central limit theorem
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 This topic has 18 replies, 12 voices, and was last updated 15 years, 4 months ago by Theo.

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January 5, 2007 at 7:37 am #45716
A. NoborikawaParticipant@A.Noborikawa Include @A.Noborikawa in your post and this person will
be notified via email.Hi All,
I’m new to this site. My question to all of you is, “In what type of business situations would central limit theorem be used?” Any suggestioons would be appreciated. Thanks!
Amy0January 5, 2007 at 7:57 am #149986hi amy…more than ‘use’ we can ‘relate’ the CLT to any business or situation. In simple words for example:
If average score of Student ‘A’ in all his exams is 80, Then…
according to the CLT it can be stated that the probability of ‘A’ scoring 80 in his next exam is highest at 80 & the probability decreases as the score increases or decreases from 80, when plotted with score as Xaxis & frequency of occurance as Yaxis.
It is a Normal Distribution Curve with Mean=0 & SD=1.0January 5, 2007 at 1:39 pm #149991?
0January 5, 2007 at 2:13 pm #149995To get a better response, you might want to elaborate on your question. Why do you want to know? What situations are you faced with? What measurements do you do? Etc.The answer to your question is every business situation has a potential to use the central limit theorem.
0January 5, 2007 at 7:30 pm #150015This forum has frustrated me at times, with caustic replies to innocent inquiries. I believe that it is ok to ask some simplistic questions without being told to “be sure and look through this site in its entirety.”
BUT…both the simplistic inquiry and caustic response are more correct than answering when you don’t KNOW THE ANSWER!0January 5, 2007 at 7:35 pm #150016But half of the answers will disappear!
0January 5, 2007 at 7:37 pm #150017
Paul WhiteParticipant@PaulWhite Include @PaulWhite in your post and this person will
be notified via email.I have seen CLT used within gauge R&R to reduce measurement error by averaging the samples.
This approach was taught during my BB training but I have never really agreed with this as I feel it is ‘massaging’ the data to get a pass on R&R.
Once the team had used averaged the results to pass R&R, they then plotted individual results on the control chart. Some months down the line they are starting to realise that the chart is not that meaningful because they have a lot of measurement error on the individual results.
Therefore, how can CLT be used to pass R&R as taught during BB training? Is this just smoothing the data to get a tick in the box?0January 5, 2007 at 7:48 pm #150020The use of averaging is only valid if it is the measurement method long term.
If you don’t think it’s valid, go look at what changing the time period on an osilloscope does. It is just averaging.0January 5, 2007 at 7:50 pm #150021The technique is a way of increasing the accuracy of the gage, not the GR&R – you are supposed to increase the # of samples used in the sample plan. Your GR&R is supposed to illustrate the accuracy you can achieve if you increase your repetition of your measurement – either as a shortterm solution, or – if you can’t improve the gage – as part of the gage SOP.
If you were taught to use it only in GR&R you were taught wrong.0January 5, 2007 at 7:59 pm #150022
Paul WhiteParticipant@PaulWhite Include @PaulWhite in your post and this person will
be notified via email.OK thanks!
So, if we collected data during R&R in subgroups of 10 and used the average result for R&R calculation.
The ongoing sampling plan should be n=10 and plot the average on the control chart?
Should this be an Xbar & S chart because of the subgroup sample size or an I&MR chart because we are treating the result as an individual data point?
Cheers for the advice0January 5, 2007 at 8:08 pm #150023I&MR
0January 5, 2007 at 8:09 pm #150024
Paul WhiteParticipant@PaulWhite Include @PaulWhite in your post and this person will
be notified via email.Thank you
0January 6, 2007 at 1:38 am #150029
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.Hey Obiwan,
Happy New Year to you. Hope you and the family are doing well. See, someone else can be a jerk besides me :). That should warm your heart. May the Force be with you.0January 6, 2007 at 1:43 am #150030
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.You don’t really “use” the Central Limit Theorem in business situations. There are certain mathematical operations that you might perform which might reflect the CLT. For example, if you collect samples in an inspection scheme, the resulting distribution of the samples might follow the principles of the CLT and might be used to make some inference about the population of items you did not sample.
0January 6, 2007 at 6:43 am #150039Nice to see that no one has fallen into the error of claiming that control charts depend on the central limits theorem.
0January 6, 2007 at 11:28 am #150046
Marlon BrandoParticipant@MarlonBrando Include @MarlonBrando in your post and this person will
be notified via email.But it is the basic for the XR Control Chart,when means will be normally distributed regardless of the parent distribution.
0January 6, 2007 at 12:41 pm #150048
AnonymousParticipant@Anonymous Include @Anonymous in your post and this person will
be notified via email.Here we go again: Wheeler versus Montgomery. This argument is not going to end in agreement, so you stick to your use of Control Charts as Run Charts with rough reference lines based on chebyshev theorem, and I’ll stick to normal distribution theory. It seems that both work in practice.
0January 6, 2007 at 8:32 pm #150051Chebychev assures us that every distribution has a 3 sigma coverage of at least 88.9%.
Standard XmR charts do far better than this for most situations. For skewness squared less than 3, and any kurtosis value, you get 98% cover !
For practical purposes, you can forget about normal distibutions, Box Cox and the rest.0January 7, 2007 at 10:39 am #150054You may find this helpful:
http://www.spcpress.com/ink_pdfs/Good%20Data,%20Bad%20Data.pdf0 
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