# Rolled Throughput Yield (RTY)

Rolled Throughput Yield (RTY) is the probability of the entire process producing zero defects. This metric is increasingly relevant when a process has excessive rework. Rework is considered the hidden factory costs. A RTY measurement has the advantage of showing the losses related to high defect and/or rework cases.

Since this rework involves many of the 7-wastes and contains the hidden factory opportunity, it is relevant to guide the team in the right direction.

RTY is the product of each process’s throughput yield, TPY. Using the same process as shown below as in the TPY example:

Calculation from above example:

RTY = Process 1 TPY * Process 2 TPY * Process 3 TPY

RTY = 40/50 * 34/46 * 37/46

RTY = 0.8000 * 0.7391 * 0.8043

RTY = 0.476 = 47.6%

There is a 47.6% chance of the entire process producing zero defects or rework cases.

Review:

Process 1: There were 50 units that entered Process 1 and 40 of them were neither reworked or scrapped. This means 40 of the 50 went through Process 1 without a defect which = 80%.

Process 2: There were 46 units that entered Process 2 and none were scrapped but 12 were reworked. This means 34 of the 46 went through Process 2 without a defect = 73.9%

Process 3: There were 46 units that entered Process 3 and 9 were scrapped and none were reworked. This means 37 of the 46 went through without a defect = 80.4%.

Multiply the TPY for each process and this becomes RTY for the entire process.

CAUTION:

At the end of the entire process there are 37 units left of the original 50 units. The RTY is not 37/50 = 74% because that value of 74% only accounts for scrapped units and not the reworked units.

Once the reworked units are incorporated into the calculation at each step does the RTY become accurate. This emphasizes the importance of including the reworked units, especially if the rework is very costly or near the cost of scrapping a unit.

If the rework cost is very low relative to a scrapped unit then the incorporation of rework figures is reduced in its importance.

Another shortcut that does not work is to add all the reworked units + scrapped units across all the processes and divide by the starting quantity. A total of 18 units reworked + 13 scrapped = 31 and some would think that 19 must have gone through without a defect. That does not equate to the correct Rolled Throughput Yield.

In this case it would give an answer of 19/50 = 38% which is not correct.

EACH process has its own numerator and denominator that is dependent on the previous process so take each process in order and calculate as shown above.

RTY and other yield metrics can serve as baseline scores (MEASURE Phase) and final scores for Six Sigma projects (CONTROL Phase).

The baseline score provided in the MEASURE phase does not have to be a z-score and often the yield metrics are easier for team and other company employees to relate with and understand.

## Other Rolled Throughput Yield Formulas

Another formula is shown below to estimate RTY or TDU if the defects per unit or defects and units are known. TDU = Total Defects Per Unit

This is an ESTIMATE. The ESTIMATES becomes more accurate to match the ACTUALS as the DPU decreases. Notice the two examples below.

Using the figures in the example above example see the ESTIMATES vs. ACTUAL below. Notice that the ESTIMATES are higher than the ACTUALS. Now, let's change the DPU to a much lower value for each process.

Notice that the ESTIMATES are very close to the ACTUALS (we have increased the units to show a much lower DPU in each process). ## RTY Template and Calculator Click here for a template that calculates RTY and other yield metrics. There are also a variety of other templates to a Six Sigma Project Manager.

## Another example

A 3-step process has the following yields:

Y1 = 98.7, Y2 = 99.4, Y3 = 97.8

What is the Total Defects Per Unit (TDPU)?

This is a two step problem. First find the RTY:

RTY = 0.987 * 0.994 * 0.978 = 0.959494

Recall the TDPU = -ln (RTY)

Therefore, the TDPU = -ln (0.959494) = 0.041

## Other YIELD calculations

Final Yield, FY.

Throughput Yield, TPY.

Normalized Yield, NY.

Templates, Tables, and Calculators

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