Sample size calculation for Binary Data

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    I have a binary data set (pass/fail). My projects target is to improve to a 100% pass rate (I currently collect 1 data point per quarter). How do I calculate (preferabley using Minitab) the sample size required to show statistically significant success? 
    Appreciate your help!



    Euh Max,
    I expect that all your managers will have moved to a new job before you have enough data with only 4 data/year.
    Forget this approach and put all your effort into finding a way to get data more often (and of the contiuous type). The good news is that you have at least 3 months before the next datapoint makes your question a little bit more urgent.
    By the way: you cannot calculate sample size if there is no variation. So you have choose how many zero’s there have to be behind the percentage decimal point.



    I would be looking for a way to get more frequent measurements of performance – is there a reason the data is only available quarterly?
    Sometimes implementing a more effective measurement system is a key deliverable of a Six Sigma project (before you can even improve the process).
    I’d also consider whether 100% quality rate is really necessary.  Accepting absolutely no defects is expensive – and may not necessarily be required – depending on the process. 
    Having said that, here are the sample size calculators I developed and use for these calculations –



    I believe what Max is looking for is, given that data are collected once per quarter, how large should each quarterly sample be?  There is no one right answer, since it depends on how large each production run is, what the cost is of sampling and inspection is, what the cost of a production run failing inspection is, and a host of other factors.  Ball bearings are different than automotive air bags are different than hip prosthetics.
    I would agree that once per quarter is insufficient if the sample is only drawn from a single day’s production during the quarter.
    I disagree with remi that you need continuous data, since the inspection results in only a pass/fail binary (i.e., binomial, not continuous, data) result.

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