Calculations of Yield, Sigma Level and Cpk

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    Logan Luo

    Currently, I am working on developing a database which will calculate DPU, DPMO, Yield and Sigma Level in three levels (process level, product line level, overall level) automatically.
    Let’s say I have a ten steps process and I collected the process input and output based on work order and Traveler. Please tell me if following calculations are correct.
    For each process, I calculate DPU, DPMO, Yield and Sigma Level by following:
    DPU= defect/ process input
    DPMO= (defect/total input * opportunities )*10^6
    Yield = 1- DPU
    Sigma Level= 0.8406 + SQRT(29.37 – 2.221 * (ln(DPMO)))
    Cpk= Sigma level / 3
    In the product line level (on monthly base), DPU and DPMO and Sigma Level are calculated by following
    total defect = defect in process 1 + defect in process 2+….. + defect in process 10
    total opportunities = input in process 1 * opportunities + input in process2 * opportunities+…+ input in process 10* opportunities
    DPU = total defect/ total input
    DPMO= (total defect/total opportunities)* 10^6
    Total Yield= 1-DPU
    Sigma Level = 0.8406 + SQRT(29.37 – 2.221 * (ln(DPMO)))
    Sigma Level LT = Sigma Level -1.5
    Cpk = Sigma Level / 3
    Same methods are used in overall level. The only different is the grouping of total defect and total opportunities data.
    My question is:
    Can I group the defects and opportunities in product level and overall level and calculate Sigma Level and Cpk as what I mentioned above, or some other statistical calculations need to be brought in to normalize the data before the calculating the Sigma Level?



    You calculations look right except yield (e**-dpu), but why are you doing all of these?
    For example, if you know DPMO, your sigma level is already determined; if you know dpu, your yield is already determined.
    Metric overload is not a blessing — simplify.


    Logan Luo

    Thanks Stan.
    What is the difference between Yield=e**-DPU and Yield=1-dpu? The formula has been used in iSixSigma Calculator is Yield=100-defect percent.
    The reason for doing all these is because I am trying to develop a general-purpose software to ease the calculation process of all Six Sigma measurements. Different people may need/like different measurements.




    e**(-dpu) is the probability of finding defect free (rework free) products.  If dpu is small, say less than 1%, e**(-dpu) is almost equal to (1-dpu). Go ahead check it out for yourself in Excel.  That is because e**(-x) can be approximated to 1- x + x*x/2 – x*x*x/6…….


    Logan Luo

    Thanks Ram. Now I know the difference between these formulae.
    I have another question.
    In iSigma’s dictionary Yield is defined as
    “Yield is the percentage of a process that is free of defects.” [not the probability of process free of defect]OR”Yield is defined as a percentage of met commitments (total of defect free events) over the total number of opportunities.”
    And in the iSigma calculator, Total Opportunities has been considered.
    Yield= 100- defect percentage
    Defect percentage= D / Total Opportunities
    Can I say these formulae are more appropriate to describe Yield, and e**(-dpu) is for the calculation of the Probability of Defect Free Product? Sometimes I am confused by different interpretations from different sources for a same measurement.



    Although it may be trivial, I found a miss in equation.
    DPMO= (defect/total input * opportunities )*10^6
    I think the following is right expression.
    DPMO= defect/(total input * opportunities )*10^6


    Dr. Dave Stimley

    Use these formulae:  RTY= e^-(Sum of DPU) or -ln(RTY) = Sum of DPUs whichever is more convienient. 
    Then DPMO = (Sum of DPUs*1000000)/sum of OE’s
    Then Convert your DPMO’s to Sigma.
    To get to Cpk: Once you know DPMO,  Take the DPMO value and divide it by 2 then find the Z value from a Z table.  For Example, 2700DPMO/2 = 1350DPMO or as a fraction .001350.  The Z table value for this fraction is 3. This is the unshifted distribution.  Now subtract 1&1/2 to get the shifted Z (3-1.5=1.5).  Cpk = Z/3 for the shifted distribution .  So Cpk in this case would be 0.5.
      Dr. Dave Stimley



    what is the justification behind the formula
    process Sigma = 0.8406 + SQRT(29.37 – 2.221 * (ln(DPMO))).
    how is it derived

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