6-Sigma Binomial Validation

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    I am a relative newbie to 6-sigma, but I have a pretty strong engineering statistics background.  I am having an issue with the following situation:
    I have been asked to statistically validate the claim that a new system can produce the 6 sigma standard of 3.4 dpm.  The test variable is a discrete binomial with objects either passing or failing and no measurable variable such as weights or volumes etc.  The testing process is also very manual, meaning that there is no way I can set up some sort of automatic data collection system to capture vasts amount of data.  As such, I was hoping someone could help me figure out a way to use a sample size small enough for a single person to gather manually to be able to say that the system can reach the required dpm level with a somewhat decent level of confidence.  I am really hoping that there is something I am missing and that the answer isn’t “take a million samples”.  Thanks in advance for your help everyone!



    Hi Gary,
    Do a search on something called sequential analysis.  Also referred to as Wald’s sequential probability ratio test (SPRT).  You may even see it in some of your engineering statistics texts. 



    Gary, I don’t think you can get what you want, because if you have a binomial process at 3.4dpm, you will never see a defect if you are manually checking them.  Your best solution is to put some effort into changing it to a variable measure.  What are you measuring specifically?  There is usually a way to change a measurement from descrete to continuous – even if it is just for process estimation. 
    If you are measuring presence/absense, then poka-yoke it to prove you can make zero defects.
    What are you trying to measure?


    John H.

    Hello Gary
    Both Sigmordial and Jim gave you excellent advice with regards to the sampling issue. I can add the following as an addendum to their comments:
    At the PPM defect level, the Poisson distribution would be more appropriate. Although Wald’s SPRT is highly efficient with regards to sampling savings, in the situation you described it would not be economical with regards to inspection. Example if you performed a Poisson SPRT test with the selected acceptance PPM defect level of Pa=3.4, rejection level of Pr=6.8, Type I alpha and Type II beta errors of .05 , the first two levels of the Sequential Sampling Table would appear as follows:
    Sample Size        Accept        Reject
     1 million                 0               10       
      2 million                5               15   
    Additionally, the Average Sample Number ASN for the example test at the 3.4 PPM level calculates as 2,500,000. If you supply your customers with large volumes of product(millions of units), I could see the possible applications for the SPRT attribute test for PPM field complaints but not for attribute inspection.
    I hope this helps.
    John H.                            

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