topic Re: Control Chart & 3 Sigma in Discussions

Control Chart & 3 Sigma

none1 — Tue, 10 Mar 2015 20:10:44 GMT

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.

Re: Control Chart & 3 Sigma

Dan_Obermiller — Tue, 10 Mar 2015 20:32:13 GMT

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.

Re: Control Chart & 3 Sigma

louv — Tue, 10 Mar 2015 20:41:18 GMT

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.

Re: Control Chart & 3 Sigma

none1 — Tue, 10 Mar 2015 20:51:43 GMT

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 ?

Re: Control Chart & 3 Sigma

louv — Tue, 10 Mar 2015 21:05:58 GMT

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.

Re: Control Chart & 3 Sigma

Steven_Moore — Wed, 11 Mar 2015 20:12:13 GMT

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.

Re: Control Chart & 3 Sigma

none1 — Thu, 12 Mar 2015 10:07:31 GMT

Also a very nice response !

Re: Control Chart & 3 Sigma

tundratoze — Thu, 12 Mar 2015 12:53:34 GMT

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.
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.
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.

Re: Control Chart & 3 Sigma

louv — Thu, 12 Mar 2015 13:32:22 GMT

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.

Re: Control Chart & 3 Sigma

none1 — Thu, 12 Mar 2015 14:05:57 GMT

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 ?

Re: Control Chart & 3 Sigma

Steven_Moore — Thu, 12 Mar 2015 14:49:29 GMT

none1, We have to be careful not to over-think or try to out-think the process behavior charts and the data. This is why it is so important to have knowledge regarding the origin, collection, and definition of the data. The software package you are using can calculate anything you want, but utilizing your knowledge and experience about the process and data is where the real value of the control chart lies. Once you have established control limits and a succeeding point shows a lack of control, then you have a signal which can be investigated. Updating control limits at every succeeding data point is dangerous. Again, Wheeler treats this situation in his writings. Ultimately, the questions are: Did the same system produce this data point as produced the previous data points? How do you know? Do you expect the change (signal) to be sustained? This takes years of practice and thought. Keep thinking....you are on the right track.

If I can be of assistance to you with data analysis, my e-mail is smoore@wausaupaper.com

Re: Control Chart & 3 Sigma

none1 — Thu, 12 Mar 2015 15:00:34 GMT

Thanks for your response Smoore.

However I dont understand, why re-calculation of limits is dangerous. Then why do have control charts. I means they are meant to provide us values based on the actual behaviour of the system and tell us if the actual system out put is Ok or not ?

Re: Control Chart & 3 Sigma

wjlevin — Fri, 13 Mar 2015 08:22:38 GMT

There's some really good discussion here about the fundamentals of control charts. Like others, I suggest you get Wheeler's book.

In it he explains that the limits play two roles. First, they pass judgement as to whether there are any out-of-control conditions. If not, then the second role they play is to predict where future output is likely to appear.

So, to your questions about recalculating limits with the onset of new data... If the process is stable, there's no need to revise the limits - they'd essentially give you the same limits you already have. If your process is unstable, then the limits are passing judgement alone -helping you identify and eliminate special causes.

An unstable process may cause you to calculate substantial changes in the limits. Calculate limits, find the special causes and eliminate them. Some have the practice of calculating "theoretical limits" based on eliminating the special cause data. Others continue to revise the limits as they collect new data while continuing to identify and eliminate special causes. Once you've had a period of time without any special causes, you can declare the process stable and freeze the limits.

Really there's no way to use the charts in the absence of process knowledge. With the aid of the charts you should have an understanding if your operation that tells you if it is stable or not. For example, you may expect changes to the chart if you swap in/out a tool. If that's the case, you'd need to have a control chart for each of the tools involved in the operation - since each is a separate process with its own "stable" pattern (assuming no special causes).

I feel I'm rambling here - do get and read Wheeler's books and they'll expose you to the comments you are getting in this thread. You are welcome to send me data at levin@predictum.com.

Re: Control Chart & 3 Sigma

Steven_Moore — Fri, 13 Mar 2015 11:10:55 GMT

Anyone interested in the absolute genius of Walter Shewhart in devising the control chart should read his original book, published in 1931. You can get a 50th Anniversary edition at Amazon.com. I have read and re-read this book several times and I always gain more insight into this simple tool backed up by 500 pages of development and theory leading to an empirical masterpiece.

In 1989 W. Edwards Deming said: "Dr. Shewhart contrived and published the rule in 1924. Nobody has done a better job since."

The August 1967 issue of Industrial Quality Control published the article “Our Debt to Walter Shewhart” which included a 1 page memo from Shewhart to his boss and a copy of the first published control chart. Amazing stuff!

Re: Control Chart & 3 Sigma

Steven_Moore — Fri, 03 Apr 2015 18:52:37 GMT

The control chart does not tell you whether or not the output is OK or not. I tells you if the process is operating with a "reasonable degree of statistical control". If yes, then the process is operating as well as it is able. If no, then there are special causes of variation that need to be removed before improving the process. Removing special causes is NOT improvement of the process. Once your process is operating as well as it is able, then changes can be made to the process itself to get it to reach a new level of performance at a more desireable average and/or with less variability.