Discrete data

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    I am currently studing to be a six sigma green belt. I am in the measure phase of my project. The output variable that I am measuring is discrete data that can only be assigned  a 1,2,3,4 with a 4 being a defect. This is a visual check performed by the operators. I was wondering how do I handle this data when performing a capabilty analysis due to the fact that this data is not normal.



    There are generally two ways to compute the process sigma. The first is to use upper and lower spec limits and as you know, requires the data to be normal. The other way is to determine the number of defects per million opportunities and use that to convert to a sigma level.


    vidyut bapat

    I understand you are measuring attribute data with 4 level classification –  1 being best and 4 being worst- being rtejected.
    Thus aim of your improvement project would be to get products with all 1 s.
    If you are taking samples of say 5 – all should be 1.
    Consider this parameter as lower the better type – does not matter if it has only discrete values.



    I suggest you to break the visual critiria as more grades, 4 levels seem less and 7 levels is basic requirement, try to do so, perhaps, the distribution have a change.
    In addition, Abnormal data also can be used to calculate process capability, it is need get the values of X0.00135 and X0.99865, you can use the software of SPC1to directly gain abnormal CPK.


    john beaudoin

    You are doing fine with your current measurement analysis.  The tool you need to use is a binomial distribution.  This is a specific tool for discrete data.  It looks at the probability that you will have a defect, which is soley based on how many runs and how many defects did you have.  If you have 32 runs and 2 defects, the probability of a defect is 6.25%.    You may also want to look at a Poisson distribution.  Since you are studying to be a greenbelt, hopefully you have a good statistics book and some software that can help you in this area.  Most people are using Minitab to help, but I am using SPC-XL an DOE-XL from the Air Acadamy (A 6-Sigma consulting group).  SPC-XL is very economical and works with Microsoft XL software.  The real advantage of using continuous data over discrete data is that your sample sizes have to be many times larger with discrete data to get the same confidence intervals.  You may consider this for future measurement systems.

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