
This thread is carried over and continued in the Current Elsmar Cove Forums 
The New Elsmar Cove Forums 
The New Elsmar Cove ForumsThe Elsmar Cove Forums
Statistical Techniques and 6 Sigma Control limit

UBBFriend: Email This Page to Someone!  next newest topic  next oldest topic 
Author  Topic: Control limit 
Kleeve unregistered 
posted 27 June 2001 11:51 AM
Does anyone know how is table for xbar & R ctrl chart derived? Well the problem is, i try to calculate the ctrl limit:UCL and LCL. Thru' understanding the limit are +/3sigma thus i obtain the sigma value,then applied x_bar+/3sigma to cal the ctrl limit. But had no idea why the result varies from using the formula (x_bar+/A2R_bar)? Very much greater... ... IP: Logged 
Rick Goodson Forum Wizard Posts: 135 
posted 27 June 2001 01:17 PM
Kleeve, It is not easy to express formula in the forums but I will give it a try. If it is difficult to follow post your email address and I will send you the derivation in a Word document. The control limits are equal to Xbar plus and minus 3 sigma sub xbar. Hope this helps. Rick IP: Logged 
Al Dyer Forum Wizard Posts: 814 
posted 27 June 2001 06:18 PM
Right on Rick, formulas are tough! Just a shot in the dark, But could the difference be that A2 is a constant based on the groups sample size, but sigma in not based on sample size? I think the only deviation (no pun intended) in sigma is that for Cpk values we use the sigma of the samples (however many), and for Ppk values we use the sigma based on the entire population. Am I getting close? ASD... [This message has been edited by Al Dyer (edited 27 June 2001).] IP: Logged 
Rick Goodson Forum Wizard Posts: 135 
posted 28 June 2001 09:53 AM
Al, You are absolutely right. The standard deviation of the universe and the standard deviation of the samples drawn from the universe are related but obviously different. Sigma of the Xbar's (standard deviation of the samples) is equal to sigma prime (standard deviation of the universe) divided by the square root of the sample size. At a sample size of 5 the standard deviation of the samples is equal to 0.45 sigma of the universe. At a sample size of 4 it is 0.50 sigma of the universe. Of course the standard deviation of the universe is an estimate based on the average range divided by the d2 factor which further confuses the issue. Rick IP: Logged 
Graeme Forum Contributor Posts: 58 
posted 29 June 2001 09:38 AM
quote: The basic mathematics for the control charts was developed in the 1920's and 1930's ... most people now simply refer to either ASTM Manual 7 "Manual on Presentation of Data and Control Chart Analysis" or ANSI/ASQC B11996 through B31996 "Quality Control chart Methodologies". Some key points are:
ASQ  http://www.asq.org  IP: Logged 
Ken K. unregistered 
posted 29 June 2001 10:22 AM
From Montgomery's "Introduction to Statistical Quality Control" (great book), pages 183 & 184: sigmahat = Rbar / d2 A2 = 3 / [d2 * SQRT(n)] Remember that we're talking about the 3 sigma limits on the distribution of Xbar, not just X, and that the standard deviation of Xbar is simga/SQRT(n. So . . . Xbar +/ 3*sigma_of_Xbar which equals: Xbar +/ 3*[sigma/SQRT(n)] which using sigmahat = Rbar / d2 equals: Xbar +/ 3*[Rbar / d2)/SQRT(n)] which equals: Xbar +/ Rbar*[3 / (d2 * SQRT(n)] which equals: Xbar +/ Rbar*A2 IP: Logged 
student without holiday unregistered 
posted 24 July 2001 08:28 AM
Simple and short question: what is the formula behind d2 (or dn, hartley's conversion constant) and is this constant limited to a sample size of 12 ? greetings IP: Logged 
Rick Goodson Forum Wizard Posts: 135 
posted 24 July 2001 01:14 PM
student without holiday Short, yes. Simple, no. The d2 factor is not limited to a sample of 12. Tables for d2 factors run from samples of 2 to over 100 (reference Statistical Quality Control, seventh edition, Grant and Leavenworth, ISBN 0070241627, Table C, page 717). I do not know the derivation of the d2 factor however it is the expected value of R bar divided by sigma of the universe at different sample sizes. For a discussion of the d2 factor see the text mentioned above or Quality Control and Industrial Statistics By Acheson J. Duncan. My edition is pretty old but I am sure it is discussed in newer revisions of the text. Regards, Rick IP: Logged 
All times are Eastern Standard Time (USA)  next newest topic  next oldest topic 
Please Visit the new Elsmar Cove Forums! All these threads are there and much more!