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  Statistical Techniques and 6 Sigma
  d2 chart value?

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Author Topic:   d2 chart value?
David Drue Stauffer
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Posts: 25
From:St. Louis, MO63132United States
Registered: Feb 2000

posted 10 January 2001 11:09 AM     Click Here to See the Profile for David Drue Stauffer   Click Here to Email David Drue Stauffer     Edit/Delete Message   Reply w/Quote
Hi folks,
I am trying to determine how the d2 values for subgroup sizes is derived. Does anyone know how this value is derived or where I can go to find out? a book, a web site, another forum, etc.?

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Jim Biz
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Posts: 275
From:ILLINOIS
Registered: Mar 2000

posted 10 January 2001 02:43 PM     Click Here to See the Profile for Jim Biz   Click Here to Email Jim Biz     Edit/Delete Message   Reply w/Quote
You Might Try Juran's Quality Handbook

Chapters 21 thru 24 deal with charting and the factors used

Glosary of symbols Defines:
d2 = ratio of the "expected value" of R bar (in sample sizes of n) to the sample estimate of sigma.

Also Table A (pg AII3 lists d2 values for samle sizes ranging from 2 to 25)

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Laura M
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Posts: 299
From:Rochester, NY US
Registered: Aug 1999

posted 10 January 2001 09:31 PM     Click Here to See the Profile for Laura M   Click Here to Email Laura M     Edit/Delete Message   Reply w/Quote
Do you mean the actual calculation that was used to generate the values in the table?

I remember deriving it a long time ago in a "Theory of Statistics" course. That would certainly stimulate some brain cells if that's what your looking for.

Laura

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David Drue Stauffer
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Posts: 25
From:St. Louis, MO63132United States
Registered: Feb 2000

posted 20 February 2001 04:02 PM     Click Here to See the Profile for David Drue Stauffer   Click Here to Email David Drue Stauffer     Edit/Delete Message   Reply w/Quote
Laura, Yes that's exactly what I mean. You can make some really useful macro charts in excel IF you know how the formula is derived.
Example: What range do I need to hold if I have a total tolerance of .030 and a subgroup size of 10, and I need a 1.67 Cp? Since the calculation for Cp is the Tolerance divided by 6 sigma and 1 sigma is Rbar times d2, to put the macro in the spreadsheet, I need to know how d2 is calculated.

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Rick Goodson
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Posts: 102
From:Wuakesha, Wisconsin, USA
Registered: Aug 2000

posted 20 February 2001 04:59 PM     Click Here to See the Profile for Rick Goodson   Click Here to Email Rick Goodson     Edit/Delete Message   Reply w/Quote
David,

I do not remember the formula nor the derivation but it has to do with the distribution of the relative range where w = R/sigma prime for different sample sizes. I do have a reference for you, but it is probably going to be hard to find. I found it in Acheson Duncan's book "Quality Control and Industrial Statistics". The paper is "The Probability Integral of the Range in Samples of N Observations from a Normal Population". It was published in Biometrika, Vol. XXXII (1941-42) pp 301 - 8. Good luck finding it. Couldn't you just load the table into the spreadsheet and use the Lookup function to find the value?

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