iSixSigma

Calc defects from Sigma and Opportunity values

Six Sigma – iSixSigma Forums Old Forums General Calc defects from Sigma and Opportunity values

Viewing 15 posts - 1 through 15 (of 15 total)
  • Author
    Posts
  • #40497

    Bob Ptacek
    Participant

    Is there a method to calculate the defects when one has only the Sigma Value and the Opportinities. I know I can back into the defects knowing opportunities and the DPMO results, but can’t seem to locate how to do it with sigma. Would appreciate and be thankful for any help or guidance.

    0
    #125843

    Mr IAM
    Participant

    You can look up the sigma value in a Z-table, found in any stats book.  This will give you the proportion defective.  You may need to adjust for shift, as a regular Z-table will show 4.5ppm @ 4.5 sigma.

    0
    #125844

    Mr IAM
    Participant

    Correction… 3.4ppm @ 4.5 sigma (Z-value).  Typing too fast….
     
     

    0
    #125845

    Bob Ptacek
    Participant

    I’m trying to do this in Excel so that I can enter any given Sigma value with the known Opportunities to calculate the defects that madeup the sigma.

    0
    #125859

    “Ken”
    Participant

    Hey Bob,
    If I understand you correctly you have the Sigma value, and the number of opportunities as the inputs–and, you would like to get to an estimate of perhaps average defect level or possibly yield as the output.  Hopefully I got your question right… 
    I believe MrIAM got you moving in the right direction.  But, there is a small adjustment to realize in these estimate of expected defect level.  First, let’s start from the beginning with an example.  Suppose you have a process with a Sigma Quality Level of 3.0, and it has say 10 process steps–where we will establish each process step as an opportunity.  In a Normal z-table for the z-value of 3.0 you receive a probability of 0.0013.  Now we know the accepted defect rate for an SQL of 3.0 is about 67,000 dpmo.  So, we need to make an adjustment. 
    First, given an SQL of 3.0 subtract 1.5 from this value, as suggested by MrIAM.  Next, go to the z-table for z=1.5 to obtain a probability of 0.0668 or 0.0668 defects per opportunity.  Next, your process has 10 opportunities–one for each process step.  Given 0.0668 defects per opportunity * 10 opportunities provides 0.668 defects per unit on average.  Finally, you can estimate the average process throughput yield by:

    Ytp(avg) = exp(-DPUavg)
    for our example, we would calculate:

    Ytp(avg) = exp(-0.668) = 0.513 or 51.3%
    Another way to do this is to recognize that that you have 0.0668 defects per opportunity, or:

    Ytpo(avg) = exp(-0.0668) = 0.935 or 93.5%
    The Rolled Throughput Yield across 10 process steps with each step providing a normalized yield of 93.5% is:

    Yrt = Ytpo*exp(# opportunities) = 0.935*exp(10)       = 0.513 or 51.3%
    Average defect rate = 1 – Yrt = (1 – 0.513)*100                                  = 48.7%
    Just a minor point.  All of these estimates rely heavily on a Normal approximation to the Poisson distribution.  There is a lot riding on the distributional requirements for these estimates.  You usually require fairly large sample sizes to achieve any reasonable confidence in these estimates.  The upshot is–use these estimates as rough approximations, and not firm knowns.  Doing so will place you on much better ground when the actual process numbers don’t match the estimates. 
    Hope this helps.
    Ken

    0
    #125884

    Bob Ptacek
    Participant

    Ken, 
    thank you so very much for the great detailed explanation. As you and Mr IAM suggested, the z-table look up is the starting point and that has been my obstacle. I know if I could get the probability, I will be able to back into the defect. It’s the z-table look up that had me stymied. Without it, I had hoped there was a formula. Is there such an animal as an electronic version of a z-table?
    Again, thank you so much for your explanation, it helped.
    Bob
     
     

    0
    #125887

    Mr IAM
    Participant

    I believe you can use the NormInv formula in excel.  I have not used it in quite some time but I’m sure this is a way to go from Z to % in excel and I think NormInv is it.  Check it out…..

    0
    #125888

    “Ken”
    Participant

    Bob,
    Glad to help.  I believe that I have an Excel conversion table that goes one better.  It lists the associated DPMOs per each Sigma Quality Level to the nearest tenth of an SQL.  I will try to find it on my PC, and if you’re interested in it please provide an email address for me to send it to.
    Cheers,
    Ken

    0
    #125889

    Bob Ptacek
    Participant

    Thank you for that suggestion. Since Excel’s NORMSINV is used to calculate the Sigma from defects and opportunities, I had hoped that the NORMINV might be able to the backward trip. But I tried some examples and just never could make it happen. Maybe I was interpreting the values to use incorrectly. I’ll go back and give that another shot.
     Thank you for your help
    Bob

    0
    #125890

    Mr IAM
    Participant

    Sorry, it’s NORMSDIST that you want :-)

    0
    #125891

    Bob Ptacek
    Participant

    Ken,
    that would be absolutly fantastic.If you find it you can send it to either of these addresses.
    [email protected]  or [email protected]
    Thanks again,
    Bob

    0
    #125892

    Bob Ptacek
    Participant

    Had not tried that one. I’ll check it out.  Between you and Ken, I am confident that I will be able to do what I want..
    Thank you so much for your help.
    Bob

    0
    #125895

    Mr IAM
    Participant

    NORMSDIST works.
    I entered 0, (zero) and then did the Normsdist excel function and got .5, as the result.  So, that makes sense.  A Z-value of Zero = .5 or 50%, half of the distribution.  That is what your trying to do I believe.

    0
    #125925

    Bob Ptacek
    Participant

    Had not tried that one. I’ll check it out.  Between you and Ken, I am confident that I will be able to do what I want..
    Thank you so much for your help.
    Bob

    0
    #126490

    Anton Javier
    Participant

    Bob, I will share my sigma calculator with you.  Please send your email at [email protected]
    This calculator should fix your problem.
     
    Anton Javier
     
     

    0
Viewing 15 posts - 1 through 15 (of 15 total)

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