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Impact of removal of tails on Cpk

Discussion in 'SPC - Statistical Process Control' started by Irfan.abdul, Jul 21, 2021.

  1. Irfan.abdul

    Irfan.abdul New Member

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    Hi:
    I want to assess the impact of removal of a certain percentile tail from the current distribution on the Cp and Cpk values. Say I have distribution of given sigma and mean. Now if I remove values below 5th and above 95 percentile from this distribution, is there a formulation that gives the impact of this on the new Cp and Cpk keeping same values for upper and lower specs.
     
  2. Miner

    Miner Moderator Staff Member

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    You can no longer use Cp/Cpk because you would no longer have a Normal distribution. Cp/Cpk assume a Normal distribution. You would have to use a nonparametric capability index such as Cnp/Cnpk that does not assume normality.
     
  3. Irfan.abdul

    Irfan.abdul New Member

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    Thanks..
    However, I am looking at hypothetical scenario where if I remove the outliers, ie tighten the normal distribution (ie reduce sigma), what is the impact on Cpk. Ie provide motivation to get rid of outliers and the associated improvement expected.
     
  4. Miner

    Miner Moderator Staff Member

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    The answer is Yes. It will reduce the variation. I ran a Monte Carlo simulation generating 100 random, Normal data points. I copied that data then deleted the points outside the 5th and 95th percentiles. The results are attached.


    upload_2021-7-21_16-4-43.png
     
  5. Irfan.abdul

    Irfan.abdul New Member

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    Thanks a lot..this is what I expected and I did the theoretical modeling, where I assumed the 5th and 95th percentile becomes the new 1st and 99th and then compute the Cp..