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Stats Question

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  • #47025

    April
    Participant

    Can anyone help me understand how to get the answer for the following question?
    Given the data below and the following requirements: Spec target 0.500”. Any rivet must be within + .004”. Assume normal distribution. What percentage of rivets is outside lower specification limit?
    N       Mean         Median        TrMean      StDev         SE Mean
    100    0.50011     0.50023      0.50013     0.00508      0.00051
     

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    #156186

    veronabill
    Member

    If you use the raw data, the answer can be determined simply enough using minitab, stat/quality tools/capability analysis / normal nad input the appropriate data columns and sd estimate.
     
    I created a random distribution of 100 numbers using the distribution parameters you supply, and the analysis indicates that about 20.6% of your parts are below the lower spec.

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    #156187

    April
    Participant

    Would it be possible to determine without the raw data somehow?  This question was in some training material but the data is not there.
    Thanks!

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    #156188

    Craig
    Participant

    Calculate Z for the lower side (Mean – LSL / stdev)
    Calculate tail area from Z table.
     

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    #156191

    BritW
    Participant

    Z=.809
    Prob=.3153 or 31.53%

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    #156192

    walden
    Participant

    The calculated z-value is -0.809. There would be 18.67% below the LSL.
    z-value = (.496-.50011)/.00508  or -0.809
    Look up -0.809 in the standard normal curve table and you get .1867.

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    #156247

    BritW
    Participant

    The formula for Z for a lower specification is:
    (Mean-LSL)/SD = +.809
    P(d) from the Z table is .8133
     
    Z for the upper side is (USL-Mean)/SD

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