# Histogram and Control chart

Six Sigma – iSixSigma Forums Old Forums General Histogram and Control chart

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• #45430

Belas
Participant

Hi all,

Need to pick your brains for a sec..

I have a set of non-normal continuous data in which Weibull is the best fit. The histogram gives me the process limits (control limits) based on the Weibull distribution. Now, I know that Control charts do not need normally distributed data (I-mr chart) and I plot the same set of data on a Control Chart with a +/- 3 sigma process limit.
The process limits on the histogram and Control chart are different. (as expected)

Would you be kind enough to advise which process limits (control limits) I should use?

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#148449

PJ
Participant

Do you know if the process is in control-often they are not. I think the sub group size for histogram is the Sq. root of the total data set. the sub group for moving avg. is two. Is there any way you could do an anderson-darling check for normality-rational sub group size might have something to do with it and which cart to use.

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#148452

The Force
Member

Please take note that control chart as two control limits — one for the mean (x, I) and other for the standard deviation/range (s, r, MR) while histogram may represent the mean alone.
Try checking the process capability using weibull for both esp if the data is not normal

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#148461

Mikel
Member

Several Questions need to answered –
1) Does it make sense that your data follows a weibull distribution? If not, find out what is going on. For a production type process, Weibull probably doesn’t make sense. For performance type characteristics, Weibull can make sense. You need to have a rational view of what is expected.
2) How many data points do you have and do they represent a long term view of the process being measured? With adequate data this is the best representation you have of your process limits.

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#148465

Belas
Participant

1- It is a production type process. I would expect data to be normal. I believe the data follows weibull dist because most values are “squashed” against upper spec limit.
2- I have about 50 datapoints. (as much as I can possibly get in 1 year)
I still feel my question wasnt answered.(my bad) let me ask you the question in another way:
which 1 is correct?:
1- I “take” the upper and lower control limit from the histogram, when the distribution is non-normal, and call it “my process limits”. (lower spec= 0; nominal=3; upper spec=4)
2- I “take” the upper and lower control limit from the I-Mr chart, and call it “my process limits”. (lower spec= 1; nominal=3; upper spec=5)
the specs are made up however, the example reflects what I am seeing.
thanks

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#148467

Mikel
Member

Anytime processes are naturally bounded (i.e. squashed against upper spec limit), normality shouldn’t be expected. I assume it is a natural bound not some sorting that going on because of spec problems.
1 has to be the right answer because 2 would give an Upper limit that does not represent reality.
Could you post a histogram of the data or provide the data set?

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#148469

Belas
Participant

let me see if the histo and I-Mr can be pasted onto here..

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#148471

Belas
Participant

i dont seem to be able to paste the graphs or the data (table). if you give me your email ill send you the spread sheet.
thanks

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#148473

Mikel
Member
#148482

W M
Member

You are correct, control charts do not need normal data.  Forget about Weibul and tests for normality.  Use the histogram as it is, to learn about the process.  Don’t try to fit distributions.  There is no benefit to you in doing this (the only benefit is to marketers of statistical software).
Control limits are only relevant to control charts, not histograms.

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#148484

PJ
Participant

I agree, control charts do not need normality. I may have been the one you were refering to about normality.I suggested this because I too was confussed about trying to use Weibul, if we are talking about typical production data. I sugested a test for normality because I wondered if some unussual subgrouping was being used.In general it does not matter what the underlying distribution is if you use rational subgrouping-you will end up with something close to normal-then generate control limits-or am I missing something?

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#148485

Mikel
Member

Which of the control chart rules will you use with an extremely skewed distribution?

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#148487

PJ
Participant

Perhaps use a Box-Cox transformation,althouth control charts should work in most highly nonnormal situations.

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#148495

W M
Member

pj,
You are close but control charts do not rely on the central limit theorem as I think you may be suggesting.
Forget all the nonsense you have learnt in your six sigma classes.  Read Shewhart, Deming and Wheeler.

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#148496

W M
Member

What do you mean by “extremely skewed”.  Can you give a real world example ?
For 3 sigma control limits:

For skewness squared < 1, kurtois < 4, cover is 99%
For skewness squared < 3, cover is 98%
Compare this with Chebychev which gives 88.9% cover for any distribution.
It is time for people to get back to basics.  Read Shewhart !!!!

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#148500

Mikel
Member

I read Shewhart for the first time in 1979. I read Deming in 84 and Deming’s notes on Shewhart’s lectures in 85. Juran’s Managerial Breakthrough in 78.
I have read everything Wheeler has published and I can’t for the life of me remember them being dogmatic and saying to do anything without understanding them.
My question and point were simple. What rules do you suggest people use when they just throw everything into a control chart. For simplicity purposes, let’s stick with the Western Electric rules.

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#148509

Belas
Participant

Stan: the data I sent you only contemplates the rule of “data points that fall outside +/-3s”.
Everyone else: My aim is to apply, in a real world situation where normal data is not always possible, process limits so to “draw the perimeter” around the process. If I use the limits shown on the histogram (lognormal distribution) I get a set of values and if I use the limits shown on the Control chart I get another set of values.
Which are the correct ones for people at Quality Control to follow/keep an eye on?
If you feel you need to see the data to reply, I am quite happy to send you the 85 datapoints.
thanks

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#148510

W M
Member

Yes, WE Rules are fine.  First start with Rule 1 and possibly add Rule 4.  More rules mean more false alarms.

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#148511

W M
Member

Forget about limits on histograms and lognormal plots.  This is pure nonsense.  Transforms will get you into a mess – there is no need for them.
Use standard control charts and histograms

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#148514

Belas
Participant

WM,
I am using standard control charts and histograms. I have made no attempt to transform the data. I am trying to stick to the basics.
cheers for the input

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#148522

Mikel
Member

Your data seems to truncate at 1.04, so having an upper control limit a lot higher than that doesn’t make sense.
Is 1.04 a natural bound or is there some adjustment or rework going on to bound it at 1.04? And why is there no attempt to achieve the target value?

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#148525

Mikel
Member

W M or can I just call you Wheeler Mantra (chant after me – control charts are my god and my everything),
I am trying to help the guy, you are spouting dogma.
I want to show you the guy’s data and a set of data that is easy to simulate. What I think the real data represents is a process that is constantly being corrected BEFORE data is being taken. What I think the production philosophy is – run as close to the upper spec as you can. What I think the correction rule is – adjust to just below the upper spec. The three columns of data are – first column, real data – second column, a process where they are trying to run to the upper spec – column three, all data above the upper spec is being adjusted down.
1.0383 1.03392 1.033921.0389 1.04207 1.038211.0366 1.03785 1.037851.0385 1.04785 1.038781.0396 1.05102 1.039101.0392 1.03995 1.039951.0315 1.04391 1.038391.0395 1.04315 1.038321.0387 1.03471 1.034711.0346 1.03980 1.039801.0371 1.03511 1.035111.0361 1.03809 1.038091.0381 1.04198 1.038201.0379 1.02875 1.028751.0397 1.03190 1.031901.0385 1.03786 1.037861.0389 1.04047 1.038051.0394 1.04012 1.038011.0393 1.03507 1.035071.0386 1.03190 1.031901.0373 1.04238 1.038241.0371 1.04529 1.038531.0387 1.04320 1.038321.0371 1.04154 1.038151.0270 1.04230 1.038231.0340 1.05140 1.039141.0350 1.03805 1.038051.0309 1.04230 1.038231.0384 1.03383 1.033831.0344 1.03463 1.034631.0356 1.04461 1.038461.0373 1.04206 1.038211.0362 1.03818 1.038181.0374 1.04094 1.038091.0367 1.04199 1.038201.0372 1.04328 1.038331.0383 1.03900 1.039001.0390 1.03658 1.036581.0382 1.04168 1.038171.0382 1.03324 1.033241.0394 1.04391 1.038391.0388 1.03757 1.037571.0389 1.04879 1.038881.0370 1.04073 1.038071.0350 1.04595 1.038591.0392 1.04530 1.038531.0362 1.04260 1.038261.0392 1.04089 1.038091.0371 1.03574 1.035741.0325 1.04351 1.038351.0350 1.04340 1.038341.0383 1.03625 1.036251.0388 1.03964 1.039641.0371 1.03451 1.034511.0369 1.03621 1.036211.0372 1.03849 1.038491.0375 1.03455 1.034551.0347 1.03593 1.035931.0385 1.03882 1.038821.0380 1.04435 1.038431.0382 1.03927 1.039271.0363 1.03139 1.031391.0380 1.03538 1.035381.0364 1.03398 1.033981.0369 1.03760 1.037601.0352 1.03243 1.032431.0392 1.03375 1.033751.0365 1.04094 1.038091.0386 1.04029 1.038031.0367 1.04321 1.038321.0376 1.02999 1.029991.0370 1.04014 1.038011.0366 1.03404 1.034041.0380 1.03781 1.037811.0361 1.03830 1.038301.0335 1.03891 1.038911.0391 1.04305 1.038301.0393 1.03490 1.034901.0258 1.03223 1.032231.0332 1.03900 1.039001.0382 1.04311 1.038311.0250 1.03605 1.03605
If your advice is taken at face value, there will be an attempt to adjust the process upward when the truth is they should move the process center to 1.03 or less. Their stated target is 1.02.
The better advice than the control chart dogma is to go understand the process and learn how to center it at target – at that point your control charts will be quite useful and will give them good advice.
Chant after me – understand the process then choose the RIGHT tools.

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#148526

Belas
Participant

looking at the data and the process I cant help to feel a bit suspicious..you can call it rework but I think there may be some “test into compliance” issue here. 1,04 is the specification and it seems that the process limit is bang on on the spec.
In addition, no one around here knows how the spec was developed/established. I would like to propose new specs, based on data.Hence the original question “where should i get my process limits from? Histogram or Control chart?”.
thanks guys for all your replies

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#148541

Mike Carnell
Participant

Stan,
You probably know this already but they may be intentionally running Max Material Condition. It may be for the calculation of bonus or it may be as simple as it is some exotic material and they want to leave room for rework if something goes wrong.
Regards

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#148545

BTDT
Participant

Belas:I have looked at the data Stan posted and read Mike Carnell’s post; they have made some good points given that data is gathered for different purposes than monitoring the process. I have to agree that there may be some skullduggery here, well, more than meets the eye at least.- The data, while following a Weibull at best, does not really fit any distribution very well.- Control charting can be done, but you need to look deeper.I would find out how the data is really gathered. Since you have only 82 or so data points, I presume the manufacturing process may be quite involved with multiple opportunities for checking and reworking to specifications.This data probably represents only the final set of measurements required for final compliance. This means the data is not representative of the process, but more the data that is available. It is likely that some customer specification has evolved into a soft specification for the line workers and everyone knows it.If you wish to have an indication of the manufacturing process itself, I suspect you may have to dig deeper into the raw data gathered during the individual process steps. The project will probably evolve into one where process control limits are determined and managed for only the subprocesses that have been determined as affecting the final specification.Going forward? I think you must:- determine tolerance limits for each process step using some of the DFSS or “Robust Design” tools.- develop individual process control limits for each step using the WE rules.Cheers, BTDT6SigmaGuru(at)gmail(dot)com

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#148546

Mikel
Member

Yea, it’s something like that. I think it’s actually a chemical process where they are measuring a density. We have seen this before in Mogadore, Ohio. Production guys doing constant adjustment before the QA lab guys take the offical sample. Density would be one of those that is easier to go down than up.

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#148549

W M
Member

Why do you guys persist in trying to fit distributions ?

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#148550

W M
Member

It’s not dogma … it’s truth.  Forget your six sigma crap !!

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#148552

W M
Member

The three columns of data are – first column, real data – second column, a process where they are trying to run to the upper spec – column three, all data above the upper spec is being adjusted down.
Is this Stan’s data or the guy with the question ?
If the 1st column is “real” it is severly truncated on the right.
What are the other 2 columns supposed to be ? Is “a process” the same as the first ? How are they “adjusting down “

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#148554

mand
Member

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#148556

BTDT
Participant

WM:I only fit distributions to understand why processes don’t always follow them.There are usually special reasons why data fit particular distributions. When they don’t, you start to understand nuances of deviations from the usual process.I have used this approach to detect fraud and quantify financial risk.Cheers, BTDT

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#148570

Mikel
Member

Such as?

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#148571

Mikel
Member

Uh, maybe to understand the process.

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#148572

Mikel
Member

Column 1 – the guy’s data, not mine. Yes it is severely truncated, but who cares? Just throw it on a control chart. Follow rules 1 and 4 and adjust the process upward and make it even worse! Great advice.
Isn’t noting that it’s truncated kind of like fitting it to a distribution?
Column 2 & 3 are just my attempt to see if I could come close to the real data pattern. Column 2 is a process set up close to the truncation point, you may note there is not any violations of rules 1 and 4. Column 3 is column 2 only I adjust downward when I exceed the truncation limit. Look at all the points flagged as out of control!
I have seen the above many times. One example is a chemical process where any vat exceeding a limit has stuff from storage tanks blended in. Yield looks okay, the lab report of the batch looks okay. Only problem is that capacity of the system is reduced to less than half.
Your message of control charts only, don’t understand things like truncated distributions is flat wrong.

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#148577

W M
Member

Why are you trying to fit distributions ?
What benefit does this serve ?
The histogram says that the data is truncated. The next step is to investigate the process to find out why.
There is no issue with using control charts with very skewed data.  If you read Wheeler’s analysis of 1143 different distributions this would become clear to you.

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#148582

Mikel
Member

As I have already pointed out, I have already read Wheeler and most writings of those who he considers his teachers. Don is a smart man, but is marketing a slant on this whole thing. I think he is smarter and more honorable than Dr. Harry (a fairly low bar to get over BTW), but he is just spinning as well.
He may have convinced you that his analysis of 1143 distributions is correct, but it is not. The data posted is but one example of coming to the wrong conclusion by just throwing it into a control chart. If you just throw it into a control chart to see the underlying distribution, I buy that. But if you throw it in even just to use WE rule 1, you would have done stupid things on this example. Maybe I just lucked across the 1 in 1143 where Wheeler could be wrong, but I doubt it.
Wheeler also gives crap advice on Measurement Systems.

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#148583

Mikel
Member

BTW, don’t you think it’s odd I spotted you as a memeber of the Wheeler cult without you ever saying anything about Wheeler.
You all have that same vacant look in your eyes.

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#148589

Hal
Participant

Readers will also notice the attempts at personal attack, when six sigma consultants like Stan are caught out preaching their nonsense.

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#148590

Dr Noel Davis
Participant

“Wheeler also gives crap advice on Measurement Systems” is a very sweeping statement.
What do you think is wrong and why ?
What are your qualifications to dispute him ?

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#148592

Belas
Participant

gentleman,
ive started this thread with a “real” question about a “real process” looking for some “real” help from you guys. please dont turn this thread into a bashing contest of “whos who”.
all of the replies, with all the diferent points of view, are quite helpful and I thank you for taking the time to explain me what was going on with the data.
see you in the next thread
over n out

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#148594

Mikel
Member

“What do you think is wrong and why ?”
First, he claims his metric is superior when it is just a different manipulation of the same numbers. Second, his advice is very vague on what is good enough. that works if we are talking about experimentation, but doesn’t work if we are talking about judgement of goods and services. Tell us what is right so that we can have a more interesting discussion.
“What are your qualifications to dispute him ?”
Experience with having to straighten out hundreds of folks who have been taught by Dr. Wheeler. You can spot these folks within minutes of starting a BB class, they want to correct everyone with statements similar to WM. You can spt them again at the report outs in weeks 2, 3, and 4 – They are not making progress and just want to debate the correctness of their knowledge.
In my experience, there are two camps of folks that have this struggle – the Wheelerites and the Shaininites. Oddly enough there is another camp that really graps this and also teach the class from their experience – that is the former Toyota employees. I wonder why that is so?
What is your experience to dispute my experience? Purely theoretical I bet.

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#148596

Mikel
Member

Hal boy,
Not preaching anything – just trying to help someone and this Wheelerite just keeps coming with nonhelp.
And you contribution here?

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#148645

Dr Noel Davis
Participant

“First, he claims his metric is superior when it is just a different manipulation of the same numbers. “
What metric ? What are you talking about ?
What has he said that is vague. Your comment about is about as vague as it gets.
“doesn’t work if we are talking about judgement of goods and services”
Another vague statement.  What are you talking about ?
“You can spot these folks within minutes of starting a BB class, “
Now I get it … you teach this six sigma nonsense.  Shame on you !!!
What are your qualifications to criticise Dr Wheeler ? A black belt perhaps ?  A B.Arts like Harry ?

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#148646

Mikel
Member

And who are you and what do you do?
By the way, before you tell people shame on them, talk to their customers and those they have taught and changed the professional lives of. These folks are in a better position to judge.

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#148647

Ashman
Member

Perhaps Stan has had a paper published, criticizing the work of the world’s No.1 statistician, Dr Donald Wheeler  ?
Or perhaps Stan has found that magazines don’t accept the ramblings of uneducated fools ?

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#148652

Mikel
Member

The world’s number one statistician? Hardly
I have been to Don’s offices in Knoxville, I know what he has. I have considered what he teaches and what he writes and use what is useable. I do not worship at the alter of Don.
What I do not respect is the claim of superior methods and measures. His discrimination ratio is the same as P/TV in so much if I know one, I know the other. His use of control charts as the end all be all is also not useful. A useful proxy to start understanding a process – absolutely. But all this fanaticism surronding what others shouldn’t be doing isn’t constructive.
I also do not agree with those that want to transform non normal data or say to just use CLT. They don’t understand what is useful about observing the distribution. Many, many problems can be solved if we have a rational view of what the underlying distribution is and compare it to what we are seeing. I tried to show that with the post that started this thread. Go read through it. My advice was right and the shots from the Wheelerite were not useful, nor would they help solve anything.
Publishing papers is not a measure of one’s work, except maybe in the academic world. Getting people without experience to believe that the Wheeler way is the best way is also not a measure of one’s work or worth.
Go fix something and get some experience.

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#148654

Ashman
Member

I’m not surprised that you have nothing published. It’s easy to make wild anonymous claims on a forum such as this.
Your objection to Wheeler seems to be “His discrimination ratio” … I have never encountered this in any of his work.  What are you claiming ?

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#148656

Mikel
Member

Why don’t you go get educated about Wheeler before wanting to fight to defend him.
PS – the high point of my encounters with Wheeler devotees was one that had taken two years to implement a control chart – quite impressive – several of us have turned around companies in less time.

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#148658

Mikel
Member

How many papers have you published?

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#148659

Ashman
Member

It is very embarrassing claiming to be an expert and never having had a word published, isn’t it Stan ?
It’s also very embarrassing having no qualifications other than the belts holding up your pants.
And here you are making totally unjustified claims about the world’s leading statistician in quality – Dr Wheeler.

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#148660

joeBB
Participant

I know, I can’t help myself.
I just want Stan to respect me.

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#148666

Ashman
Member

Sorry JoeBB, Stan hasn’t achieved anything in life … no papers … no education … so he can’t respect himself, let alone you.

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