# Calculations of Yield, Sigma Level and Cpk

Six Sigma – iSixSigma Forums Old Forums General Calculations of Yield, Sigma Level and Cpk

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• #31048

Logan Luo
Participant

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?

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#81585

Mikel
Member

You calculations look right except yield (e**-dpu), but why are you doing all of these?
Metric overload is not a blessing — simplify.

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#81589

Logan Luo
Participant

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.

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#81618

mrsixsigma
Participant

LL,
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…….
Ram

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#81619

Logan Luo
Participant

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.

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#81630

BS
Participant

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

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#81645

Dr. Dave Stimley
Participant

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

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#125593

Velasquez
Participant

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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