Sample Size for Discrete Data – Pass/Fail

Six Sigma – iSixSigma Forums Operations Manufacturing Sample Size for Discrete Data – Pass/Fail

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    I am attempting to calculate the sample size needed for the following process.

    Each machine produces 3.5 units per minute
    There are 33 individual machines
    The outcome of each machine is unique, they are not interconnected or related
    The product output of each of the 33 machines are co-mingled to a common conveyor.

    How large of a sample size do I take from the common belt to have a 95% confidence level that the sample is a fair representation of the population?

    Thank you in advance for any help.

    Mr B


    Norbert Feher


    What do You want to see from these data?

    Do you need some kind of descriptive statistics? Or Would like to know if there is a difference between the machines?

    Would you like to see some kind of trend by shift?

    Or a comparison of the actual process to the specification given by the customer?

    I believe without knowing the answer to the above question it I can not give you an answer.
    Please send me a private mail and I may be able to help You.





    Thank you for the help, unsure of how to do an email yet first time on site.

    No descriptive stats initially, as a first step I am trying to establish a base line for my process in only two categories of Pass or Fail that can be used as feed back to production supervisors.
    In my first attempt I will take a sample of one unit from each machine to compare against the random bulk sample (population) that can be used to validate the sample process.
    The primary goal is to establish a sample rate/size on 33 machines that can be extrapolated to my future machine count of 267.
    Hope this helps

    Thank you again.


    Katie Barry

    @Brad — If you become a registered member of this site, you can become “friends” with other members and send private messages to each other.

    You can also upload files directly to the forum and have the potential for other people to read/respond.



    Would the Fisher Exact Test be recommended for this comparison? I’m working on a problem where I want to compare two groups of pass/fail data and determine if there is a statistical difference in failure rates.


    Robert Butler

    If you are just looking to compare two proportions then, depending on the number of samples, either the Fisher’s Exact Test or the Chi-Square test would be an appropriate choice.

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