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Calculate Sample Size for Yield Estimate

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  • #54105

    GL
    Participant

    I would like to Compare the Test Yield for a new product version versus the existing product version.
    To do so I need to Determine the Sample Size of units for the new product version that should be run as a verification trial.
    I’ve been looking at “Power and Sample Size for 1 Proportion” in MiniTab but I’m not clear on how to correctly determine the ‘Comparison proportions’, ‘power values’, and ‘Hypothesized proportion’ values that need to be entered.
    Can anyone recommend some examples of determining Sample Size along these lines?
    What I have is lots of historical existing product version data with a Test Yield of 99%.
    And we suspect that the new product version could potential shift the Test Yield down as far as 93%
    Thanks

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    #193698

    Hi GL,
    From what you have said, it seems to me that you need 2-proportions test (existing product’s yield VS new product’s), instead of 1-proportion test (new product’s yield VS an exact target).
    1-Proportion test will consider the variation in one side only (in your case is new product) which is not fit with your situation due to you need to consider variation in both sides (existing & new).

    SK

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    #193701

    MBBinWI
    Participant

    @glewis2012 – if you use the help function in Minitab, you will get information on what each of these variables are, and it will even show you an example of what the variables should look like and how to interpret the output.

    The one thing that you will have to think about is the power value. This is your statistical value on deciding whether the possibility, in this case for evaluating proportions, that the analysis of the data concludes that there isn’t a difference when there really is one. A typical level is 80% (or 0.80), but you must determine what the level of risk is for you that is acceptable.

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    #193706

    Joel Smith
    Participant

    @glewis2012 – As was already stated, it sounds like you have a 2 Proportions test since there is some error in your estimate of current yield. However, if you have some overwhelming amount of existing data that is stable you could probably treat it as constant (perhaps a million or more parts).

    I’ll describe the 1 Porportion for now and that should make the 2 Proportion clear as well. With 1 Proportion, the hypothesized proportion would be your current yield, as that is the value you want to compare your new sample to. Comparison proportions is what proportion you’d like to be able to detect – for example, if your current yield is 0.9 you may be interested in whether you have increased that to 0.92 or more, so you would enter 0.92. You can enter multiple values in this field (0.91 0.92 0.93 for example).

    Power is the probability that, if that difference actually exists, your test will detect it. As MBBinWI said 0.8 is a common value, which would mean that if you entered a comparison value of 0.92 and there really was a new yield of 0.92, you would have an 80% chance of your test giving you a significant p-value.

    The power curve graph that is generated will give you a nice representation of where you get the most “bang for your buck”.

    Good luck!

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    #193714

    GL
    Participant

    @MBBinWI, @joelatminitab , @SK,

    Thanks for the inputs. Very helpful. I ended up using the ‘two proportions’ method and generated a power curve at 85% for multiple ‘comparison proportions p1’ (.98, .97, .95, .93, .91) vs the baseline proportion p2 of .99
    Worked well for visually identifying a practical number of sample to run.

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    #193823

    sriram
    Member

    Sample size determination:
    n = (Z*S)^2 / E^2,
    where Z is the confidence level(90%,95%,99%) values (1.645, 1.96, 2.575)
    and S – Standard deviation,
    E = Estimated Mean – True Mean (Xbar – Mu).
    Hope this clarifies…

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    #193826

    GL
    Participant

    @sriram54321
    In this case described in my original post would E = (Est Yield) – (True Yeild)?

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    #193828

    sriram
    Member

    Here is an example-

    Suppose from the past history it is known that a process yield would be 98% and based on the sample data the estimated yield is 97.25% with a standard deviation of 2%. For a 95% confidence interval, the sample size is determined as follow:

    n = (Z*S)^2/E^2 =(1.96*2)^2/(97.25-98)^2 = 15.3664/0.5625 = 27.318 ~ 27 samples

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    #193834

    Prabhu V
    Participant

    Hi to all!
    During my study on sample sizes, I remember that the term Precision was used on it.
    Like for example for the continuous data sample size calculation, the formula as follows:

    n= (Z*S/Precision)^2

    Is this a new formula?
    Can someone explain?
    Thanks in advance.

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    #193835

    sriram
    Member

    Hi,
    Error = (Estimate – Actual), also called as precision irrespective of data being continuous or discrete. It tells us how far the sample mean is away from true mean in absolute/relative/standard reference.

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    #193836

    Prabhu V
    Participant

    @Sriram – thanks for the information and i believe that the above mentioned formula only applicable for continuous data, where as for discrete data one more parameter called estimate of population proportion to be taken care.

    Like

    n=(Z/Precision)^2*p(1-p)

    p – estimate of population proportion.

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    #193837

    sriram
    Member

    Hi Prabu, thanks for the post. Yeah we can estimate sample size from mean, proportions, from standard deviations, from known and unknown population size (N known/unknown), etc. Likewise, for non-parametric analysis you can also estimate the sample sizes.

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