# Central theorem

Six Sigma – iSixSigma Forums Old Forums General Central theorem

Viewing 71 posts - 1 through 71 (of 71 total)
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• #48702

Hamid
Participant

how to solve the central limit theorem while i have only 30 samples?

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#164964

Participant

So  divide  them  into five  groups (each 6  samples)

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#164966

Craig
Participant

What are you trying to solve? If you take a bunch more of these samples and the plot the distribution of these, you will should obtain a normal distribution. If you shrink your sample size to 5, and take a bunch more, the same should hold true, but the distribution might not approximate the normal as closely.
There are ways to do this with randomly generated data. That would be the cheapest way. JMP even has a canned file that comes with the software for demonstration of this principle. I think it is the random6k file.
Is this TB Hamid?

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#164969

Ward
Participant

If you have Minitab, Minitab also has a macro that demonstrates this:
” Demonstration of the Central Limit Theorem
Provides a “guided tour” of the Central Limit Theorem, simulating multiple throws of a die to demonstrate the theorem. Concepts are explained in notes in the Session window, and graphs show the results of simulations. The theorem states that if random samples of size n are repeatedly drawn from a population with a finite mean, mu(y), and standard deviation, sigma(y), then when n is large, the distribution of the sample means will be approximately normal with mean equal to mu(y), and standard deviation equal to (sigma(y))/sqrt(n).”

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#164990

thandi
Participant

The CLT is unnecessary for control charting.  Shewhart didn’t use it.

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#164993

Ward
Participant

I agree with you but where is the reference to control charts?

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#164999

Craig
Participant

Please clarify the point about Shewhart not utilizing the central limit theorem. The recent studies I have done on control chart design have dealt with OC curves, alpha risk, and areas under the normal curve.
When you apply statistical limits to a collection of sample means, doesn’t this assume normality of these means, and hence the central limit theorem?

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#165003

Ward
Participant

It seems this thread is now deviating (no pun intended) to control charts instead of the central limit theorem.
When addressing OC curves, alpha & beta risk, area under the curve & central limit theorem, it appears there is a fundamental misunderstanding between analytical studies (SPC) and enumerative studies (hypothesis testing).I think you will find the following article very useful. I look forward to discussing further, after your review.http://www.spcpress.com/pdf/Wheeler_Neave.pdf

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#165012

Craig
Participant

O/C curves, central limit theorem, ARL, alpha risk are all very relevant to SPC. Check out Montgomeries SPC text.
Someone stated that the central limit theorem is not necessary for control charting and Sewhart did not use the CLT.  If sample means do not follow a normal distribution, what good are our statistical limits?

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#165013

leanmanagement
Participant

Instead of Montgomery you should rather refer to the founder. Notably the very reason why Shewhart has invented SPC is because he was against the use of Frequentist Probability in the Real World for it wasn’t rigorous. It’s really a shame that most spc consultants and students refer to fake gurus instead of the original ones: Shewhart and Deming.

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#165014

Ward
Participant

There is no assumption of normality for the control chart. There is no assumption of normality for the control chart. The 3 sigma limits work for the normal, uniform, right triangular, Burr, Chi-Square and exponential. Minitab cites Wheeler & Chambers when advising people of the Box-Cox transformation. “The Box-Cox transformation can be useful for correcting both nonnormality in process data and subgroup process variation that is related to the subgroup mean. Under most conditions, it is not necessary to correct for nonnormality unless the data are highly skewed. Wheeler [33] and Wheeler and Chambers [32] suggest that it is not necessary to transform data that are used in control charts, because control charts work well in situations where data are not normally distributed. They give an excellent demonstration of the performance of control charts when data are collected from a variety of nonsymmetric distributions.”Ranges will not be normally distributed, so the assumption is blown right away.Douglas Montomery? I believe he also lists A2 factors for n=2…n=6 as “0”. It is not “0”. The factor is N/A as the complete calculation is negative.

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#165015

Ward
Participant

A little cutting, but your points are valid. I reference Wheeler, who in turn references Deming and Shewhart.
“If you want to learn something new, read an old book.”

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#165031

Craig
Participant

There is an underlying distribution at the foundation of every control chart. There is an underlying distribution at the foundation of every control chart.There is an underlying distribution at the foundation of every control chart.There is an underlying distribution at the foundation of every control chart.There is an underlying distribution at the foundation of every control chart.There is an underlying distribution at the foundation of every control chart.There is an underlying distribution at the foundation of every control chart.

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#165032

Ward
Participant

Feel better?

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#165035

Brandon
Participant

Good one Pete – I was thinking about how to hassle him when I popped your response open. So I’ll let it go now.
Tough

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#165036

Brandon
Participant

I meant to say….
Tough to type when you’re laughing anyway.

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#165038

Chris Seider
Participant

Pete,
What bothers Hacl and some others, including myself, is some of those who argue about the lack of need for normality have not actually used SPC charts on non-normal data.  There is nothing more powerful to block usage of SPC is incorrectly calculated 3 sigma limits causing alpha errors and improper adjustment to the process.
Operators/Process Participants are humans and they know when a tool is broken.
To be clear, I am not advocating not using SPC charts if non-normal data is existence but the sigma limits should be handled use the distribution type and not the Rbar technique.

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#165046

Glenn
Participant

Try this for an exercise, it should take no more than 5 minutes.Open up Excel. Use Tools-Data Analysis-Random Number Generation to generate, say, 100 rows by 6 columns of random data, use any distribution you like, for example uniform. Calculate the mean of each row and plot a histogram of the means. You will always get a normal distribution if the process distribution is stable, and if the subgroup size is sufficiently large. Six will usually be enough.A common problem is when you get a mixture of two, or more, normal distributions with very different means (a bimodal distribution). For example, a repair job that takes an average of 15 minutes unless a new part is needed, in which case the average time is an hour. In that case control charts don’t work unless you can separate out the distributions.

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#165053

Ward
Participant

C,I appreciate the tone of your response. I do think a new discussion thread should of been started regarding control charts. We seemed to have moved away from

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#165054

Ward
Participant

C,…Hamids original inquiry into the central limit theorem. My bias is evident, as I was trained by Dr. Wheeler (spcpress.com). I still go back to the practicality of the I-mR chart. When non-normal data is evident, then it is better to modify the rules for interpretation, than attempt elegant transformations to normality. Variables charts for sub-grouped data (x-bar, R, & x-bar, S). Should not non-normal too often. Remember this a bout process, not mathematical models. Shewhart came up with a pretty powerful technique that workers on the shop floor could understand and you can imagine what version of Minitab that was! :)

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#165064

Mikel
Member

posts. I too believe there is great value in reading Shewhart,
Deming, Wheeler, but also Montgomery (Doug has done great
things in the understanding of DOE and RSM), Grant and
Leavenworth, Box, Crosby (yes Phil did a lot to accelerate the
discussion that is is really about money – we are all business
people first), Feigenbaum (a slooooow read) and others. My
biggest disappointment in all the SS stuff in the last 12 years is
that we did not do a good job of creating learning beyond the BB
stuff – BB is a good start and thats all.My question for you is about the importance of Wheeler’s point in
your cited link. My experience with SPC is the problem does not lie
in whether it is taught with or without probabilities and
mathematical rigor, the problem is that most don’t do a damn
thing with the information generated. Lack of action on points that
clearly are not part of the system is the real issue.My opinion.

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#165071

Ward
Participant

Stan,Thanks for the response. I meant no disrespect to Montgomery. I reference his DOE book often. One of my first SPC texts was also Grant & Leavenworth. I whole-heartedly support Crosby’s idea that “Quality is Free”. If Six Sigma waves are not more than paying for themselves, something is wrong. Yes. You are spot with your regard to action on the control charts. That is why Deming believed SPC began with management, not with people on the shop floor. SPC is discipline and most people still accept in spec is good, out of spec is bad. They don’t understand that processes that are stable, may occasionally produce non-conforming product or service, if there is excessive variation. Most management still wants answers and changes for the out of spec occurrence. Until processes are understood, causal factors are understood, and ultimately variation is understood, they will repeat that questioning over and over again, to no avail. It will be frustrating cycle.
Thanks for sharing your opinion.

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#165075

Chris Seider
Participant

Glad we agree……some others don’t understand what we are agreeing to.
Oh, and tone is hard to convey on this forum…. LOL

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#165076

Ward
Participant

The real learning is I don’t type so well, prior to having a cup of coffee. My typos were embarrassing. I am new to the discussion forum, but it already appears there are many contributors that would be great participants in a six sigma summit.

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#165079

Chris Seider
Participant

And I thought coffee would make one jittery…..well opposite of world here with my client so I’ll keep the coffee to a minimum at this time of evening.
Yes, it would be really interesting to have a summit where some of these usual contributors would sit around a table and be given any topic to talk about for 5 minutes.  Of course, with many of these regular posters here, we’d have to have the talking stick to control things! LOL    Kind of like McLaughlin Group….

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#165082

Ward
Participant

I vote for Nancy Grace as a moderator. Just kidding!Actually, Terry Tate “Office Linebacker” might be more appropriate.

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#165084

Mikel
Member

You mean a summit where it’s not just a bunch of consultants and and corporate types telling each other how great they are? And no \$100,000 for a video conference on the big screen with Jack.
A summit where people come to teach and learn?
It will never work, but count me in.

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#165085

Brandon
Participant

How about having it at a hunting lodge in Montana? Dr. S can bring that barrel of houch he researched. Then we could all get VERY intelligent!!

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#165086

Ward
Participant

Montana? Count me in. I have worked in 46/50 states and that is not one of them, and I can almost drive there!

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#165087

Ward
Participant

Yeah, sadly I the conferences I wish to attend on the location, and time of year. Miami in February? Count me in! Rarely is it based on the keynote or the workshops.

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#165088

Mikel
Member

Hey Carnell and I know this great place down in the Keys. Oysters and beer, Key Lime pie and beer, good looking ladies by the pool, iffy diving in February (just means we stay by the poolside bar longer).
I’ll put it together for \$1,000 a person if we can get 25. Entry is by invitiation after we know what you want to share. We’ll let Carnell and Darth judge the worthyness of the applicant.
Who is in?

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#165092

Chris Seider
Participant

I wanna come if just for the Key Lime Pie although I’m partial to Jack or Silver Patron….gotta watch my carbs!…..  I don’t get to kick someone’s butt in racquetball anymore and it’s showing….
Yes, I know there are more than a few carbs in key lime pie!

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#165097

Mikel
Member

There are some great outdoor courts nearby. Jack or tequila works for me, we’ll make the 1.5 debate the entertainment after the shots.

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#165099

Chris Seider
Participant

Yea, I’ve noticed you’ve changed on your perspective on the 1.5 or maybe I didn’t fully appreciate your stand way back then…
I just remember your great story of how a certain lady argued with you and you simply stated “go get data and see what the shift is for her process”.  I hope you think some shift exists…..because I know SHIFT happens or is it @&*%    !
Signing off for the night….

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#165109

Mike Carnell
Participant

Stan,
Luckily Grasshopper was reading this. I am way to jet lagged to be very creative.
Count me in. The Keys sound great and I will bring back some Havana Club for a little pool side R&R.
You sure about Darth? He sounds a little grumpy these days but that just makes him more interesting.
A belated Happy Birthday. I have to get some sleep. I will check back in in a couple hours.
Regards

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#165110

Ward
Participant

Sorry. You have to earn your right to attend.

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#165112

Ward
Participant

Attendance is based on your ability to construct and interpret a dive profile and Jimmy Buffet trivia. If you think you can hang, then you are invited.

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#165114

Mike Carnell
Participant

Pete,
Check out Stan’s post. I have been invited.

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#165115

Mike Carnell
Participant

I have done a few profiles and been to my share of Buffet concerts.
Like I said I have my invitation.

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#165116

Mikel
Member

If that is the criteria, Mike’s in.
Mike’s been known to dive with sharks in a six foot chop and zero visibility.
He will do the pre-Buffett trivia, also known as what do you know about Jerry Jeff.
“Jerry Jeff has bounced in and out of my life like the Mad Hatter on the way to the tea party.” –Jimmy Buffett …

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#165117

Ward
Participant

Oddly enough, I missed Stan’s invite. Hmmm…
Enjoy South Africa. Look forward to talking with you when you return.

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#165118

BC
Participant

I will be heading to the Keys in a couple weeks for R&R.  PLEASE don’t ruin it.  BTW I understand Key limes come from Mexico.

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#165120

Mike Carnell
Participant

That was both of us in the chop and with the sharks.
If you caught that remark about Terry Tate. How many have actually hired a linebacker coach from the Pittsburg Steelers to “facilitate” their meeting. We were both in on that one as well. Damn I don’t miss the good old days.
If you like Jerry Jeff you have to get hold of some Robert Earl Keen cd’s. Check out the No. 2 Live Dinner – “Gringo Honeymoon” “Amarillo Highway” “Merry Christmas From the Family” and everybody’s favorite “The Road Goes On Forever” You’ll be on your way to Gruene Hall in a heartbeat.
S__t now I am awake again. I have to shut this thing off or I am going to be up all night.
Regards

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#165121

Ward
Participant

Back in ’98, my wife and I were trying to enjoy a quick drink in Sloppy Joe’s and a guy sits down next to me and says, “Please don’t tell me you came all the way down to Key West to teach Six Sigma to Sloppy Joe’s. The guy was a Green Belt I had trained while in Stamford. I bought him a drink and assured him I wasn’t there for that!

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#165122

Ward
Participant

Want me to read to you? (It just worked for my two year old)

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#165123

Mike Carnell
Participant

Punta Cana Pete?!!!

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#165124

BC
Participant

Let me guess, it was Ernest Hemingway working on his book, For Whom the Belt Tolls.

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#165127

Ward
Participant

He shoots! He scores!
“Monty, tell our contestant what he has won!”

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#165129

Mike Carnell
Participant

I was in Sloppy Joe’s with a friend from Australia about 10 years ago and he got thrown out. What can you do in Sloppy Joe’s to get thrown out? It is like that guy that got thrown out of Guns and Roses. When that stuff happens it is time to check into the clinic of a couple weeks.

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#165130

Ward
Participant

No, I think he had jet skied to Cuba.

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#165131

Mike Carnell
Participant

Let’s talk trivia. How about Janice Pennington to show us what is behind door number 3.
You know you guys don’t use your full names for this stuff. Now I have to explain this string to the next customer that googles.
The Hmmmm gave you away.
Regards

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#165132

Mikel
Member

I’ll give it a try.
I’ve been listening to the new Steve Earle and Sones de Mexico – their “Esta Tierra Es Tuya,” is a good thought in the imigration debate.

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#165134

Mikel
Member

By the way, Dr. Scott is going to be pixxed when he sees this thread. I think we have gotten off topic.

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#165135

Ward
Participant

I don’t see it. I think Hemingway’s “theorems” are “central” to life in Key West.

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#165136

Mike Carnell
Participant

That sounds interesting. I will have to give it a try when I get back. I have a feeling it won’t be easy to find here.

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#165138

Mike Carnell
Participant

Clever. That is the the stuff that causes all those geeks in your classes to give you s__t on your reviews.
Keep up the good work. I love that stuff.

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#165140

Mikel
Member

I think you are right, but that Dr. Scott likes to crack the whip on stuff like this.

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#165141

Ward
Participant

No more reviews. Done. I walked away.
Now I rake leaves and talk to my son, who has seen his dad more consecutive days, than he ever has.
It’s been especially nice not having to deal with United (“We’re not happy, ’til your not happy!”) Airlines every weekend.

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#165144

Ward
Participant

We need a separate thread for important stuff like this.

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#165146

Mike Carnell
Participant

Glad to hear the domestic lifestyle is working for you. The great part is you caught it before it slipped away. Not all of us were that smart.
What is that airline stuff all about. Everybody I know loves flyinf from Denver to LA so they can spend all night flying to Charlotte and after sleeping in those comfortable seats all night walk into teaching a Six Sigma class about 10 minutes before it begins. That United Airlines?
If you are into self flagelation jump on a Delta luxury liner for about 18 hours from Atlanta to Joburg. I better shutup I have to ride them home in about a month.
I love being a million miler on American and go to check in and they want to show you how to do it yourself. Virgin sends a car 2 hours each way to pick us up and take us to the airport and they check us in at the curb. That doesn’t suck.
No wonder thses guys don’t want Virgin Airlines flying inside the US. They look like Rent-A-Wreck next to them.
Hope thing continue as well for you in the future. You two have done your time. Enjoy it.
Regards

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#165148

Ward
Participant

Yep. That United. I am really pulling for Sir Richard Branson. I am ashamed to say my son turned two in July and he became a United Premier traveler this month. That could be seen by some as child abuse. I like to say to say that every 100,000 miles flown on UAL takes one year off your life. I have dropped 14 years. After all that, I am subjecting myself to UAL for, you guessed it, a trip back to Punta Cana.

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#165150

Craig
Participant

Good humor in this thread! More importantly, I am in Central Florida which is a “puddle-jumper” away from the keys.
We waited for Carnell to show up a few years ago for a Mahi Mahi adventure, but work got in the way.
I am still wanting to meet Stan and Darth too for some 12 ounce curls.
HACL

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#165153

Nats
Participant

Stan,
You write as if you are educated and others are not?
Where and when did you receive your statistics training?
I cannot locate your name as a contributor to any of the statistic or quality literature?
Perhaps you could lead me closer to your work contributions?
Nats

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#165155

Ward
Participant

Nats,I read Stan’s postings as more of a deeper inquiry, not as a challenge. It is kind of tough to understand a person’s tone with the response. I didn’t interpret his response as picking on anyone else’s education or lack thereof. eteP

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#165157

Frau Mirckel
Participant

Nats
Go east or  west
Stan is  the  best
Go back  to  your  nest
and
Drop  yourself  from  the  list

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#165171

Sloan
Participant

Nope, he was working on “The Old Man and the C-Chart.”

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#165177

BC
Participant

Good one!  I didn’t realize Hemingway was such a prolific 6s author.  That puts him right up there with Deming, Monty, et al.

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#165178

clb1
Participant

Hemingway a 6 Sigma author – this is definitely old news.
For Whom the Bell Tolls – A classic dissertation on the use and abuse of the normal distribution.
Islands in the (Data) Stream – An analysis of clustering
The Sum Also Rises – Analysis of the effect of the proper use of DMAIC on the bottom line
The Fifth Column – An introduction to the statistical functions on Excel spread sheets

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#165179

BC
Participant

Don’t forget
Death in the Afternoon – preparing your tollgate review.

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#165306

BJWheat
Participant

Come on Carnell – I’ve never seen you too jet lagged to come up with