Control Chart & 3 Sigma

[#1]

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.

[#2]

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.

[#3]

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 ?

[#4 · Accepted 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.

[#5]

I'm not sure I'm in the position to say which is the "best way" but from my experience in the manufacturing environment for 30 years as I understand it the IR-MR charts were desirable since they were easy to calculate and easy to train the operations how to calculate much more so than a standard deviation calculation. You have to realize that very often control charts were kept on the production floor with graph paper and operations would fill in the data accordingly. The key I believe is to choose a technique and utilize the value of that technique and respond to the "voice of the process" when there is an out of control signal.

[#6]

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.

[#7]

Also a very nice response !

[#8]

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:

1. Ultimately we're trying to find an economic way to investigate outliers, which is kind of the purpose of control charts.
   1. 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.
2. 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.
   1. Wheeler's paper titled "Are You Sure We Don't Need Normally Distributed Data?" got me to thinking about this concept.

[#9]

There is a larger discussion here as well. For me the control charts were the "Voice of the Process" thus a smoke detector so to speak of when a "stable" process may be migrating off course due to special cause. It is very wasteful to chase common cause variability which is all too prevalent. Then of course there are specifications which in a perfect world are set based upon "fitness for use" and performance which is an entirely another discussion worth having but not enough room here to expound upon. Our quality system was founded upon specification built around fitness for use which were derived via Design of Experiments and understanding the various fingerprint impurities in a process and their impact on the penultimate specification, customer use. So often material specifications are set under the guideline that higher quality is better however many times certain "impurities" are synergistic and beneficial to the performance of the final product or process and just blindly optimizing a process for specification does not always give the best performing product/process. I just wanted to add this to the discussion since process/product understanding is the key and control charts are an integral part of that understanding but not the entire story. However, that being said, an excursion into a special cause is not necessarily a bad thing but rather an opportunity to learn about ones process/product since you may find out that the excursion provided a process/product that performs better in your customers hands so the key is to evaluate the impact of the excursion and gain process knowledge from it which is the scientific method.

[#10]

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 ?