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DOE and the Quality Loss Function

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  • #48464

    Jose
    Participant

    I am trying to solve a problem in a Simulation for Six Sigma Book.  The book analyze a DOE and calculate Quality Loss Function Grouping.
    How they calculate The Quality Loss Function with the use of the Minitab 15.  What is the purpose of the calculation.
    Then they perform a regression analysis with the Total QLF versus the Critiacl to Quality Variables?
    What they can get with the calculation?.
    What is the relationship of the QLF and the Six Sigma calculation ? ( If any)
    How can I improve the QLF?
    Thanks so much for your help
     
    Jose
     
    I can send the chart at any mail.  Thanks

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    #163450

    fake accrington alert
    Participant

    First  understand the  function QLF and then  use  the  Minitab.
    good  luck

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    #163452

    Jose
    Participant

    Thanks so much and then the question is What is the Quality Loss Function?.
    Thanks so much

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    #163456

    fake accrington alert
    Participant

    A continuous “Taguchi” function that measures the cost implications of  product  quality.A common  form is  the quadratic loss  function:
    L=k(y-m)^2 Where L is  the  loss associated with  a  particular value of  the indepedent variable y.The  specification  nominal value  is m,while  k is a  contrant depending on  the  cost and  width of  the  specification  limits.This  type  of  philosophy encourages,for  example,a television manufacturer to  continually strive  to  routinely manufacture products that  have  a  very high  quality  picture.
    Hope  that  helps

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    #163497

    Erik L
    Participant

    Jose,
     
    There is a nice linkage between DOE and the QLF that you have sighted.  DOE is a key tool in the creation of a causal transform equation that explains the behavior in the response from either its central tendency and/or its variability.  DOE points you to the key parameters (x’s) that impact the response and through tools like Response Optimizer provides what settings those x’s should be at to achieve certain objectives for your response. 
     
    As long as you have a believable cost to replace/repair defective output (part of the loss coefficient and remember that this is suppose to capture internal as well as external costs) and a meaningfully derived tolerance you can look at what combination of settings create a predicted average response (and associated s.d.).  Ala Monte Carlo simulation you could then come up with a prediction of the average loss for a process if it’s run at those settings (Assuming target is best is the best model for the response).  You would feed your data into the equation L(y)=$[s^2+(average –Target)^2].   Iterating through various ‘what if’ scenarios you could then begin to appreciate the sensitivities of the factors in your model and which settings are most impacting the projected loss of the process.
     
    There is a direct linkage between Six Sigma thinking and the Taguchi loss function.  Both measures are positively impacted by achieving the nominal (targeted) response with a minimum of associated variation relative to the Voice of the Customer (VOC).  My personal choice in defining ‘quality’.  Sigma levels of a process are calculated as the number of standard deviations that exist between the average of the process and the closest of either the upper/lower specification limit.  Typically if we can count six standard deviations we feel that we have a high quality product which will generate low COPQ and high Customer Sat.
     
    So, how can one improve QLF?  1.)  Adjust your processes average so it hits the customers desired target.  2.)  Minimize the variation of your response.  3.)  Combine both options #1 and #2. 
     
    Regards,
    Erik

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