# Finance:Rolled throughput yield

Rolled throughput yield (RTY) is the probability that a process with more than one step will produce a defect free unit. It is the product of yields for each process step of the entire process.

For any process, it is ideal for that process to produce its product without defects and without rework. Rolled throughput yield quantifies the cumulative effects of inefficiencies found throughout the process. Rolled throughput yield and rolled throughput yield loss (RTYL) are often used in Six Sigma.

## Calculation

Rolled throughput yield is calculated by multiplying the yields of each process step. Calculations can become increasingly complicated as more parallel processes are introduced. It is first necessary to calculate the yield of each process step. We can estimate the yield of a process step by dividing units accepted by the number of units produced for that step. Suppose a process step produced 10 units and only 8 were good units. The yield of that step would be 8/10 or 0.80.

RTY example:

RTY = yield of process step 1 * yield of process step 2 * ... * yield of process N

Suppose a process had 3 steps. Step 1 produced 10 units and 2 were defective, the yield of step 1 would be 8/10 or 0.80, Step 2 had a yield of 0.9 and step 3 had yield of 100%. The rolled throughput yield for this entire process would be:

RTY = 0.80 * 0.90 * 1.0 = 0.72

RTY = 72%

The probability of this 3 step process producing a defect free product is 72%

Rolled throughput yield loss is the inverse of RTY, RTYL = 1 - RTY

Total number of audited samples are divided by total sample size. This gives the "first pass accuracy". When it is divided by total yield it gives the rolled throughput yield.