Definition Throughput Yield (TPY) or First Pass Yield Calculation - Help Needed

L

Licht

#1
Hello.

Suppose I have a process that I want to calculate the TPY:

Data:
Units (U) = 140 parts
Defectives (D) = 140 parts

1) First situation - all parts pass without defects

TPY = (140/140) * 100 = 100% or
TPY = e^(-D/U) * 100 = e^(-0/140) * 100 = 100%

2) Second situation - any part pass without defects

TPY = (0/140) * 100 = 0% or
TPY = e^(-D/U) = e^(-140/140) * 100 = 36.79%

I did not understand why the results of item 2 are not the same. Can anyone help me, please ? :confused:

I get the TPY formula from Six Sigma Material site.

:thanx:
 
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L

Licht

#3
Harry,

First thank you for the reply.
I read the doc you've mentioned last post, but I could not find the answer for my question. :confused:
My doubt: two different methods give me different results in TPY calculus.

Data:
Units (U) = 140 parts
Defectives (D) = 140 parts

> When all parts pass without defects:

Method 1: TPY = (140/140) * 100 = 100%
Method 2: TPY = e^(-D/U) * 100 = e^(-0/140) * 100 = 100%

> When any part pass without defects:

Method 1: TPY = (0/140) * 100 = 0%
Method 2: TPY = e^(-D/U) = e^(-140/140) * 100 = 36.79% (????)

Could someone help me explaining it pls ?


:thanx:
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#4
A clarifying question: if 'any part passes without a defect' why do you put 140 defects/140 units tested in the second formula? shouldn't it be 0 defects/1 part? or did you mistate the question?

If you meant (as your math seems to indicate) that the second scenario was that the defect rate was 140 defects and 140 units tested, then the answer lies in the difference bewteen the binomial and the Poisson equestions.

in the straightforward yield formula you are dividing the number of failing units by the number of units tested (binomial distribtion). in this case there may be more than 1 defect on any given unit*, but the equation is asking the number of passing (1-failing units), not the number of defects.

in the Poisson estimate of yield the exponential is asking for the number of defects not the number of defective units. The Poisson handles the case where there can be more than one defect on the unit and the number of defects is randomly distributed among the units. so you could 140 defects but they land on only 63 of the parts. Therefore you would have 37 parts that yield (they do not have any defects so they are not defective)

*defect = a single 'thing not right'. a unit could have a scratch, a broken piece and a dimension out of tolerance. parts can have multiple defects. This is modeled by the Poisson, your method 2.

defective = a part that has one or more defects. this is modeled by the binomial, your Method 1
 
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