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Why Is 6 Sigma Better Than 3 Sigma ?

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  • March 24, 2009 at 7:38 am #52088

    Sigma Novice
    ★ 10 Years ★
    Member

    Why is 6 sigma better than 3 sigma ?
    I understand that 6 sigma is 3.4 DPMO and that 3 sigma is 66,800 DPMO but surely being 6 standard deviations away from the mean (or what the customer wants) is not good. This means that you have a wider range of variation doesn’t it ?
    For example, if a customer has a requirement for a bolt length to be 2cm and the following values (cm) are produced the standard deviation is 1.34 (the mean of the data set being 2.7cm)
    PRODUCTION RUN ‘A’ : 4,1,2,2,1,5,2,3,4,3
    Assume now that the following lengths are produced (only the first length changes, from 4cm to 10cm);
    PRODUCTION RUN ‘B’ : 10,1,2,2,1,5,2,3,4,3
    The standard devaition is now 2.67 (and the mean of the data set is 3.3).
    Now, if we assume that 6 sigma (or 6 standard deviations from the mean) is better than 3 sigma (or 3 standard devaitions from the mean) then are we to assume that Production Run ‘B’ is better than Production Run ‘A’ (2.67 -v- 1.34).
    How can this be? Production Run ‘B’ appears to be further away from the customer requirement of 2cm ?
    Any clarification would be appreciated.

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    March 24, 2009 at 8:55 am #182671

    Natanyahoo
    ★ 10 Years ★
    Participant

    You are completely confused.I suggest that you read the basic before jumping into wrong conclusions!

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    March 24, 2009 at 9:34 am #182674

    Brijesh Agarwal
    ★ 10 Years ★
    Participant

    Dear,
    Your Interpretation is wrong due to:
    1- In case 1 the data are normally distributed, P-value is 0.447 & for 95% confidence Interval for mean you will get 1.7432 cm to 3.6568 cm.
    2- In case 2 the data are not normally distributed, P-value is 0.017 & for 95% confidence interval you will get 1.3909 cm to 5.2091.
    From the above it is very clear that case 1 has less variations than case 2.
    Brijesh

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    March 24, 2009 at 5:05 pm #182689

    BritW
    ★ 10 Years ★
    Participant

    Follow the advice from the other post – read up on six sigma a little more.
    A 6 sigma level, in basic terms, means you can fit 6 standard deviations between a mean and the closest spec limit.  If you can fit 6 SD’s between the mean and spec, then the SD is much smaller than it would be if you could only fit 3 – meaning the process has much less variation at the 6 sigma level.
    You need to understand the difference between sigma level (Z value from the normal distribution) and sigma (the greek symbol for standard deviation).

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    March 24, 2009 at 5:15 pm #182690

    GB
    ★ 10 Years ★
    Participant

    Brit!   Simple, concise, correct…
    Long time, no see -hope you are well.
    Heebee

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    March 24, 2009 at 5:30 pm #182691

    Stevo
    ★ 10 Years ★
    Member

    The advice of the previous gentlemen and lady (HB) is for the most part right.  However, look deep enough and we can prove your theory.
     
    Let’s say you are taking a test that is graded on a curve. If you score a 99.99966% on it, two linebackers and a defensive end will flunk and you end up getting the snot beat out of you.  But if you score 93.30%, everyone passes and you live another day.  Well, then I believe that 3 sigma is better then 6 sigma.
     
    Always here to help,
     
    Stevo
     
    Ps.  Go Gonzaga!
    Pss. Boo North Carolina!

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    March 24, 2009 at 5:52 pm #182692

    Sloan
    ★ 10 Years ★
    Participant

    Sigma Novice,
    Part of your confusion might come from the overly simple example that you gave. You stated that the customer’s specification for bolt length is 2cm. What you actually gave was the customer’s target specification, but you did not give the customer’s upper and lower specification limits. A customer will gernerally have a specified tollerance range around their target spec. For example, your customer may specify a bolt length of 2cm +/- 0.6cm.
    Now the explanation of sigma level becomes much easier to visualize. If you set up your production to target 2cm bolt length and make your production variation so small that you can fit 6 standard deviations (measured from your actual process) between your production sample mean and your customer’s nearest spec limit then your process is performing at a level of “six sigma” or 3.4 defects per million opportunities. So in this example, say your production average is eactly 2.000cm and your standard deviation is 0.1cm (how convenient) you can now fit 6 of your standard deviations between your mean and the nearest spec limit, say the upper spec limit of 2.6cm. That is much better than if your mean was 2.000cm and your standard deviation was 0.2cm in which case you could only fit 3 standard deviations between your mean and the customer’s upper spec limit of 2.6cm.
    Does that make more sense to you?

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    March 24, 2009 at 5:55 pm #182693

    Mikel
    ★ 10 Years ★
    Member

    As always, your logic is impeccable.
    Go Spartans.

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    March 24, 2009 at 5:58 pm #182694

    GB
    ★ 10 Years ★
    Participant

    Stevo, I agree w/ Stan..Right on!
    Go Cats!

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    March 24, 2009 at 5:59 pm #182695

    Sloan
    ★ 10 Years ★
    Participant

    Stevo,
    I like your theory on test grades. I think that must be why North Carolina can’t seem to field a strong football team.
    However, BASKETBALL is a different story!
    Boo Gorganzaga (sorry, I always get them confused with the cheese)
    Yea Tarheels!

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    March 24, 2009 at 7:24 pm #182702

    BritW
    ★ 10 Years ★
    Participant

    Thanks!  Small hiatus.  Hope you and yours are well also.

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    March 24, 2009 at 8:39 pm #182706

    Hal Frezik
    ★ 10 Years ★
    Participant

    Mikel Harry has recently shown that 6 sigma is actually a statistical correction to what should have been 6.2 sigma.  It also changes the metric from 3.4 to 3.43 dpmo.
    Anyone who is serious about quality and accuracy should implement these corrections.

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    March 24, 2009 at 9:00 pm #182707

    Sloan
    ★ 10 Years ★
    Participant

    Oops, Hal, you went the wrong way. 6.2 sigma is only 1.3 DPMO not 3.43. Dr. Mikel would not be pleased. Does this mean that you’re not serious about quality and accuracy?

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    March 24, 2009 at 9:03 pm #182708

    MrMHead
    ★ 10 Years ★
    Participant

    I’ve always stumbled over “3.4 dpmo” – I understand the “spirit” or intent of the mesure, but isn’t “A Defect” a discreet measure?
    I can’t have 3.4 smashed pumpkins in my delivery of 1 million.
    Non-BB/LSSers are probably more familiar with “Five-9’s”  (99.999%) – which is a bastardized way to describe it quickly.

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    March 25, 2009 at 12:19 am #182713

    Sigma Novice
    ★ 10 Years ★
    Member

    If you are confused then think of it this way;
    3 errors per 882,353 occurances !

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