# Rolled Throughput Yield

One of the best metrics that companies use to evaluate their process performance is this Rolled Throughput Yield (RTY) but many companies don’t even know what is this Rolled Throughput Yield (RTY) and how to find out RTY in the correct way. So if you are one of them then this blog is specially for you.

Before understanding what is ** Rolled Throughput Yield** ? Let’s us first familiarize with word “

**Yield**” and

**TPY**(Throughput Yield). Many companies don’t know how to find out RTY in the correct way. The below example will helps clear all the confusion related to Rolled Throughput Yield .

# Yield :

It is also known as First time Yield. It is defined as % of non-defective items of all the produced items.

## First Time Yield

First Time Yield (FTY) is simply the number of good units produced divided by the number of total units going into the process. First time yield takes in to account what goes into a process as Input and what comes out as Output without the consideration of rework

**Example: **

-Total units produced=100 units .

-Total units pass compliance check=85 units

-Number of defective units=> 100-85=15

-Process Yield = **85/100=85%**

This means the process yield of that particular product is 85% i.e 85 units are defect free and have passed compliance check successfully.

**TPY** : Throughput Yield

Throughput Yield is also known as First Pass Yield (FPY) .

It is defined as the number of units coming out of a process divided by the number of units going into that process over a specified period of time.

First pass yield is different, and it takes in to account what goes into a process as Input and what comes out as Output with the consideration of rework.

__Rolled Throughput yield (RTY)__

__Rolled Throughput yield (RTY)__

** Rolled Throughput yield (RTY)** is a metric that takes in to account entire process steps or operations from start to end. It is defined in percentage as probability that particular process with more than one steps will produce defect free parts. It is calculated by defining the Throughput Yield for each sub process and then based on whether these processes are in series or Parallel or combination we calculate RTY.

## **Example: **

-Total units produced=10 units

-Total units pass compliance check for 1st Process =10-2-2 units

–**TPY for Process (1) = 6/10 = 60%**

-Total units pass compliance check for 2nd Process =8-1-0 units

–**TPY for Process (2) = 7/8 = 87.5%**

-Total units pass compliance check for 3rd Process =8-1-1 units

–**TPY for Process (3) = 6/8 = 75%**

–**RTY= TPY 1 x TPY 2 x TPY 3**

–**RTY= 60*87.5*75 = 40 %**

## How to Calculate Rolled Throughput Yield for 3 different cases :

Another way to calculate rolled through yield is by using formula **RTY = e ^{-DPU}**

^{ .}, Where

**DPU = Defect per Units**. So lets understand these three cases :

**Case 1:**Process are in arranged in Series.**Case 2:**Process are arranged in Parallel.**Case 3:**Process are arranged in combination of Series and Parallel.

**Let’s see first how to calculate RTY for series and Parallel. **

**Case 1:** Process are in arranged in Series. Let assume the Process A, B and C operates in series. 10 Parts enter Process A, 2 are rejected and only 8 parts are good. These 8 parts enter Process B, 1is rejected and only 7 parts are good. Now these 7 parts enter Process C, 1is rejected and only 6 parts are good . Lets calculate the TPY for each process in series:

** TPY (Process A)= **e

^{-DPU }

*TPY (Process B)= e*^{-DPU}TPY (Process C)= e^{-DPU}*DPU _{A} = 2/10= 0.2 DPU_{B} = 1/8= 0.2*

*DPU*_{c}= 1/7 = 0.1*DPU _{A = }0.2*

*DPU*_{B = }0.125

*DPU*_{C = }0.142** TPY _{A}= **e

^{-0.2}

**e**

*TPY*_{B}=^{-0.125}

**e**

*TPY*_{C}=^{-0.142}

** TPY _{A}= **0.8187

**0.8824**

*TPY*_{B}=**0.8676**

*TPY*_{C}=**RTY = Process _{A}TPY * Process _{B}TPY * Process _{C}TPY**

**RTY = 0.8187* 0.8824* 0.8676**

**RTY (Series) = 0.626**

**Case 2:** Process are arranged in Parallel. Let assume the Process D, E and F operates in parallel. 10 Parts enter Process A, 2 are rejected and only 8 parts are good. 10 Parts enter Process B, 3 are rejected and only 7 parts are good. 10 Parts enter Process C, 1 are rejected and only 9 parts are good. Lets calculate the TPY for each process in Parallel:

** TPY (Process D)= **e

^{-DPU }

*TPY (Process E)= e*^{-DPU}TPY (Process F)= e^{-DPU}*DPU _{D} = 2/10= 0.2 DPU_{E} = 3/10= 0.3*

*DPU*_{F}= 1/10 = 0.1*DPU _{D = }0.2*

**3**

*DPU*_{E = }0.

*DPU*_{F = }0.1** TPY _{D}= **e

^{-0.2}

**e**

*TPY*_{E}=^{-0.3}

**e**

*TPY*_{F}=^{-0.1}

** TPY _{D}= **.8187

**.7408**

*TPY*_{E}=**.9048**

*TPY*_{F}=**RTY = Minimum of ( Process _{D}TPY OR Process _{E}TPY OR Process _{F}TPY**

**RTY = 0.8187* 0.7408* 0.9048**

**RTY (Parallel) = 0.5487**

**Case 3:** Process are arranged in combination of Series and Parallel. Let assume the Process A, B operates in Parallel and C in series . 10 Parts enter Process A, 2 are rejected and only 8 parts are good. 10 Parts enter Process B, 3 are rejected and only 7 parts are good. These two process A and B are in Parallel. so we will first calculate the TPY for each process and later Process AB and Process C are in Series.

** TPY (Process A)= **e

^{-DPU }

*TPY (Process B)= e*^{-DPU}*DPU _{A} = 2/10= 0.2 DPU_{B} = 3/10= 0.3*

*DPU _{A = }0.2*

**3**

*DPU*_{B= }0.** TPY _{A}= **e

^{-0.2}

**e**

*TPY*_{B}=^{-0.3}

** TPY _{A}= **.8187

**.7408**

*TPY*_{B}=**RTY ( _{AB} ) = Minimum of ( Process _{A}TPY OR Process _{B}TPY )**

**RTY ( _{AB} )** = 0.8187 OR 0.7408

** RTY ( _{AB} ) = **0.7408

Now **Process C** is in Series with both **Process A and Process B**

Lets first calculate :** TPY (Process C)= e^{-DPU} **=

*DPU _{C} = 1/7 = 0.1428*

**= e**

*TPY (Process C)= e*^{-DPU}^{-0.1428}=.8669

** TPY (Process C)** =0.8689

**RTY (Total) = RTY( _{AB} ) * TPY (Process C)= e^{-DPU}**

**RTY (Total)** = 0.7408 * 0.8689

**RTY (Total)** = 0.6422

**Watch this animated YouTube video for more details explanation :**

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