# Rolled Throughput Yield (RTY) Calculator for a Multi-Step Process

> Source: https://netray.co/tools/rolled-throughput-yield-calculator-multi-step
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Multiply first-pass yields across up to five process steps to get RTY, defects per unit and the hidden factory your final yield hides.

## Category

quality

## Industry

Discrete Manufacturing

## Audience

- Quality engineer
- Six Sigma Black Belt
- Process engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Step 1 first-pass yield

**Key:** y1

**Type:** number

**Default:** 98.5

**Min:** 0

**Max:** 100

**Step:** 0.1

**Unit:** %

**Help:** Units passing step 1 with no rework or scrap, as a percent.

#### Step 2 first-pass yield

**Key:** y2

**Type:** number

**Default:** 97.2

**Min:** 0

**Max:** 100

**Step:** 0.1

**Unit:** %

#### Step 3 first-pass yield

**Key:** y3

**Type:** number

**Default:** 99.1

**Min:** 0

**Max:** 100

**Step:** 0.1

**Unit:** %

#### Step 4 first-pass yield

**Key:** y4

**Type:** number

**Default:** 95.8

**Min:** 0

**Max:** 100

**Step:** 0.1

**Unit:** %

#### Step 5 first-pass yield

**Key:** y5

**Type:** number

**Default:** 99.4

**Min:** 0

**Max:** 100

**Step:** 0.1

**Unit:** %

**Help:** Enter 100 for any step you do not use.

#### Units started

**Key:** start_qty

**Type:** number

**Default:** 10000

**Min:** 0

**Step:** 100

**Unit:** units

**Outputs:**

#### Rolled throughput yield

**Key:** rty

**Expr:** (y1 / 100) * (y2 / 100) * (y3 / 100) * (y4 / 100) * (y5 / 100) * 100

**Format:** percent

**Primary:** true

**Description:** Probability a unit passes every step first time with no rework.

#### Total defects per unit (DPU)

**Key:** dpu

**Expr:** 0 - ln(rty / 100)

**Format:** decimal

**Description:** Poisson-based: DPU = -ln(RTY).

#### Normalized yield per step

**Key:** norm

**Expr:** pow(rty / 100, 1 / 5) * 100

**Format:** percent

**Description:** Geometric mean of the five step yields.

#### Units good first time

**Key:** good

**Expr:** start_qty * rty / 100

**Format:** integer

**Primary:** true

#### Units needing rework or scrap

**Key:** rework

**Expr:** start_qty - good

**Format:** integer

#### Weakest step yield

**Key:** worst

**Expr:** min(min(min(y1, y2), min(y3, y4)), y5)

**Format:** percent

**Chart:**

#### RTY as step 3 yield changes

**Type:** line

**X:** y3

**From:** 90

**To:** 100

**Steps:** 21

**Series:**

- rty

**Disclaimer:** Treats steps as independent and assumes first-pass yield excludes any rework loop. DPU = -ln(RTY) is the Poisson approximation.

## Content

**Intro:** Final yield at the end of the line tells you how many units shipped. Rolled throughput yield tells you how many units were good the first time at every step, which is what the process actually costs you. Enter first-pass yield for each step and see RTY, defects per unit and units reworked.

**Sections:**

#### How to use the calculator

**Body:** Enter the first-pass yield for each step as a percent. First-pass yield counts only units that pass without rework, repair or retest, so a unit fixed and shipped counts as a failure at that step. Use 100 for steps you do not have. Enter the number of units started to see how many came through clean. The chart sweeps step 3 so you can see how much a single improvement moves the whole line.

**Bullets:**

- Use first-pass counts, not final counts
- Pull step yields from the same period and same product family
- Set unused steps to 100
- Change one step at a time to compare projects

#### The formula behind it

**Body:** RTY is the product of the step first-pass yields: RTY = Y1 x Y2 x ... x Yn. Five steps at 98 percent each give about 90.4 percent, not 98 percent. Defects per unit follows from the Poisson relationship, DPU = -ln(RTY). Normalized yield is the nth root of RTY and gives a per-step figure you can compare across lines that have different numbers of steps. It is the number to feed into a sigma-level conversion.

#### Reading the result

**Body:** With the default values the weakest step is step 4 at 95.8 percent, yet the line RTY is only about 89 percent. That gap between the best single step and the rolled figure is the hidden factory: rework labour, retest, extra WIP and expedites that never show in the final scrap number. Fix the weakest step first, but check the chart. Because yields multiply, the same one-point gain is worth slightly more on a line that is already high.

#### Common mistakes and ERP notes

**Body:** The usual error is counting reworked units as good. Another is averaging step yields instead of multiplying them. In an ERP, first-pass data is rarely held directly: SAP QM inspection lots, Infor SyteLine job transactions with reject quantities, and Epicor or Oracle operation scrap give you scrap but not rework, so you often need a rework routing or a reason code to separate the two. Make sure operation scrap is captured per operation before you trust the result.

**Bullets:**

- Do not count reworked units as passes
- Do not average yields, multiply them
- Capture rework by operation, not only scrap

**Cta:** If your step yields live in your ERP as operation scrap and rework transactions, we can build a read-only report that calculates RTY per routing automatically.

**Faq:**

#### What is the difference between FPY and RTY?

**Answer:** First-pass yield is the share of units that pass a single step without rework. Rolled throughput yield is the product of first-pass yields across all steps, so it is the chance a unit makes it through the whole process clean the first time.

#### Why is my RTY so much lower than my final yield?

**Answer:** Final yield counts units that eventually ship, including those reworked. RTY counts only units that were right first time. The difference is rework, which consumes labour and capacity and is invisible in a scrap-only report.

#### Can I use more than five steps?

**Answer:** This tool takes five. For more, combine adjacent steps by multiplying their yields and entering the product as one step, or run two passes and multiply the two RTY results together.

#### Is DPU = -ln(RTY) always right?

**Answer:** It assumes defects occur randomly and independently, the Poisson model. It is a good approximation when defect rates are low, but it understates DPU when defects cluster on the same unit.

## Search terms

rolled throughput yield calculator, RTY calculator six sigma, first pass yield calculator, rolled throughput yield formula, normalized yield calculator, defects per unit from RTY, hidden factory yield

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