iSixSigma

3 or 6 StdDev

Six Sigma – iSixSigma Forums Old Forums General 3 or 6 StdDev

Viewing 16 posts - 1 through 16 (of 16 total)
  • Author
    Posts
  • #50825

    Deka
    Participant

    Question: When a company asks you if your process is Six Sigma, do they mean Plus/Minus 3 StdDevs or  Plus/Minus 6 StdDevs

    0
    #175224

    Remi
    Participant

    Deka:
    +/- 6*S within the specs chosen by your customer where S is short term Sigma (=> Cp=2)
    (+/- 3*S covers 99.7% of the data and corresponds with Cp=1)
    +/- 4.5*S if S = long term Sigma (the 1.5 Z-shift is then incorporated => Ppk = 4.5)
     

    0
    #175259

    Ravi Kanth
    Participant

    Hi,
    Put simply, its +/- 3 sigmas(standard deviations) on either side of  the mean value.

    0
    #175266

    Deka
    Participant

    I may be way off base, but I want to challenge that. If Sigma is related to z score and z -score looks at a one sided dist. I beleive you just described a 3 sigma process. I think Six Sigma is +/- 6 Std Dev from the mean, related to a normal dist

    0
    #175269

    NameWithheldForSaftey
    Participant

    I may be wrong but…..
    I think your confusing two things here.
    Standard Deviation tells you how much variation you have in your process where as your sigma score tells you how you perform compared to your customers operating limits.
    So what they’re asking is now many errors do you have in your system? 6 Sigma generaly known as being 3.4 defects for every million opportunities to make a defect.

    0
    #175272

    Bill Fowlkes
    Participant

    Six Sigma really means that a product is produced in a high quality manner such that it’s components have a failure rate of  3.4 defects for every million opportunities to make a defect.
    All the rest, such as +/- 6 stn.dev. depend on the details of the governing distributions and statistical behavior.
    By the way, Ravi is flat out wrong, +/- 3 sigma is not correct.

    0
    #175282

    Jonathon Andell
    Participant

    I agree with your concenr. The “process sigma” is the number of standard deviations between the mean and the NEAREST specification limit.

    0
    #175289

    Deka
    Participant

    I understand the connection between Z score and Sigma Level..but my thick head cant connect the dot to Std Dev and Sigma Level.  Most tables list DPMO, Sigma, and CPK together, but not Std Dev.

    0
    #175291

    Jonathon Andell
    Participant

    For continuous process data the Z score simply counts how many standard deviations fit between the mean and the nearest specification limit. That computation depends on three things: 1) the value of the mean (X-Bar), 2) the gap between mean and specification limit, and 3) the value of the standard deviation (s). No doubt you have seen the equation a zillion times.
    If you improve the process by making “s” smaller, you will be able to fit more standard deviations between the mean and the specification limit. That’s why small s leads to high Z.
    If I failed to answer the same question you are asking, let’s have another go at it…

    0
    #175307

    Remi
    Participant

    hai Deka,
    here is the ‘formula’ between Sigma-lvel (Zlt) and Sigma(lt):
    Zlt = 3* Ppk = Minimum(USL-Mu,Mu-LSL)/Sigma(lt).
    This is the same as what Jonathan said, but in mathematic language.
    – USL and LSL arer the specs the Customer has wished for.- Mu you don’t know but you fill in Xbar- Sigma(lt) you don’t know but you fill in the Sigma that your customer typically will see (all longterm variation included; whatever the causes)
    Remi

    0
    #175316

    Deka
    Participant

    Understood. Now… If the Z Score and associated sigma level are based off of the nearest spec limit and your data is slightly moved to the right (for example). How are all of the defects that are on the left (below the Lower spec limit) accounted for? They cant be ignored?

    0
    #175317

    Remi
    Participant

    Hai Deka,
    they are not accounted for with Cpk, Ppk or Zlt or Zst. They are accounted for by Yield%, Reject% and a SixSigma term called Z-bench.Z-bench is a translation into Six Sigma language (sigma-level) from Yield%; in the same way that Zlt is a translation of Yield%-at-the-worst-spec. What you do is calculate total yield% and transform into Z-value. minitab can do it automatically if you have data (Stat->CAPAN; options: “Z-bench instead of Ppk”). There is also a way to do it if you only know Yield% + Nomality.
    And ofcourse with Z-bench you also have the Z-shift dilemma (compensate with 1.5 or not). Other threads discuss this dilemma in detail.
    In Improvement-projects in general Zlt gives you a good indication of how good your process is: “the other side is better so improve this side first””. If the process is centered Zlt corresponds with half the Reject%.
    Remi

    0
    #175319

    Jonathon Andell
    Participant

    In some instances the tail beyond the nearest spec limit has virtually all of the defects. For instance, suppose the mean happens to lie 2 standard deviations from the upper spec limit, and 4 standard deviations from the lower limit. This means there is about a 2.3% likelihood of a defect beyond the upper limit, but only a 0.003% likelihood of a defect below the lower limit – a factor of 70,000 times as many defects in the upper tail.
    In other instances, both tails might be important. If Z(Upper tail) is 2, and Z(lower tail) is 2.2, then you have to account for both sides of the distribution.
    Most software packages do this by adding both tails’ probabilities together, and computing an “equivalent” Z value that corresponds to that total number of defects.
    I have a simple Excel template that handles this. You enter the process mean and standard deviation, along with one or two specification limits, and it computes the Z value. If you send me your email I will send it along. If the “isixsigma powers that be” want to make it available for all, I will be happy to share.
    Bear in mind: if the data are discrete, or if continuous data are non-normal, this template is the wrong one to use. I also have a template for discrete data.

    0
    #175320

    Deka
    Participant

    Jon,
     
    yes..please..send both to:
    [email protected]
    Great input..thanks

    0
    #175332

    Craig
    Participant

    Your process mean is at least 6 standard deviations from the nearest spec limit. It could be 6 std dev from one spec limit and 100 std dev from the other….depending on the location of the mean, and the magnitude of the std dev.
     
     
     

    0
    #175527

    Mikel
    Member

    Pls send the two Excel charts to me at [email protected].
    Thank you.
    Stan

    0
Viewing 16 posts - 1 through 16 (of 16 total)

The forum ‘General’ is closed to new topics and replies.