Formula for D2 constant
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 This topic has 64 replies, 43 voices, and was last updated 11 years, 11 months ago by SemiMike.

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July 22, 2008 at 9:57 pm #50588
G SnodgrassParticipant@GSnodgrass Include @GSnodgrass in your post and this person will
be notified via email.I need to be able to calculate the D2 constant for any subgroup size, therefore, I want to know the formula that I would use to do so. (I would need a table larger than any that I have found so far)
0July 22, 2008 at 10:21 pm #174049Jeez, can these questions get any easier??? Try this on for size and take it from here:
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.0July 23, 2008 at 6:00 am #174053
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi C SnodgrassI’ve created an Excel spreadsheet that calculates d2 for n=2 to n=100 which I’ll be happy to send you if you post an email address. There was some correspondence on this topic earlier this year.Best WishesBower Chiel
0July 23, 2008 at 7:44 am #174054
Michael MeadParticipant@MichaelMead Include @MichaelMead in your post and this person will
be notified via email.Hello Bower. Thanks I hope this is right. I know I saw this somewhere before but could not find it.
I did a regression and came up with this formula, where x is the sample size: .3x .037x^2 + .0003x^3 – .0000017x^4 + 3.1 log(x)
It is accurate to within .04 for all values of x, and the worst cases are the small sample sizes.
I wish I could find that fornmula again.0July 23, 2008 at 12:57 pm #174073Michael,
This is what I got with an r sq of .999
d2 = – 0.3721 + 0.9419X – 0.09940x**2 + 0.003983x**30July 23, 2008 at 2:07 pm #174076
Michael MeadParticipant@MichaelMead Include @MichaelMead in your post and this person will
be notified via email.Darth, I tried a linear regression, and I had high r^2. But I looked at a scatter plot and saw that is was a log function. I had to play a little with the factors, sort of trade them off to get the answer I had. Take a look at your residuals, you will find taht some of the data points are quite a bit off. Probably the low numbers. A regression has the best fit in the middle of the range.
0July 23, 2008 at 2:33 pm #174080Michael, I used Minitab and fitted a cubic line. Didn’t get as far as a log.
0July 23, 2008 at 4:32 pm #174091When Darth is showing up,Stan disappears
0July 23, 2008 at 5:02 pm #174093Forum: 1
Stanly: 00July 23, 2008 at 6:45 pm #174095
BrandonParticipant@Brandon Include @Brandon in your post and this person will
be notified via email.HB, how do you import a photo?
0July 23, 2008 at 7:13 pm #174097
Heegeebeebee BBParticipant@HeegeebeebeeBB Include @HeegeebeebeeBB in your post and this person will
be notified via email.right click/copy on an html version of the pic as you would find in an image search. Paste in the message field
0July 23, 2008 at 7:57 pm #174098You don’t, they just sneak across the border when the sun goes down.
0July 23, 2008 at 8:27 pm #174102
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi!
While admiring the pragmatic aproaches of Michael Mead and Darth might I suggest getting back to the underlying theory? It was published by the English industrial statistician L H C Tippett in the 1920’s, so on hand when Shewhart was developing the control chart. (So why is it often called Hartley’s constant?)To obtain d2 for sample size n you have to integrate the function: 1(1F(x))^n[F(x)]^nfrom minus infinity to plus infinity. F(x) is the distribution function of the standard normal. There is no analytical answer so you have to resort to numerical integration. I’ve created an Excel spreadsheet to do the calculations. It is certainly accurate up to n = 100 and hopefully beyond. Anyone wishing a copy please post an email address or send me an email at [email protected] WishesBower Chiel0July 24, 2008 at 1:27 am #174114
Michael MeadParticipant@MichaelMead Include @MichaelMead in your post and this person will
be notified via email.Thanks Bower,
I just couldn’t find the formula anywhere. Where would we be without guys like Tippett and Duncan–not the most recognized names, but certainly pillars of today’s quality control.0August 2, 2008 at 8:33 pm #174506Could you please forward?
Kind Regards,
Shannon Mc0August 3, 2008 at 2:48 am #174513Not a problem, my pleasure. I have sent it to the address provided so please be on the lookout for it. You won’t be disappointed.
0August 12, 2008 at 5:30 pm #174796Darth,Could you please send me your spreadsheet of d2 values. I have some charts that have large sample sizes and cannot find the d2 values for the calculations….Thanks [email protected]
0August 12, 2008 at 9:45 pm #174816Shaun, my spreadsheet is for illustrative purposes and does not have the ability for handling large samples. Another poster indicated he had one for large samples. Possibly he will read this and respond to you.
0September 14, 2008 at 3:21 am #175743Darth, I am also interested in the work you’ve done computing d2 values. Could you also please send me your spreadsheet of d2 values. ….Thanks rmorenomicropac.com
0October 14, 2008 at 10:43 am #176705Can anyone provide an Excel Shhet with D2 valuse in for subgroups of n=2 TO n=100
0December 4, 2008 at 2:13 am #178302hi G!!
Did you get any valuable information or spreadsheet regarding the d2 value that you can share with me because I have the same dilema?
my email is [email protected]
thanks in advance
jrod
0December 4, 2008 at 10:02 am #178305
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi LeeIf you post an email address I’ll send you a copy of my spreadsheet.Best WishesBower Chiel
0December 4, 2008 at 11:03 am #178311I would be interested in that spreadsheet also.
0December 7, 2008 at 7:01 pm #178427
InvestorParticipant@Investor Include @Investor in your post and this person will
be notified via email.Can I also get the spreadsheet? I am desperately looking for formula for d2 as I need to find the relation between Cpk and Ppk (or/and Cp vs. Pp). As the difference is only standard deviation I assume that d2 factor was calculated based on zshift assumption of 1.5 – do I get it right?
Thanks,0December 7, 2008 at 10:12 pm #178430
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi InvestorPost an email address and I’ll happily send you, or anyone else who is interested, a copy of my Excel spreadsheet that calculates the value of d2 for any sample size you enter.For random samples of size n from a normal distribution the mean sample range equals the appropriate d2 times the standard deviation, sigma. You therefore get an estimate of standard deviation from a series of sample of size n by dividing the mean range Rbar by d2. It has absolutely nothing whatsoever to do with a 1.5 sigma shift.Best WishesBower Chiel
0December 7, 2008 at 11:05 pm #178431
InvestorParticipant@Investor Include @Investor in your post and this person will
be notified via email.Please send d2 formula to my email address:
[email protected]!0December 7, 2008 at 11:13 pm #178432
InvestorParticipant@Investor Include @Investor in your post and this person will
be notified via email.Is there any way then to find relation between Cpk and Ppk? I will apparently be able to answer the question as soon as I getthe spreadsheet from you but maybe you Bower Chiel or anybody else can also help me with this by a quick answer?
0December 8, 2008 at 8:41 pm #178465
PRPatelParticipant@PRPatel Include @PRPatel in your post and this person will
be notified via email.Cp and Pp (or Cpk and Ppk) are relates by formula only.
Recall that Cp = (USLLSL)/(6*std. dev) and Ppk is given by min(((xLSL)/(3*Std. dev)), (ULSx)/(3*Std. Dev)).
For the Cp and Cpk, the value for Std. Dev is given by MR/d2 This is getting an estimation of the Std. dev using the part to part range.
The Pp and Ppk uses the overall standard deviation (from excel, this would be like using the =STDEV( ) formula) to estimate the long term standard deviation.
From my learnings, there is no other relationship, maybe someone else can shine a brighter light on this…?0December 8, 2008 at 8:44 pm #178466
PRPatelParticipant@PRPatel Include @PRPatel in your post and this person will
be notified via email.This is a message to all the people posting on this message. If you’re doing Cp / Cpk analysis to support product launch, product optimization, etc…why would you not go to a statistical package like Minitab or JMP or alike.
Their formulas / macros to clculate these statistcs have been verifed, and in some cases even validated for accuracy.
Just a thought…?0December 8, 2008 at 9:26 pm #178468
Praveen GParticipant@PraveenG Include @PraveenG in your post and this person will
be notified via email.It very simple. Use six sigma table to calcluate sigma and this make it easy to draw control chart.
0December 12, 2008 at 6:29 pm #178679Would like to get a copy of your d2 spreadsheet.thanks in advance for the help.
0December 14, 2008 at 9:40 pm #178710
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi GordonPost an email address and I’ll happily send you, or anyone else who is interested, a copy of my Excel spreadsheet that calculates the value of d2 for any sample size you enter.Best WishesBower Chiel
0December 15, 2008 at 5:45 pm #178733Thanks in advance for the spreadsheet. Email is [email protected]
0January 12, 2009 at 9:46 pm #179639could you send me a copy of that D2 spreadsheet too? appraciate it!
0January 12, 2009 at 10:20 pm #179645
TaylorParticipant@ChadVader Include @ChadVader in your post and this person will
be notified via email.Its on the way
0January 14, 2009 at 10:06 am #179713
Boer ChielParticipant@BoerChiel Include @BoerChiel in your post and this person will
be notified via email.Hi Need
Post an email address and I’ll send you the spreadsheet.
Bower Chiel0March 10, 2009 at 8:59 am #182198
Denis CailléParticipant@DenisCaillé Include @DenisCaillé in your post and this person will
be notified via email.Hi Bower,
Can you send me your speadsheet for calculation of d ?
adress : [email protected]
Best regards
Denis
0March 10, 2009 at 12:59 pm #182203
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi DenisI’ve sent the spreadsheet that computes d2. I’ve also sent a table of values of both d2 and d3 for n =2 up to n = 100 that I’ve created with the help of a mathematician at Edinburgh Napier University. This table also includes corresponding values of d2* for 1 to 20 subgroups. I’ll happily send both to anyone posting an email address.Best WishesBower Chiel
0March 10, 2009 at 2:27 pm #182205Hi Bower Chiel,
Please snd me a copy of the Excel SS.
[email protected]
Thanks0March 31, 2009 at 8:47 pm #183023
Oscar HerreraParticipant@OscarHerrera Include @OscarHerrera in your post and this person will
be notified via email.Dear Bower Chiel
I have great interest to know your an Excel spreadsheet that calculates d2 for n=2 to n=100. If you think it is possible to send me a copy I’ll apreciate for sure.
Bes Regards,0March 31, 2009 at 9:31 pm #183025
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi OscarPost an email address and I’ll send it.Best WishesBower Chiel
0March 31, 2009 at 10:48 pm #183027
Oscar HerreraParticipant@OscarHerrera Include @OscarHerrera in your post and this person will
be notified via email.Thank You Bower for your promptly response. This is my eaddress:
[email protected]0April 12, 2009 at 9:24 pm #183324
Mario RioParticipant@MarioRio Include @MarioRio in your post and this person will
be notified via email.Please I should like not only to know about the tables on “constants for control charts.
Dr. Wheeler and Dr. Chamber book, probably brings something about this question.
But by books on the matter, most of them, refer to Standards like: ASTM, Mil, ISO. But which of these explain well the nature and how to get the constants. But not only on constants, but also on the matter: “Sampling acceptance on quality control”.
My best regards,
Mario Rio0April 14, 2009 at 11:54 am #183389dear Bowel Chiel,
Please send me the table also. My email address is [email protected]
Thanks and best regards,
Nuke0April 16, 2009 at 3:34 pm #183488BC:I have done the Monte Carlo calculations for n=115 and and my results agree with the ASTM guidelines. Your spreadsheet for N=2 to N=100 AND 120 subgroups must be huge.This hobby project has turned out to be quite big, but has really grabbed my attention. I should be done by mid next week.Cheers, Alastair
0April 22, 2009 at 5:11 pm #183608BC:I have calculated the table values for normal and nonnormal distributions for n=250. Could you send your spreadsheet so I could compare the results?6sigmaguru(at)gmail(dot)comCheers, Alastair
0April 22, 2009 at 5:48 pm #183609Bower Chiel,
I’d love to take a look.
heebeegeebeebb (at) gmail (dot) com0May 27, 2009 at 2:30 pm #184410Hi Bower,I am very interested to know how d2 is calculated for n=2 to n=100.
I would highly appreciate if you could email me a copy of the Excel file you have.
My email is ab.ssbb at gmail.comThanks0September 11, 2009 at 1:46 am #185360Hi Bower,
Can you send me your speadsheet for calculation of d ?
Contact :yellowinskiyahoo.com
Best regards
Adamu0September 22, 2009 at 2:39 am #185582Hello Bower Chiel: I would appreciate a copy of the spreadsheet that computes d2. [email protected]
0September 22, 2009 at 7:11 pm #185601Hi Bower,
I’d love to see that spreadsheet for d2 calculations too. Thanks.
[email protected]0September 22, 2009 at 8:51 pm #185602I’d like a copy of the spreadsheet too. ealanni(at)windstream(dot)net.
Now a question: To keep life simple on the production floor, I almost always (40 or 50 instances) have a sample size of 5. In one or two instances a sample size of 10. Because of the desire to keep the sample size small enough to keep things simple I do not need D2 values beyond what any readily availble source provides. So, my question is this: What causes the need for the sample sizes of >100 and abandoning simplicity/speed of analysis on the plant floor?
0September 23, 2009 at 5:28 am #185605
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi Eugenie
I’ve emailed you a copy of the spreadsheet as requested.
With automatic data capture in some industries it is easy to monitor processes with sample size in excess of 25, the maximum value for which d2 is usually give in text books. I wrote the spreadsheet in response to a query a while back and not because I had a need for d2 values for sample size in excess of 25. Hopefully others will be able to add further comments.
Best Wishes
Bower Chiel0October 21, 2009 at 2:20 am #186266
KarishmaParticipant@Karishma Include @Karishma in your post and this person will
be notified via email.Hi Bower,
Could you please send me copy of the d2 spreadsheet?
Thank you in advance.
Email: [email protected]
Kind Regards,
karishma0October 27, 2009 at 9:44 am #186401
Atul AggarwalParticipant@AtulAggarwal Include @AtulAggarwal in your post and this person will
be notified via email.I want to know about hartley’s constant
0November 12, 2009 at 8:28 am #186767Hallo Bower Chiel,
Thanks please send me the excell sheet for D2. I will also like to know How this Emperical relation deviced for Rbar / d2 = std deviation.
My email Adress is [email protected]
Regards
Pradeep
0November 12, 2009 at 9:32 am #186769
Mamta SharmaParticipant@MamtaSharma Include @MamtaSharma in your post and this person will
be notified via email.Hi Bower,
Pls send me the excel sheet. My email id is [email protected]
Thanks a lot,
Mamta Sharma
0November 12, 2009 at 3:13 pm #186777Hi Dear Bower Chiel,
I am interested in D2 values for N2….N100
My email address is [email protected] or [email protected]
Please mail.
Regards
Pradeep0November 18, 2009 at 7:27 am #186892
Formula for D2 ConstantParticipant@FormulaforD2Constant Include @FormulaforD2Constant in your post and this person will
be notified via email.Hi Bower Chiel,
I am also interested in d2 values for n=2 to 100. Please send me the excel sheet.
My email address is sakaguchiimes.co.jp
Regards
Keiki0December 16, 2009 at 11:51 am #187567
Dave SkalaParticipant@DaveSkala Include @DaveSkala in your post and this person will
be notified via email.Hi Bower,
could you send your D2 spreadheet on email [email protected]
Thank you in advance
Best David0January 7, 2010 at 3:03 pm #188077Bower,
could you send your D2 spreadheet on email [email protected] Thank you in advance
Best JP0January 7, 2010 at 3:49 pm #188082
MBBinWIParticipant@MBBinWI Include @MBBinWI in your post and this person will
be notified via email.Let’s see, if I want to get a message to Bower I’m going to post a reply to a posting by… Skala, yea, that’ll do it.
I heard that they can’t send this via email. Please tie a red bandana around your mailbox and they’ll print out a copy and drop it off.0February 1, 2010 at 1:58 am #188895Hi Bower,I am interested also with a copy of your excel spreadsheet that calculates the value of d2..My email address: [email protected]
0February 12, 2010 at 1:09 pm #189338I would be grateful if somebody could send me an excel copy of the d2 constants. [email protected] Many thanks
0February 12, 2010 at 1:32 pm #189339Amazing interest in this subject. Hope every knows that MUCH of the time, subgroups in modern industry do NOT follow Shewhart’s assumptions of IID, naming INDEPENDENT data. MUCH of the time in MANY industries, the values in the subgroup are CORRELATED and if sample size is 10 or 100, the real EFFECTIVE sample size is usually 1 or 2 or slightly higher if studied carefully over 20 or so batches. I have personally NEVER seen large subgroup sample sizes showing effective sample size even NEAR those numbers.
rbar/D2 is dangerous much of the time.0 
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