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Sigma level of a process

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  • #28503

    Ovidiu Contras
    Participant

    Looking at the Minitab output for Capability Analysis , we have Cpk and PPM “Overall” as direct Sigma level indicators .
    My question is : If the data is normal and if the Sigma level given by Cpk*3 is different from the one resulted from the PPM , is this an issue? Which ( Cpk or PPM ) is the one that should be taken into account in this situation ?

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    #71158

    Erik L
    Participant

    Ovidiu,
    I hate to use this reply, but it depends. What are you looking to do with the data? If you’re looking at developing a short-term perspective of the process then you would use the Cpk calculation (and the associated PPM for ‘within’). Look at what Minitab give you for hints. Cpk statistics are created based on ‘within’ which should trigger a short-term estimate of the variability of the process. Remember from control charting, the basic questions revolved around what factors and noise are captured within and between subgroups and these were used to diagnose where the greatest source of variation lay in the process. The PPM statistics for ‘within’ will give you the short-term estimate of the process. The ‘overall’ calculations for PPM are looking at the long-term picture of the process. The variability calculated for this process will not only factor the ‘within’ component, but also the ‘between’ component. Traditional interpretation of Cpk, or the ensuing Z score obtained, is the short-term since standard deviation will be estimated by Rbar/d2.  Assumptions typically include a state of control for confidence in this estimate.  Bottom line, you’re looking at different ways of calculating variability (short-term vs. long-term) when you look at the statistics that you’ve mentioned.
    Regards,
    Erik

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    #71159

    Ovidiu Contras
    Participant

    Thanks for the reply Eric ,
    now let’s look at the actual output : PPM total for “within” is 294,000 which gives a sigma level of about 2 ; Cpk is 0.2 , which gives another sigma level  of 0.6 …..should I use Cpk ?

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    #71161

    Erik L
    Participant

    Which parameter are you looking at?  The ‘oberved’ or the ‘expected’?  If you take the PPM from the ‘expected’ this should sync up with 3*Cpk.
     
    Regards,
    Erik

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    #71187

    TCJ
    Member

    I think that your data is not syncing because you did not factor in the 1.5 sigma shift.  If you are using PPM and the standard normal tables to obtain your Process Sigma (Z), they do not correspond directly to Z (Cpk *3) from a normal PDF.  Add 1.5 to your calculated Z then see if the PPM defectives match.

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    #71191

    Keshri
    Participant

    Q – If the data is normal and if the Sigma level given by Cpk*3 is different from the one resulted from the PPM
    If  Cpk1 = (USL – Mean)/ sigma  and Cpk2 = (Mean -LSL)/ sigma
    Cpk is the lower value of Cpk1 and Cpk2
    PPM is calculated adding the two  DPMO calculated as indicated by Cpk1 and Cpk2
    So the Sigma level calculated on the basis of PPM and Cpk*3 will be diffrent. and Cpk*3 will be higher than the sigma value calculated on the basis of PPM.
     
     
     
     

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