# RTY: Rolled Throughput Yield

**RTY** is a process performance measure
that provides great insight into the cummulative affects of
an entire process. It measures the yeild for each of
several process steps and provides the probability that a
unit will come through that process defect free.

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## Rolled Throughput Yield

**Rolled Throughput Yield** allows us to
expose the "hidden factory" by providing visibility into
the yield of each process step. This helps us identify the
poorest performing process steps and gives us clues into
where to look to find the most impactful process
improvement opportunities.

In this module we will discuss the method of calculating Rolled Throughput Yield. Before we get into it's calculation there are a few abbreviations that we need to cover and then a couple of supplemental calculations.

- Defects = D
- Unit = U
- Yield = Y
- e = 2.71828

### Calculating DPU

DPU stands for "Defects per Unit" and it's a simple straight forward calculation. Just as it's description states DPU is calculated by dividing the number of defects by the number of units.

*DPU = D/U*

For Example, if you have a process step that produced 65 defects over 598 units then your DPU = 65/598 = 0.109

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### Calculating Yield

The yeild of a process step is the success rate of that step or the probability that the process step produces no defects. In order to calculate yield we need to know DPU and then we can apply it to our Yield equation:

Y = 2.718 ^ -0.109 = 0.8967 rounded, Y = 90%

### Calculating RTY

Now that you can calculate Yield, Rolled Throughput Yield is found by multiplying the yields of the first process step with the yield of the second process step and continuing this multiplication until you have carried it out for all process steps.

### RTY Example

Let's take this 5 step process and calculate it's Rolled Throughput Yield using the multiplication method mentioned above.

The calculation is: RTY = 0.90*0.91*0.99*0.98*0.97 = 0.77

therefore RTY = 77%

Looking at the same data with a little more information (defects and units per step) we can see the yield of each process step and multiplying them brings us to our Rolled Throughput Yield of 77%.

If we were to simply count all the defects and divide by the total units we would get a mean DPU for our process steps. This is a different but not necessarily less valuable perspective than RTY. Rolled Throughput Yield provides the probability that a unit comes through your process defect free.