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Sample Size? Please Help!

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  • #47913

    Bryce
    Participant

    Ok~ I just received this question from one of my co-worker.
    One of our clients, a high speed semiconductor manufacturer has a current defect rate of 1,600 / 1,000,000.
    They came up some improvement methods which they think might help to reduce their defect rate.
     
    However, the question they’re asking is:”How big a sample size do they need to show a statistic difference?”
    They can’t provide Std. Dev.
    Plz help (they want the answer tonight!)
     

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    #160300

    Robert Butler
    Participant

       It depends on what they mean by a statistical difference.  Usually, circumstances of this type will not just want to see some difference that is statistically significant (the alpha) they will also want to know the significance level associated with the significant difference (the power).
      The current defect rate is .0016.  If reductions by 10%, 20%, etc. are going to be considered significant then total sample size needed to claim these percentage reductions from a defect rate of .0016 with a power of 80% would be as follows:
            Reduction    Actual                 By       Power       N Total
                    10%       0.8         1861270                20%       0.8           440862                30%       0.8           185066                40%       0.8             97984                50%       0.8             58794
       Where N total is the total number of samples from the old process and the new process.  So, for 80% power for a 10% reduction you would need 930,635 samples from the old method and 930,635 from the new method. 

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    #160720

    Acedown
    Participant

    Robert,
    Very interesting post.  I’m a rookie here so I’ll need some clarification on your stated numbers.  Do they apply to everything?  For example, for those of us in a non-manufacturing environment, obtaining such high numbers of samples would be unrealistic but yet we want to show both the level and power of the proposed intervention/solution.  How would we decide on the appropriate sample size?

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    #160723

    Anton Javier
    Participant

    Hi Bryce, I have 2 sample size calculators which you might wish to use.  It is intuitive and you get results as soon as you input 1 or 2 required data.  
    You might like to send me your email address and I will send you the 2 sample size calculators.  This should do the trick for you.  My email is [email protected]
    Anton Javier                                                                
     
      

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    #160810

    Rick Haynes
    Member

    Others gave you some answers, but I want to talk about the standard deviation question.
    Defective data has a binomial distribution, which has an approximate standard deviation of sqrt((p*q)/n).  This uses the normal approximation of the binomial, which is adequate if n*p and n*q are both greater than 5.  Your data would meet this condition.
    Now if you really mean defect data, where more than one defect can exist per item, then it is a poisson distribution where the standard deviation = the mean of the distribution.
    If you always assume normality, many of the standard tools are not going to work for you.
    Good luck

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    #160811

    Bryce
    Participant

    Thank you all for the support.  It really helped.  But the sample size turn out to be too big.
     
    But thx for all the help

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