Does the data in a control chart have to be normally distributed?

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#31
But you need to know the process is 'in control' before establishing the control limits, regardless of the type of control chart. Knowing the distribution can help establish that. X-bar does help stabilize a non-normal distribution because the averages tend to be normally distributed, even if the individual distribution is not. (Central limit theorem)
Doing a capability study is a good way to establish control limits, distribution data, etc. Using a run chart for that purpose is helpful. Using an X-bar -R chart will destroy any evidence of a uniform distribution, as it causes operators to adjust the process to "run to the mean" which is classic overcontrol. It will generate what appears to be a normal distribution - but it will be Representative of the operator's adjustments - not the process. It is the worst thing you can do for a precision machining process, and should be avoided at all costs.

If you had read the link to the past thread, you will find that whether or not the average tends to be normally distributed, in the tool wear scenario the average of the measurements of a sample of parts is meaningless. It will appear to be normally distributed because its primary variation will be measurement error from roundness or parallelism (not GR&R) - which is a normal distribution. But, that error is not what you are trying to control. In fact, in the process laid out in the link, you remove that error from your charting. Once you have removed it, you will find a uniform distribution. Any subset of a uniform distribution is a uniform distribution. "Central Limit Theory" does not apply.:eek: Sorry. :mg: It goes back to the total variance is equal to the sum of the variances. If the main variance is tool wear (uniform distribution), but your data is based on measurement error (normal), it will clearly appear normal - but it will be wrong. Eliminate measurement error (or reduce it to statistical insignificance), and only the uniform distribution will be exhibited.

You need to know something about the process before just putting a control chart on it, including whether or not the process is in control or stable.
This is absolutely true. Knowing the process, rather than rubber stamping X bar-R charts is the way to go. :agree1:

Trend charts have been used successfully for tool wear.
The discussion of the link provides a more statistically sound approach to tool wear. Trend charts still miss out on the measurement error problem - and the approach at the link actually utilizes that problem to the user's benefit. :cool:
 
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Statistical Steven

Statistician
Staff member
Super Moderator
#34
I rarely recommend using transformations, as they mask information found in the original distribution. When possible, it is best to analyze the original distribution directly. I find transformations are typically useful for "normalcentrics" that simply cannot handle data unless it is in a normal form. Any port in a storm - but not a good port...:cool:
Bob -

I do not know your background, but based on your detailed posts I assume you have a firm understanding of statistics. The people you call
"normalcentrics" are the people who took statistics in college and hated it. Why did they hate it? Because it was not made simply for them. By transforming data and using normality, most non-statisticians can grasp the concepts of statistics. The debate I continue to have with my fellow statisticians is the question of "Is it better to not use any statistics or to use normal statistics on data that is not truly normal?" There is no real answer, just different opinions depending on the nature of the lack of normality and the risk of making the Type I or Type II error.

Back to the idea of should you combine 25 dimensions into a single control chart? Probably not, but if the alternative is not doing any control charting, I would opt to have the summary chart over no chart.

Just my :2cents:
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#35
The debate I continue to have with my fellow statisticians is the question of "Is it better to not use any statistics or to use normal statistics on data that is not truly normal?" There is no real answer, just different opinions depending on the nature of the lack of normality and the risk of making the Type I or Type II error.
Just my :2cents:
I must say, I have run into this issue with people who are well heeled statisticians (some with PhDs) that still hang onto the aura of the Gaussian curve. Others are victims of plant managers that told them they had to implement QS9000 or TS16949 in six months - causing them to rubber stamp the AIAG SPC book all over their shop. Still others are working in SPC software companies - much to the chagrin of people in precision machining (which I do not believe is a small portion of their clientele.)

Unfortunately, that notion is what has caused a disproportionate amount of pain in the field of precision machining - people trying to control a non-normal process with normal statistics. Interestingly enough, back before statistics, the old hands actually were doing it correctly (or more closely to correct). But, forcing X-bar and R charts on them messed up the control for years, creating frustration and overcontrol under the impression that they were actually improving their control.

Let's consider the analogy: Is having a gun better that not having a gun at all? Depends on what you do with it...:notme:

Trust me, I get it and I understand your point. I have lived it, and fortunately broke loose from it. I use the term to help others face the fact that they may be inflicted with the disorder - the first step to coming to terms with it. It is not a mystery that this is a soap box for me, but it is an honest attempt to help people in the industry. Using the correct SPC in precision machining relieves a huge pressure and cures a prevailing madness. :cool:
 

Stijloor

Staff member
Super Moderator
#36
I must say, I have run into this issue with people who are well heeled statisticians (some with PhDs) that still hang onto the aura of the Gaussian curve. Others are victims of plant managers that told them they had to implement QS9000 or TS16949 in six months - causing them to rubber stamp the AIAG SPC book all over their shop. Still others are working in SPC software companies - much to the chagrin of people in precision machining (which I do not believe is a small portion of their clientele.)

Unfortunately, that notion is what has caused a disproportionate amount of pain in the field of precision machining - people trying to control a non-normal process with normal statistics. Interestingly enough, back before statistics, the old hands actually were doing it correctly (or more closely to correct). But, forcing X-bar and R charts on them messed up the control for years, creating frustration and overcontrol under the impression that they were actually improving their control.

Let's consider the analogy: Is having a gun better that not having a gun at all? Depends on what you do with it...:notme:

Trust me, I get it and I understand your point. I have lived it, and fortunately broke loose from it. I use the term to help others face the fact that they may be inflicted with the disorder - the first step to coming to terms with it. It is not a mystery that this is a soap box for me, but it is an honest attempt to help people in the industry. Using the correct SPC in precision machining relieves a huge pressure and cures a prevailing madness. :cool:
Bob,

You continue to mention "precision machining" in your posts. Allow me to mention that there are so many more (manufacturing) processes where "traditional" SPC methods and techniques would be very applicable.

In addition, there is nothing wrong with an X-Bar & R chart when correctly applied.

Also, the AIAG SPC manual has been successfully used in many industries.

We can not take a too narrow view of SPC.

Just my :2cents:

BTW, I am not a statistician, just a practitioner that's trying real hard.:D

Stijloor.
 

Statistical Steven

Statistician
Staff member
Super Moderator
#37
I must say, I have run into this issue with people who are well heeled statisticians (some with PhDs) that still hang onto the aura of the Gaussian curve. Others are victims of plant managers that told them they had to implement QS9000 or TS16949 in six months - causing them to rubber stamp the AIAG SPC book all over their shop. Still others are working in SPC software companies - much to the chagrin of people in precision machining (which I do not believe is a small portion of their clientele.)

Unfortunately, that notion is what has caused a disproportionate amount of pain in the field of precision machining - people trying to control a non-normal process with normal statistics. Interestingly enough, back before statistics, the old hands actually were doing it correctly (or more closely to correct). But, forcing X-bar and R charts on them messed up the control for years, creating frustration and overcontrol under the impression that they were actually improving their control.

Let's consider the analogy: Is having a gun better that not having a gun at all? Depends on what you do with it...:notme:

Trust me, I get it and I understand your point. I have lived it, and fortunately broke loose from it. I use the term to help others face the fact that they may be inflicted with the disorder - the first step to coming to terms with it. It is not a mystery that this is a soap box for me, but it is an honest attempt to help people in the industry. Using the correct SPC in precision machining relieves a huge pressure and cures a prevailing madness. :cool:
Sounds like the issue is something that is inherent in the precision machining industry. In most other industries, you cannot get people to use statistics blindly. If they are confused, they do not use it. I can tell you that in the FDA regulated industry, people use the wrong statistical methods all the time. It is far worse for them to use the wrong method then none at all, but the FDA wants to see it, so they plead ignorance when the audit comes.

This is not an easy issue, just realize not everyone is as smart as you in statisitcs. Not everyone will see that the normal distribution is wrong. Not everyone can fit the underlying distribution to data. Sometimes you have to realize that textbooks are written assuming normality in the data.
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#38
Bob,

You continue to mention "precision machining" in your posts. Allow me to mention that there are so many more (manufacturing) processes where "traditional" SPC methods and techniques would be very applicable.

In addition, there is nothing wrong with an X-Bar & R chart when correctly applied.

Also, the AIAG SPC manual has been successfully used in many industries.

We can not take a too narrow view of SPC.

Just my :2cents:

BTW, I am not a statistician, just a practitioner that's trying real hard.:D

Stijloor.
I agree, in fact when used in the correct applications, the AIAG book is one of the best books on SPC there is. I am not denigrating the value of that book - just the misuse of it. I also agree that, and understand, there is nothing wrong with an X-Bar & R chart when correctly applied. It is absolutely incorrectly applied when used for processes with the predominant variation as tool wear. SPC has been used in industries that think they have used it successfully for years, but really have not because they do not know better (no fault of their own). I am not taking a narrow view, I am using a specific example concerning the application of statistical control to non-normal distributions and the lessons learned there.

BTW, I am also not a statistician, just a practitioner that had to learn statistics to survive automotive industry. :tg:

Sounds like the issue is something that is inherent in the precision machining industry.
So far, it is the area I have found the issue to be the most prevalent. There may be more, but its need in precision machining was based on my personal experiences there, and my need to resolve the issues for my own good. From there, I have tried to share this information for others in the same situation.

This is not an easy issue, just realize not everyone is as smart as you in statistics. Not everyone will see that the normal distribution is wrong. Not everyone can fit the underlying distribution to data. Sometimes you have to realize that textbooks are written assuming normality in the data.
I appreciate the compliment, although most of this came from shop floor empirical evidence that was then used to determine the correct statistical tools. Your point is well taken, which is why I keep trying to share this information with people to break them from the "normality syndrome". I know people are stuck in that rut, and that it is reinforced incorrectly in many different ways. I see it here in the forums. It is not their fault.

In fact, to add to the discussion, many folks are trained to determine if their data is normal or not. I think they are better served to find out which distribution they have - rather than whether it is go/no-go normal. Using software such as (not a recommendation, just an example):

http://www.mathwave.com/products/easyfit_features.html

may provide more "profound knowledge." Something to ponder...:cool:
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#39
Sounds like the issue is something that is inherent in the precision machining industry. In most other industries, you cannot get people to use statistics blindly. If they are confused, they do not use it. I can tell you that in the FDA regulated industry, people use the wrong statistical methods all the time. It is far worse for them to use the wrong method then none at all, but the FDA wants to see it, so they plead ignorance when the audit comes.

This is not an easy issue, just realize not everyone is as smart as you in statisitcs. Not everyone will see that the normal distribution is wrong. Not everyone can fit the underlying distribution to data. Sometimes you have to realize that textbooks are written assuming normality in the data.
well, it's actually not that uncommon and certainly not confined to precision machining. I have experienced it in many industries. I've searched out various approaches that work for different situations (developed by statisticians in various industries that struggled with the standard set of charts commonly taught.) I now have a lot of choices at my disposal. I teach them and use them regularly.

I take the position that we need to be intellectual leaders in using, demonstrating, teaching and educating others from suppliers to customers and our own organizations on how to select and use the appropriate tools for each situation. (this includes structured experiments from the 'simplest 1 factor 2 level test to multiple factor and multipel level tests). In my experience, one of the reasons statistics gets a bad rap is that many proponents stay stuck in what Bob accurately describes as the Normal centric universe. I would add that it's not just Noramlity but also AIAG (by the way today's US automotive industry is not a sterling example of how to do things right - why, oh why do we hold the AIAG standards so high???). Things like the standard Gage R&R or the use of Cpk are just as mediocre and limited.

There is a better way; and it's not just a difference in opinion...if anything it's a difference in understanding - or maybe experiences with - the vast diversity of the real world. I've had great success and fun by getting off the beaten path and thinking and learning and teaching and doing it.

there are more than 3 black and white channels on television...

and as an after thought: I'm not proposing we throw away all of the 'old standards' but lets' ADD to our toolbox. (well, OK I do propose throwing away the AIAG Gage R&R and the capability index things as the alternatives are so much more valuable)
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#40
I'll just say I've had good luck getting managers and non-statisticians to use SPC. And again, SPC does not depend upon the normal distribution. I think the SPC is intuitive enough that it doesn't need a lot of statisical explanation, and folks usually get in trouble trying to invoke the Central Limit Theorm and normal distribution probabilities. I believe Dr. Deming was right when he said that SPC was an empirical tool, and any attempts to turn it into a probability exercies confuses the issue and misuses the tool.

I get to give a presentation that includes SPC to a rather large audience of non-statisticians at the Washington State Governor's Industrial Safety Conference in September - see http://www.wagovconf.org/files/GISHC_08.pdf for my smiling picture, and my CEO's smiling picture.
 
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