First Time Yield and Rolled Throughput Yield (2024)

First Time Yield and Rolled Throughput Yield are two important standard yield metrics for processes.

First Time Yield (FTY): The ratio of the number of good “units” coming out of the process to the number of “units” going in.

Rolled Throughput Yield (RTY): The probability that the process produces a good “unit” the first time through.

Unlike First Time Yield, Rolled Throughput Yield explicitly accounts for rework and scrap thus surfacing the “hidden factory.”

In two videos, Academic Gain Tutorials, a free online resource for study materials from many disciplines, describes First Time Yield and Rolled Throughput Yield.

You can view these videos through the listed links for First Time Yield and Rolled Throughput Yield.

First Time Yield

Of course, using the example in the video for the three steps in series, we see that

(95/100)*(85/95)*(80/85) by cancellation = 80/100 simply the definition of First Time Yield, the number of good units exiting divided by the number of units entering.

Rolled Throughput Yield

As described, the RTY calculation is simple if all the process steps are in series and rework is only done once in a given process step.

Suppose however that rework is done not once but say twice in a process step? And what if some of the process steps are in parallel?

We will address both questions with examples.

First: Rework is done more than once

We’ll look at the “true” rolled throughput yield focusing on Step 1 for the above example.

We use a subscript to indicate whether scrap or rework is done during the first pass or a second pass, etc.

Step Good Units In Defects Numerator for True Yield

True Yield Out

1 100 10 scrap1 5 rework1 100 – (10 + 5) = 85 85/100 = 0.85

The above is the case that most material simplifies to, only one pass through.

But if we’re really trying to get at the hidden factory and look at the amount of waste, we have to track every pass through a step and take into account whether the results were good or bad.

Let’s assume there was an only second pass through. We could generalize to as many as there are although in practice, we recommend that after a given part is reworked a certain number of times, it should be scrapped.

The true throughput yield for Step 1 is therefore 80 percent.

The number of good units going into Step 2 would be 88 = (100 – 12 scrapped).

One would then continue as usual to compute the system Rolled Throughput Yield.

Next: Some process steps are in parallel

Often Lean Six Sigma material only covers RTY for serial operations.

If we know the individual RTYs for any operation, and we have a combination of series and parallel operations, how do we calculate the RTYoverall for the system?

First, we need some assumptions for the approach we describe.

  1. Independence: defects made in one operation do not influence the defects made in another operation
  1. In the general case, must all products or services pass through all non-identical parallel operations?

If we know the number of units being processed and the fraction of them going through the different parallel operations, then the RTY for the parallel “block” as a whole is the weighted average of the individual RTYs making up the block.

However, as we will see, the calculations simplify in that if we know the total going in, the total amount of rework, and the total amount of scrap for the block, we can use those numbers to get the RTY for the entire block.

3) All rework is done by the same operation that produced the defect.

See Also

Let us work an example where we know the number of units, how they split among the parallel steps, and the amount of scrap and rework.

Legend: RW = Rework, SC = Scrap

We started with 300 units and finished with 275 having scrapped 25 units. However, much rework was done.

The Throughput Yield (YTP) for an operation = (In – RW – SC)/(In)

Therefore YTP1 = (300 – 0 – 12)/300 = 288/300 = 0.96


YTP2 = (288 – 18 – 5)/288 = 265/288 = 0.92

YTP3 = (102 – 10 – 3)/102 = 89/102 = 0.873

YTP4 = (97 – 8 – 3)/97 = 86/97 = 0.887

YTP5 = (84 – 7 – 1)/84 = 76/84 = 0.905

YTP6 = (276 – 27 – 1)/276 = 248/276 = 0.899

We now need to compute the overall RTYSystem

Ops 1, 2, and 6 are in series, and the resultant RTY is computed in the usual way through multiplication.

Ops 3, 4, and 5 are in parallel. As a result, the RTY3, 4, 5 = the weighted average of the individual YTPs weighted by the fraction of units passing through those operations.

RTY3,4, 5 = (102/283)(0.873) + (97/283)(0.887) + (84/283)(0.905) = 0.887

However, if we use the original fractions for the individual YTPs, we see the following:

RTY3,4,5 = (102/283)(89/102) + (97/283)(86/97) + (84/283)(76/284)

But using the obvious cancellation, we have

RTY3,4,5 = 89/283 + 86/283 + 76/283 = 251/283 = 0.887

But this is simply, taking the block as a whole,

RTYBlock = (INBlock – REWORKBlock – SCRAPBlock)/INBlock

= (283 – 25 – 7)/283 = 251/283 = 0.887

Now we can calculate RTYSystem.

RTYSystem = YTP1*YTP2*RTY3,4,5*YTP6 = 0.96*0.92*0.887*0.899 = 0.704.

What if all we have are the individual YTPs for every operation without the original scrap and rework numbers? How then do we compute the RTY for a parallel block?

If we assumed that the products or services going in were equally split among the operations in the parallel block, which might not be the case, then we could simply average the individual YTPs to get the RTYBlock.

However, since we don’t know that, a better approach is to take the geometric mean of the individual YTPs.

Recall that the geometric mean is simply the nth root of a product of n numbers.

In the above example, then,

RTYBlock = (0.873)( 0.887)(0.905)1/3 = (0.7008)1/3 = 0.888

Of course, in more general cases with series and parallel loops, rework, repair, scrap, etc. a simulation model would probably be required to get a good estimate. This is what Pyzdek recommends – Pzydek, T., The Six Sigma Handbook, McGraw Hill,pp. 488-489, 2003.

First Time Yield and Rolled Throughput Yield (2024)


What is first time yield and rolled throughput yield? ›

The key difference between Rolled Throughput Yield and First Time Yield is that RTY considers the total number of defects in a multi-step process, while FTY only focuses on the defects in the first step.

How do you calculate first time yield? ›

First Time Yield (FTY) is a measure of a process's efficiency, calculated by dividing the number of error-free products by the total units produced, then multiplying by 100 to get a percentage. This metric helps in understanding how well a process is producing items correctly on the first attempt.

What is the difference between First Pass Yield and rolled throughput yield? ›

First pass yield is a measure of quality. It's defined as the percentage of parts produced correctly on the first try and can be used in further production. Rolled throughput yield is a measure of efficiency, and it measures how many parts you can produce per hour using your machines, tools, and labor force.

How do you calculate rolled throughput yield? ›

The equation is: RTY = Min (TPY of process 1, TPY of process 2, TPY of process 3). You'd repeat this comparison for the following four stages of the wrench and screwdriver assembly lines. After identifying the minimum throughput yield for all four stages, you'd multiply those figures to determine the overall RTY.

What is the difference between first time yield and first pass yield? ›

First time yield, also known as first pass yield, is the percentage of the time that a product or service passes through a process step without any defects on the first attempt.

What is first yield formula? ›

First pass yield = (number of good units produced / total number of units produced) x 100First pass yield refers to the turnout of a production cycle or the number of goods a company can actually sell to customers after the production process.

How to calculate right first time? ›

First time right defined

It boils down to this formula: FTR = (number of usable products divided by the total number of products) x 100.

How do you calculate yield method? ›

The earnings yield is the inverse ratio to the price-to-earnings (P/E) ratio. The quick formula for Earnings Yield is E/P, earnings divided by price. The yield is a good ROI metric and can be used to measure a stocks rate of return.

What is the purpose of rolled throughput yield? ›

Rolled throughput yield, or RTY, measures the probability that an object or process is completed with no errors through multiple steps. If a process has an RTY of 75%, this means that 75% of products are produced with no errors at any point along the process chain, and 25% of products have an error or flaw.

How to calculate RTY from FPY? ›

To calculate RTY, multiply the FPY of each process steps to get the answer. In this case, your equation will be the multiplication of five FPY values which will result in 0.6372.

How do you implement First Pass Yield? ›

The First Pass Yield Formula

Calculating FPY is rather simple, as it simply divides the number of good parts by the total number of parts that began the process, and accounts for the parts that require rework. To run through an example. Here is the situation: Total Units Produced: 100.

How to calculate first time yield? ›

The way we calculate first time yield, throughput yield or first pass yield is simple by dividing the number of GOOD UNITS (excluding any rework or scrap) by the THE TOTAL NUMBER OF UNITS GOING THROUGH THE PROCESS.

What is yield and throughput yield? ›

The Throughput Yield (Yt) is calculated using the Defects per Unit (DPU). As such, it provides more information than the classic Yield metric, which considers the number of defective units rather than the total number of defects occurring on those units.

How do you calculate throughput? ›

Calculate Throughput: Divide the total output volume by the duration of the measurement period to determine the average throughput.

What is the difference between FPY and RFT? ›

There are a lot of abbreviations; all reflecting to the same KPI: FPY = First Pass Yield. FTR = First Time Right. RFT = Right First Time.

What is First Pass Yield in Lean Six Sigma? ›

The FPY simply tells you what percentage of items go through the manufacturing process without needing any extra work or getting thrown away. A high FPY shows that everything is running like a well-oiled machine, where resources are used wisely, waste is avoided, and clients end up satisfied.


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