# Rolled Throughput Yield (RTY)

Rolled Throughput Yield is the probability of the entire process producing zero defects. This metric is increasingly relevant when a process has excessive rework.

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 = 0.800 * 0.739 * 0.804

RTY = 0.475 = 47.5%

There is a 47.5% chance of the entire process producing zero defects.

Review:

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%.

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%

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 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 is tried 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 RTY.

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.

Another formula is shown below to estimate RTY if the defects per unit or defects and units are known:

## 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.

## Other YIELD calculations

Final Yield, FY.

Throughput Yield, TPY.

Normalized Yield, NY.

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