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**Purpose**

To help understand Rolled Throughput Yield let's first take a look at Throughput Yield.

Throughput Yield is used to calculate the true measure of a process step's effectiveness taking into account the "Hidden Factory".

Since this measure considers the "Hidden Factory", it is said to be the complete and true assessment of process effectiveness. The Throughput Yield (YTP) of any given process step represents the probability of producing a defect-free unit at that process step.

**Anatomy**

Probability of producing a defect-free unit at that process step.

Reference: The Vision of Six Sigma: A Roadmap for Breakthrough

**Terminology**

A. Number of units going into a process. Each unit (u) contains (m) opportunities for defect.

B. Process operation step.

C. Defects (d) produced during the execution of the process step.

D. Point in process where Throughput Yield is calculated (prior to inspection or test).

E. Operator verification step.

F. Inspection after the process step.

G. Formula to calculate the Throughput Yield, where e = 2.718282 and dpu = no. of defects (d)/no. of units (u)

H. Throughput yield is also calculated using this formula, where m = number of opportunities per unit and dpo = no. of defects (d)/no. of opportunities (o)

**Major Considerations**

YTP is reflective of the true cost structure of the process.

Calculation of YTP must be done prior to any form of correction or rework of the output.

Calculation based on discrete or continuous data.

The Poisson approximation can be applied when the opportunities for nonconformance is large and the probability of an event is small. If these assumptions prove to be unreasonable, then the binomial model can be used.

**Application Cookbook**

1. Count the number of units going into a process (u).

2. Define the number of opportunities for defect contained in each unit (m).

3. Count the number of defects produced (d). This count shall be done prior to any form of rework or correction to the output.

4. Compute DPU or DPO.

5. Compute Throughput Yield.

**Purpose**

Rolled Throughput Yield is used to calculate the probability that a unit of output will be defect free after a series of k process steps.

**Anatomy**

Probability that a unit of output will be defect free after a series of process steps.

Reference: The Vision of Six Sigma: A Roadmap for Breakthrough

**Terminology**

A. Process step (typical).

B. Throughput Yield of process step 1.

C. kth process step (last in the series to calculate the Rolled Throughput Yield).

D. Throughput Yield of process step k.

E. Formula to calculate the Rolled Throughput Yield (RTY).

**Major Considerations**

Since the concept of yield represents the probability of producing zero defects, and process steps are assumed to be independent, the probability of producing zero defects after k steps is equal to the product of the yield values for each step (see concept Basic Probability Theory – Sets, Theorems).

RTY is a function of the number of defects in the process step.

**Application Cookbook**

1. Calculate the Throughput Yield (YTP) for each step or process (steps 1 through k).

2. Multiply the Throughput Yield of each step.

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