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]

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

[#3]

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 ?     

[#4]

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.

[#5]

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!

[#6]

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.