creating an Individual and Moving Range chart. You need to understand how Individual and Moving Range charts are created. They use an ESTIMATE of the standard deviation for the control limits. The standard deviation can be estimated in several ways. Because these charts were created before calculators, a moving range is typically used, not the sample standard deviation, s.

To get a chart with the limits you are proposing, that chart is called a Levey-Jennings chart.

Dan Obermiller

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Mar 10, 2015 1:51 PM
(9524 views)

Thanks to both of you for your quick response. Amazing how fast you are.

So the question is what is the best way to plot a control chart in an industrial setting:

A L-J plot or the IR chart ?

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Mar 10, 2015 1:41 PM
(19049 views)

You are correct when you say "thumb rule" of 3 sigma since in actuality the IR control chart (subgroup size 1) uses the moving range for the calculation.

The formula for the limits are as follows

UCL = mean + 2.66 (0.406) = 73.93 + 1.08 = 75.01

LCL = mean -2.66 (0.406) = 73.93-1.08 = 72.85

The 0.406 is the calculated mean of the moving range in your data.

I have attached the file with the moving range column added.

I highly recommend Donald Wheeler's book on Statistical Process Control.

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Mar 10, 2015 2:05 PM
(9524 views)

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Mar 11, 2015 1:12 PM
(9524 views)

If I may weigh in.... The I-mR chart is the "Swiss Army Knife" of Process Behavior Charts. It is very useful for almost any data set and is robust. It is NOT dependent on the distribution of the data; i.e., the data does not need to be normally distributed. The use of the standard deviation of the data to calculate upper and lower control limits is almost always WRONG. The reason is this: Your data is time-ordered; otherwise a control chart is useless. The stanadard deviation calculation gives the same result regardless of the order of the data. The moving range gives a time-ordered dispersion statistic, and IS time order dependent. The moving range multiplied by 2.66 gives an estimate of 3-sigma for the data. As LouV says, Wheeler's book is excellent. You can find many of Wheeler's articles at www.qualitydigest.com. I also suggest you look at the work of Davis Balestracci.

Steve

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Mar 12, 2015 3:07 AM
(9524 views)

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Mar 12, 2015 5:53 AM
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https://www.linkedin.com/groups/Does-Run-chart-require-data-3696237.S.63802395

The link above is a LinkedIn thread on whether control charts require normal data or not. Though this is not the exact topic of your question, there were a couple things that I, as someone who is certainly not a statistical expert, found personally useful for putting things into perspective and may help you as well:

- Ultimately we're trying to find an economic way to investigate outliers, which is kind of the purpose of control charts.
- Per one of the contributors:
*The 6 sigma = +-3 sigma is an operational economic boundary. Since my point of view, Shewhart was a clever man who tried to find robust operational definition to identify when it is justified to investigate and when consider just as a NOISE.*

- Per one of the contributors:
- Sometimes we get so wrapped up in being exactly correct, that we lose sight of whether or not our quest actually yields very different results. In other words, are we splitting hairs just to split hairs. I don't know in your case, but it might be interesting to plot your data on both charts and observe whether the number of alarms is different or not.
- Wheeler's paper titled "Are You Sure We Don't Need Normally Distributed Data?" got me to thinking about this concept.

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Mar 12, 2015 6:32 AM
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Mar 12, 2015 7:05 AM
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So, now I have a situation. The process has suddenly results which lie out side the 3 sigma calculated so far. Therefore the process appears to be out of control.

However if I include these new points which have gone out of the 3 sigma limit into the sigma calculation, the new sigma appears to be Ok. Can I therefore say that my process is in control or is this a fraud ?