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Formula for D2 constant

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  • #50588

    G Snodgrass
    Participant

    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)

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    #174049

    Darth
    Participant

    Jeez, 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 0-07-024162-7, 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.

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    #174053

    Bower Chiel
    Participant

    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 e-mail address. There was some correspondence on this topic earlier this year.Best WishesBower Chiel

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    #174054

    Michael Mead
    Participant

    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.

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    #174073

    Darth
    Participant

    Michael,
    This is what I got with an r sq of .999
    d2 = – 0.3721 + 0.9419X – 0.09940x**2 + 0.003983x**3

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    #174076

    Michael Mead
    Participant

    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.

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    #174080

    Darth
    Participant

    Michael, I used Minitab and fitted a cubic line. Didn’t get as far as a log.

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    #174091

    Stanly
    Member

    When Darth is showing up,Stan disappears

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    #174093

    GB
    Participant

    Forum: 1
    Stanly: 0

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    #174095

    Brandon
    Participant

    HB, how do you import a photo?

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    #174097

    Heegeebeebee BB
    Participant

    right click/copy on an html version of the pic as you would find in an image search.  Paste in the message field

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    #174098

    Darth
    Participant

    You don’t, they just sneak across the border when the sun goes down.

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    #174102

    Bower Chiel
    Participant

    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-(1-F(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 e-mail address or send me an e-mail at [email protected] WishesBower Chiel

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    #174114

    Michael Mead
    Participant

    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.

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    #174506

    Shannon
    Member

    Could you please forward?
    Kind Regards,
    Shannon Mc

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    #174513

    Darth
    Participant

    Not 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.

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    #174796

    watkins
    Member

    Darth,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]

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    #174816

    Darth
    Participant

    Shaun, 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.

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    #175743

    Moreno Sr.
    Member

    Darth, 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

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    #176705

    Ronald
    Participant

    Can anyone provide an Excel Shhet with D2 valuse in for subgroups of n=2 TO n=100

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    #178302

    jrod
    Participant

    hi 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 e-mail is [email protected] 
    thanks in advance
    jrod
     
     

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    #178305

    Bower Chiel
    Participant

    Hi LeeIf you post an e-mail address I’ll send you a copy of my spreadsheet.Best WishesBower Chiel

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    #178311

    Kev
    Participant

    I would be interested in that spreadsheet also.

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    #178427

    Investor
    Participant

    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 z-shift assumption of 1.5 – do I get it right?
    Thanks,

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    #178430

    Bower Chiel
    Participant

    Hi InvestorPost an e-mail 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

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    #178431

    Investor
    Participant

    Please send d2 formula to my email address:
    [email protected]!

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    #178432

    Investor
    Participant

    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?

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    #178465

    PRPatel
    Participant

    Cp and Pp (or Cpk and Ppk) are relates by formula only.
    Recall that Cp = (USL-LSL)/(6*std. dev) and Ppk is given by min(((x-LSL)/(3*Std. dev)), (ULS-x)/(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…?

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    #178466

    PRPatel
    Participant

    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…?

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    #178468

    Praveen G
    Participant

    It very simple.  Use six sigma table to calcluate sigma and this make it easy to draw control chart.

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    #178679

    Gordon
    Participant

    Would like to get a copy of your d2 spreadsheet.thanks in advance for the help.

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    #178710

    Bower Chiel
    Participant

    Hi GordonPost an e-mail 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

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    #178733

    Gordon
    Participant

    Thanks in advance for the spreadsheet. Email is [email protected]

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    #179639

    need
    Participant

    could you send me a copy of that D2 spreadsheet too?  appraciate it!

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    #179645

    Taylor
    Participant

    Its on the way

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    #179713

    Boer Chiel
    Participant

    Hi Need
    Post an e-mail address and I’ll send you the spreadsheet.
    Bower Chiel

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    #182198

    Denis Caillé
    Participant

    Hi Bower,
     
    Can you send me your speadsheet for calculation of d ?
    adress : [email protected]
    Best regards
    Denis
     
     
     

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    #182203

    Bower Chiel
    Participant

    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 e-mail address.Best WishesBower Chiel

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    #182205

    Deka
    Participant

    Hi Bower Chiel,
    Please snd me a copy of the Excel SS.
    [email protected]
     
    Thanks

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    #183023

    Oscar Herrera
    Participant

    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,

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    #183025

    Bower Chiel
    Participant

    Hi OscarPost an e-mail address and I’ll send it.Best WishesBower Chiel

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    #183027

    Oscar Herrera
    Participant

    Thank You Bower for your promptly response. This is my e-address:
    [email protected] 

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    #183324

    Mario Rio
    Participant

    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 Rio 

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    #183389

    Nuke
    Participant

    dear Bowel Chiel,
    Please send me the table also. My e-mail address is [email protected]
    Thanks and best regards,
    Nuke

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    #183488

    BTDT
    Participant

    BC:I have done the Monte Carlo calculations for n=1-15 and and my results agree with the ASTM guidelines. Your spreadsheet for N=2 to N=100 AND 1-20 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

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    #183608

    BTDT
    Participant

    BC:I have calculated the table values for normal and non-normal distributions for n=2-50. Could you send your spreadsheet so I could compare the results?6sigmaguru(at)gmail(dot)comCheers, Alastair

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    #183609

    GB
    Participant

    Bower Chiel,
    I’d love to take a look.
    heebeegeebeebb (at) gmail (dot) com

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    #184410

    AB
    Participant

    Hi 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.comThanks

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    #185360

    Nuhu
    Participant

    Hi Bower,
    Can you send me your speadsheet for calculation of d ?
    Contact  :yellowinskiyahoo.com
    Best regards
    Adamu

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    #185582

    rsand
    Member

    Hello Bower Chiel:  I would appreciate a copy of the spreadsheet that computes d2.  [email protected]

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    #185601

    Fontanilla
    Participant

    Hi Bower,
    I’d love to see that spreadsheet for d2 calculations too.  Thanks.
    [email protected]

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    #185602

    Lee
    Participant

    I’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?
     

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    #185605

    Bower Chiel
    Participant

    Hi Eugenie
    I’ve e-mailed 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 Chiel

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    #186266

    Karishma
    Participant

    Hi Bower,
    Could you please send me copy of the d2 spreadsheet?
    Thank you in advance.
    Email: [email protected]
    Kind Regards,
    karishma

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    #186401

    Atul Aggarwal
    Participant

    I want to know about hartley’s constant

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    #186767

    S
    Participant

    Hallo 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
     

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    #186769

    Mamta Sharma
    Participant

    Hi Bower,
    Pls send me the excel sheet. My email id is [email protected]
    Thanks a lot,
    Mamta Sharma
     

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    #186777

    S
    Participant

    Hi Dear Bower Chiel,
    I am interested in D2 values for N2….N100
    My email address is [email protected] or [email protected]
    Please mail.
    Regards
    Pradeep

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    #186892

    Formula for D2 Constant
    Participant

    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
    Keiki

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    #187567

    Dave Skala
    Participant

    Hi Bower,
    could you send your D2 spreadheet on email [email protected]
    Thank you in advance
    Best David

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    #188077

    Pilar
    Participant

    Bower,
    could you send your D2 spreadheet on email [email protected] Thank you in advance
    Best JP

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    #188082

    MBBinWI
    Participant

    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 e-mail.  Please tie a red bandana around your mailbox and they’ll print out a copy and drop it off.

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    #188895

    I’Anson
    Participant

    Hi Bower,I am interested also with a copy of your excel spreadsheet that calculates the value of d2..My email address: [email protected]

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    #189338

    Ginga
    Participant

    I would be grateful if somebody could send me an excel copy of the d2 constants. [email protected]  Many thanks

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    #189339

    SemiMike
    Member

    Amazing 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.
    r-bar/D2 is dangerous much of the time.

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