Calculations of Yield, Sigma Level and Cpk
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 This topic has 7 replies, 6 voices, and was last updated 16 years, 3 months ago by Velasquez.

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December 18, 2002 at 3:29 pm #31048
Logan LuoParticipant@LoganLuo Include @LoganLuo in your post and this person will
be notified via email.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.
Lets 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= 1DPU
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?0December 18, 2002 at 5:28 pm #81585You 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.0December 18, 2002 at 6:16 pm #81589
Logan LuoParticipant@LoganLuo Include @LoganLuo in your post and this person will
be notified via email.Thanks Stan.
What is the difference between Yield=e**DPU and Yield=1dpu? The formula has been used in iSixSigma Calculator is Yield=100defect percent.
The reason for doing all these is because I am trying to develop a generalpurpose software to ease the calculation process of all Six Sigma measurements. Different people may need/like different measurements.0December 19, 2002 at 1:44 pm #81618
mrsixsigmaParticipant@mrsixsigma Include @mrsixsigma in your post and this person will
be notified via email.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 (1dpu). 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…….
Ram0December 19, 2002 at 4:05 pm #81619
Logan LuoParticipant@LoganLuo Include @LoganLuo in your post and this person will
be notified via email.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]ORYield 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.0December 20, 2002 at 12:39 am #81630Although 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 )*10^60December 20, 2002 at 2:13 pm #81645
Dr. Dave StimleyParticipant@Dr.DaveStimley Include @Dr.DaveStimley in your post and this person will
be notified via email.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 (31.5=1.5). Cpk = Z/3 for the shifted distribution . So Cpk in this case would be 0.5.
Dr. Dave Stimley
0August 22, 2005 at 5:51 pm #125593
VelasquezParticipant@martin Include @martin in your post and this person will
be notified via email.what is the justification behind the formula
process Sigma = 0.8406 + SQRT(29.37 – 2.221 * (ln(DPMO))).
how is it derived
0 
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