# How are the d2 values for subgroup sizes derived?

D

#### David Drue Stauffer

d2 chart value?

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.?

J

#### Jim Biz

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)

L

#### Laura M

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

D

#### David Drue Stauffer

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.

R

#### Rick Goodson

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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