# Calculating Rolled Throughput

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• #44735

Pace
Participant

Hello-
Please explain (in a very simple example) “How to calculate rolled throughput”.  This process of metrics is very new to me.
Thanks for your anticipated responses

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#143937

Jones
Participant

Here’s my less than perfect response.
Consider an operation that has three process steps.  Each process step yields 90% (0.9) succes at the first attempt – meaning the 10% ar either rejects or rework.  The RTY would then be 72.9% (0.9*0.9*.09).

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#143944

EdG
Participant

Although I cannot accept credit for this, I don’t remember who provided me with this write-up on RTY (it could very well have been on this website).  I hope that it helps…
Rolled Throughput Yield (RTY) is the probability that a single unit can pass through a series of process steps free of defects.Next we will turn our attention to a Rolled Throughput Yield example. If you will remember, the First Time Yield calculation we did (FTY) considered only what went into a process step and what went out. Rolled Throughput Yield adds the consideration of rework. Using the previous example:Process A = 100 units in and 90 out Process B = 90 in and 80 out Process C = 80 in and 75 out Process D = 75 in and 70 out.If in order to get the yield out of each step we had to do some rework (which we probably did) then it really looks more like this:Process A = 100 units, 10 scrapped and 5 reworked to get the 90. The calculation becomes 100-(10+5)/100 = 85/100 = .85 This is the true yield when you consider rework and scrap.Process B = 90 units in, 10 scrapped and 7 reworked to get the 80. 90-(10+7)/90 = .81Process C = 80 units in, 5 scrapped and 3 reworked to get the 75. 80-(5+3)/80 = .9Process D = 75 units in, 5 scrapped and 10 reworked to get the 70. 75-(5+10)/75 = .8Now to get the true Rolled Throughput Yield (Considering BOTH scrap and the rework necessary to attain what we thought was first time throughput yield) we find that the true yield has gone down significantly:.85*.81*.9*.8 = .49572 or Rounded to the nearest digit, 50% yield. A substantially worse and substantially truer measurement of the process capability.

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#144091

Cherukara
Participant

Another way to look at it is as Process Yield and Plant Yield (Rolled Throughput).
Process Yield – the yield at each processes. (eg A, B, C ….n)
Plant Yield = Rolled Throughput – the total yield of the processes. (AxBxCx….n)
Cheers ! Dominic

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#144092

Cherukara
Participant

Another way to look at it is as Process Yield and Plant Yield (Rolled Throughput).
Process Yield – the yield at each processes. (eg A, B, C ….n)
Plant Yield = Rolled Throughput – the total yield of the processes. (AxBxCx….n)
Cheers ! Dominic

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#144276

Prabhu
Participant

Defining the process steps and capturing the input and out put of each step of process is the key in calculating RTY.
Process RTY and plant RTY are the two different metods all together . suggest to start with measure only process RTY . In a plant theres may be more than one process.

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#144326

Jonathon
Participant

Everything you say is correct. I’d like to build on it.I think of RTY as akin to the “bucket brigade” in old cartoons. Every time the bucket changes hands, a little water sloshes out until there’s hardy any left to throw on the fire. SImilarly, every time a unit of work exits a process step, there’s a likelihood that some “right-first-time” product has experienced a defect.One last thing to realize: just because a unit of work didn’t make it through the line without experiencing a defect, does NOT mean its only disposition is scrap. That’s why RTY can be useful in estimating how much of the line’s resources are diverted into rework.

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#144358

Ron
Member

Great answers above!
One other formula you may see is: RTY = e^(-DPU).  All this means is that if you know DPU you can calculate RTY.
The easiest way to do this is in Excel.  Simply type:
=EXP(-“insert DPU value”)
Note: Do not include paranthesis around the DPU value when you do this for real.

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#144364

Sah
Member

I’ve 1 defect per unit and using your formula I get rty=0,37, but my all pcs are fail, because each one have 1 defect. could you explane me?

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#144367

Ron
Member

This has to do with “DPU modeling” and can get a bit complicated.
Without going into lots of discussion on the Poisson Model I will just say that the formula I offered is used to estimate the probability of a discrete event (good/bad) when sampling from a relatively large population.  If this assumptions is not met you should proceeed with caution.
In the formula RTY = e ^-dpu, dpu is the average number of defects per unit.
When we have a process with 1 DPU on average, we say there is a 36.79% chance of finding a unit with zero defects in the future.  So from the perspective of defectives we have a  2 sigma process.
There is another more complicated formula you can use where you use dpu (average # of defects per unit), e (base of the natural log), and r (the specific number of defects found during sampling) to “predict” future performance.
Don’t sweat all this math though.  If you use the formulas others offered (multiplying each process yield by each other) you will be fine.
Sorry if I over complicated this for you!
Ron

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#144375

boettler
Member

Assuming process sequenceProcess A = 95% yieldProcess B = 90% yieldProcess C = 85% yieldRolled Throughput Yield is 0.95×0.90×0.85 = 0.73

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