Dear Fellow Professionals,

I am conducting a hypothesis test of sorts and I would like to obtain some opinion data from you to ensure my hypothesis is not limited to only my opinion.

A part of my hypotheses deals with control charts. I have chosen the X-bar,R chart for this part of the hypothesis.

Below are the construction guidelines, tests, and modification guidelines I plan to use for my X-bar,R chart. These guidelines and tests are where I would like your opinion.

Construction Guidelines.

1. Establish trial control limits (LCL, CL, UCL) for the control chart using the first 25 data points.
2. Verify the trial control limits against the process requirements:
a. CL = target (or as close to target as can be tolerated)
b. UCL and LCL are narrow enough to provide the required capability and performance indices.
3. Given the conditions in 2 above are true, plot the CL, UCL, and LCL on the chart and lock these values, otherwise correct the process and reestablish new trial control limits.

Tests for process in control. Use the following test for possible out of control indications (commonly used conditions, not all possible test conditions):

1. One point >UCL or <LCL
2. Six points in a row all increasing or decreasing.
3. Nine points in a row >CL or <CL on the same side.

Adjusting control limits. If any of the control chart tests fail, adjust control chart limits ONLY if:
1. The data points are not returning toward normal without adjustments to the process.
2. The data points do not trend back toward normal following an adjustment to the process.
3. The data points appear to have established a new permanent mean.

Displaying the control chart. Display the last 25 points. Display more than the last 25 points if there is important trending to display, and the chart is not too cumbersome to read with the additional information displayed.

I would appreciate your opinions and comments on the above conditions.

I realize that the answer to most of the issues could be “it depends” I am just looking for your ideas on the most common cases.

I appreciate your opinions and comments.

Jim Shelor
PMP, CSSBB

Hello there, Jim. Below looks like textbook, so I don't really know if anything I add will be beneficial.

As you probably know, Steve's your man. I think he does control charts for breakfast everyday :D




Construction Guidelines.

1. Establish trial control limits (LCL, CL, UCL) for the control chart using the first 25 data points.
2. Verify the trial control limits against the process requirements:
a. CL = target (or as close to target as can be tolerated)
b. UCL and LCL are narrow enough to provide the required capability and performance indices.
3. Given the conditions in 2 above are true, plot the CL, UCL, and LCL on the chart and lock these values, otherwise correct the process and reestablish new trial control limits.


Based on what I recall, these are fairly standard approaches to setting up a control chart.



Tests for process in control. Use the following test for possible out of control indications (commonly used conditions, not all possible test conditions):

1. One point >UCL or <LCL
2. Six points in a row all increasing or decreasing.
3. Nine points in a row >CL or <CL on the same side.



Are these based on the Western Electric guidelines? I don't have it in front of me, so I am not for sure.

I'm sure you have seen them in posts here on the Cove, but there is some subjectivity regarding when to recalculate control limits. I think Steve usually quotes Wheeler on when to readjust. I came from a more liberal camp, and adjustment occurs more frequently. Based on his experience and sheer # of control charts, Steve's experience is probably more validated than anything I would have.

Where is your concern? The only thing I even raised an eyebrow on was the 25 data points to establish limits. That's not very much data. How often will you be sampling and what size samples?

Hello there, Jim. Below looks like textbook, so I don't really know if anything I add will be beneficial.

As you probably know, Steve's your man. I think he does control charts for breakfast everyday :D




Based on what I recall, these are fairly standard approaches to setting up a control chart.



Are these based on the Western Electric guidelines? I don't have it in front of me, so I am not for sure.

I'm sure you have seen them in posts here on the Cove, but there is some subjectivity regarding when to recalculate control limits. I think Steve usually quotes Wheeler on when to readjust. I came from a more liberal camp, and adjustment occurs more frequently. Based on his experience and sheer # of control charts, Steve's experience is probably more validated than anything I would have.

Where is your concern? The only thing I even raised an eyebrow on was the 25 data points to establish limits. That's not very much data. How often will you be sampling and what size samples?
Brad,

The construction guidelines came primarily from “Statistical Process Control”, Grant & Leavenworth as well as discussions with Steve and Tim Folkerts. I have discussed some of these techniques with Minitab because Minitab will not allow you to do control charts this way. For example, you cannot lock the control limits on Minitab. You can put a boundary on the limits, but you cannot lock them. Minitab and I are still talking, but they tell me they will look in to what I am telling them as a change to Minitab.

As you know, there are many tests for control that can be applied for control charts. Most texts tell you not to use all the tests, rather use the tests that are most appropriate to your case. I am just trying to see if the set I have picked is the common set most people use. I think it is, but it certainly does not hurt to check.

The guidelines for revising limits came from Grant&Levenworth and again from discussions with Steve and Tim. Again, I am just wondering if this is in agreement with the way most people are employing the monitoring strategy.

As far as sampling, I am setting up a random number generator to generate the sample values and then using subgroups of 5 for the samples. I am not actually monitoring a process, this is a step in a mathematical proof I am working on. But if my charting techniques do not conform to the norm, my proof could be off target.

The number 25 for the points to establish the trial limits comes from the rule that a minimum of 25 points are necessary to establish limits for an X-bar,R chart (Grant & Leavenworth; Breyfogle; Steve, and Tim.)

Thanks for the quick reply.

Jim Shelor
PMP, CSSBB

As far as sampling, I am setting up a random number generator to generate the sample values and then using subgroups of 5 for the samples. I am not actually monitoring a process, this is a step in a mathematical proof I am working on.


What about the chronological element? Average-and-range charting presents a picture of process performance as time passes, (tooling wears, operators change, etc.) and if you don't have that element, I'm not sure how useful your results might be.

I too, am not sure about the random number generator. I think I would not be far off to suggest that process data is not completely random.

You might use one or two set of data for modeling your proof. Then, verify it with other sets of data.

Being a SSBB, I would think you should have several sets of data to utilize.

One of my books is at work. I am looking at Foundations of Operations Management (Ritzman and Krajewski).

I see no significant deviation from set up that you have listed. The rules for readjusting/reassigning control limits are more inline with what I was taught. Basically, in the continuous process improvement mindset, as improvements are made and variance is decreased, new mean, s.d. and control limits are recalculated.

NOTE: I do not do control charts everyday like Steve does (Tim, are you doing control charts?) Thus, my approach to recalculating is more academic, whereas Steve's is more practical (but based on academic rational). Thus, I would defer that interpretation to him.

One other thing (I'm sure you already know this). Traditional approaches to control charts is based on normality of data and bell curve. Steve bases his approach on... I'm not even going to attempt his name.. inequality. Not sure how detailed/deep you're going with this. If you're pushing to publish this, it might be worth mentioning.

I've documented the logic I use for Hanford control charts here and on the internet. It is primarily based upon an old Department of Energy publication - DOE Standard 1048-92, written back when the DOE tried to go TQM. It is also merged with Acheson Duncan's Quality Control and Industrial Statistics, which is the book from which I learned to do SPC from a course at the Naval Postgraduate School in Operations Research. I picked up a lot from Phil Monroe and Bill Cooper of DEMCOM, who are documented in one of Mary Walton's books.

A smart person I met from the Deming Electronic Network once told me that if you really want to understand SPC, you need to go back to the source. Dr. Shewhart's Economic Control of Quality of Manufactured Product was reprinted by ASQ in 1980. It is well worthwhile going through. Jim, I have a copy if you would like to borrow it. (Both Jim and I live in the Tri Cities Washington).

By the way, I am off next week to the University of Washington in Seattle to provide a two day course in statistics and performance measures to their financial department and other staff.

What about the chronological element? Average-and-range charting presents a picture of process performance as time passes, (tooling wears, operators change, etc.) and if you don't have that element, I'm not sure how useful your results might be.
Jim,

I have the time element build in to the model.

I also have a second variation generator that adds a component of special cause variation (tool wear).

Thanks

Jim Shelor

I too, am not sure about the random number generator. I think I would not be far off to suggest that process data is not completely random.

You might use one or two set of data for modeling your proof. Then, verify it with other sets of data.

Being a SSBB, I would think you should have several sets of data to utilize.

One of my books is at work. I am looking at Foundations of Operations Management (Ritzman and Krajewski).

I see no significant deviation from set up that you have listed. The rules for readjusting/reassigning control limits are more inline with what I was taught. Basically, in the continuous process improvement mindset, as improvements are made and variance is decreased, new mean, s.d. and control limits are recalculated.

NOTE: I do not do control charts everyday like Steve does (Tim, are you doing control charts?) Thus, my approach to recalculating is more academic, whereas Steve's is more practical (but based on academic rational). Thus, I would defer that interpretation to him.

One other thing (I'm sure you already know this). Traditional approaches to control charts is based on normality of data and bell curve. Steve bases his approach on... I'm not even going to attempt his name.. inequality. Not sure how detailed/deep you're going with this. If you're pushing to publish this, it might be worth mentioning.
Brad,

The random number generator is being used to set the common cause variation. I have a second variation model to add in a component of special cause variation.

I planned to use 10 runs on different sets of data as the proof.

The random number generator produces a normal distribution, I checked it.

As far as the adjusting of control limits, one of the chartacteristics I plan to demonstrate is the radically different chart you get if you do it by the guidelines I have specified compared to the way Minitab does it, which is essentially a continuous adjustment as the samples are plotted on the chart.

If the proof works out the way I hope it will, I will be publishing it.

I had planned to put it on this forum for comment in draft form. What do you think?

Thanks for the comments.

Jim Shelor
PMP, CSSBB

Post away! Let me know if there is anything I can help you with.

Have you thought about which publication you'll be shooting for? I ran across a couple of articles on control charts the other day. I can find them, if you think you'd be interested.

Post away! Let me know if there is anything I can help you with.

Have you thought about which publication you'll be shooting for? I ran across a couple of articles on control charts the other day. I can find them, if you think you'd be interested.
Brad,

Yes I would be interested in the articles.

If the proof works out, I was thinking Quality Progress and Six Sigma Forum.

Thanks for the help,

Jim

One other thing (I'm sure you already know this). Traditional approaches to control charts is based on normality of data and bell curve. Steve bases his approach on... I'm not even going to attempt his name.. inequality. Not sure how detailed/deep you're going with this. If you're pushing to publish this, it might be worth mentioning.

Tchybychev, or Chebychev. Shewhart invoked Tchybychev. Duncan invoked both Tchybychev, and the Camp-Meidel extension. Deming invoked that it (SPC) is an empirical method that works.

It may also be worth noting that Dr. Shewhart tested his scheme with a 1930's random number generator - numbered hat tokens in a bowl. He made up three sets - normal, rectangular, and triangular distributions. The random numbers he ended up drawing are laboriously reprinted in Economic Control of Quality . . .

Tchybychev, or Chebychev. Shewhart invoked Tchybychev. Duncan invoked both Tchybychev, and the Camp-Meidel extension. Deming invoked that it (SPC) is an empirical method that works.

It may also be worth noting that Dr. Shewhart tested his scheme with a 1930's random number generator - numbered hat tokens in a bowl. He made up three sets - normal, rectangular, and triangular distributions. The random numbers he ended up drawing are laboriously reprinted in Economic Control of Quality . . .

Hello,

For those who want to learn more about this remarkable person.

http://en.wikipedia.org/wiki/Pafnuty_Chebyshev

I found it very interesting...

Greetings.

Stijloor.

Brad,

The construction guidelines came primarily from “Statistical Process Control”, Grant & Leavenworth as well as discussions with Steve and Tim Folkerts. I have discussed some of these techniques with Minitab because Minitab will not allow you to do control charts this way. For example, you cannot lock the control limits on Minitab. You can put a boundary on the limits, but you cannot lock them. Minitab and I are still talking, but they tell me they will look in to what I am telling them as a change to Minitab.


I'm away from Minitab for the next week, but I believe there is a way to do this. Buried within in the options for the chart, you can indicate which rows to use (or exclude) from calculations. If this works the way I think, then you could tell it to only use the first 25 points when calculating the limits. This might also prevent minitab from plotting the other points and performing the tests on them - in which case this wouldn't work.

You could also do the calculations after 25 and found out what the control limits are. I'm pretty sure there is a way to manually set the control limits, so you could just type in the numbers you found with 25 points. But that is not a very elegant solution.

Tim F