Last Updated on 21 September 2023

Rolled Throughput Yield (RTY or YRT), sometimes Rolled Through Yield is the probability of an item completing all opportunities for defects in a process without having a defect. In essence, it’s the proportion of the items you start work on that will make it all the way to finished goods without reworks.

This is an important metric for Six Sigma processes, as it will have a strong correlation with both DPMO and the cost of quality, two of the most important things in Six Sigma. It will also make clear the waste that is occurring through reworking defective product, which will be hidden if you only measure those units that are disposed of.

## What is Yield?

If you have a process where you make units, you will have a certain amount of good (defect free) units coming out, and a number of defective units, which are any units with at least one defect.

The number of good units as a percentage of all the units going through the process will be the **yield **of the process.

Yield % = good units / total number of units

So a process where for each 100 units there are 98 defect free and 2 with defects, your Yield % is 98%.

## First time yield

Traditionally, you would look at yield by looking at how many of your products end up with the customer, and how many end up as scrap. If a product comes through with minor issues, these are fixed and it still counts as part of your yield.

Six Sigma instead looks at ‘first time yield’ (FTY), or the amount of product that passes their first inspection. This reflects that these minor issues will still cost your organization time effort and money, that is often hidden from view. For an efficient operation, we need to make sure that products are produce right first time to remove these costs, and so first time yield is used.

The hidden rework stations and defect repairs that go on usually unnoticed is called the ‘hidden factory’ in Six Sigma. It is one of the aims of an efficient system to remove this ‘hidden factory’ so that its efforts can be redirected to value added work. Using first time yield and Rolled Throughput Yield (which is based on FTY), you can make this hidden factory visible so that its impact can be known and removed.

## Rolled throughput yield

Most production lines don’t just have one process though, and a product usually has to go through several processes to get from raw material to finished goods. Each of these processes will have a yield of their own.

The rolled through yield is the total of all of these processes, and can be thought of if you start with the raw materials for 100 units, how many defect-free finished goods will you end up with at the end?

The rolled throughput yield is the product of all of the yields of the processes in the chain.

## When is it useful?

A core part of Six Sigma is deceasing the amount of defects that occur in the system. Measuring RTY over time will therefore give you a good indication of the progress you are making. You can even use it to help calculate your cost of poor quality to add a dollar value to your process improvement efforts, helping you to justify and secure resources for your efforts.

It will often therefore first be used in the Define phase of DMAIC, the process improvement methodology. You can use it as part of your Project Charter to get sign-off for the project, as you can use it to quantify the improvements made. You will also want to measure it as part of your baseline data during this phase.

Rolled Through Yield is a metric that will be affected by a large proportion of the issues in your organization. By investigating your RTY and the reasons for it being lower than you would like, you can quickly find the problems that are causing you the biggest quality issues. This makes it a fantastic tool for finding Six Sigma projects, as by focusing on improving this metric, you can quickly improve your organization and reduce your quality costs.

## Worked example

For example if you have three processes, P1, P2 and P3 of first time yields 80%, 75% and 90% respectively. In other words for each 100 items going through process 1 you’d get 80 good units, for 100 items going through process 2 you’d get 75 good units, and for 100 units going through process 3 you’d get 90 good units.

### What’s your Rolled Throughput Yield (RTY)?

- Putting 100 units through process 1 as we’ve said will give you 80 good units, with 20 being rejected as defective
- The 80 units will go through process 2, from which we’ll get 80 x 75% = 60 good units, with another 20 being rejected at this stage
- The 60 remaining units will go through process 3, for which we’ll get 60 x 90% = 54 good units, with 6 being rejected

Our rolled through yield is therefore the 54 good units, so 54/100 = 54%. This is the three process yield percentages multiplied together.

## Rolled throughput yield formula

The formula for a three-stage process becomes:

Rolled throughput yield (RTY) = Y1 x Y2 x Y3

Where Y1 is the yield % of process 1, Y2 is the yield of process 2 etc. Rolled throughput yield is therefore the ‘yield’ for the chain of processes. If your chain is longer, you simply add (well multiply) the yields on to the end of the formula.

The rolled throughput yield is a key metric for production. Increasing it will increase the percentage of good units from each batch of raw material. It can often most easily be improved by improving those processes with the lowest yields, as this will have the largest effect on the rolled through yield.

You can also calculate it from your Defects Per Unit (DPU), using the formula:

RTY = e-DPU

where DPU is the number of defects divided by the number of defects produced

## RTY on complex processes

It soon becomes obvious that with modern complicated processes the need for high levels of quality and reaching Six Sigma becomes urgent. If you have a process with many steps, even seemingly high yields can cause huge issues.

To illustrate this, 35 processes in a row each with 98% yield will give a RTY less than 50%! This means you will be producing more scrap than good units! In complicated processes with lots of steps or opportunities for error, you will need to have very good processes to keep RTY at acceptable levels.

This is easy to see if you map yield against cumulative yield (cumulative yield equals RTY on the last process):

In the 12 process operation, the yield on each of the processes is over 80% (which can be easily hidden by reworks), but the RTY is only 28.4%. This would lead to huge amounts of waste through reworking the products to make them sellable.

In a 3 step process each with 90% yield, your rolled through yield will be 72%, which is a huge amount of waste. In a 20 step process, this drops to 12%; even if these errors are later fixed your ‘hidden factory’ will end up using up a large proportion of the resources of your organization.

You can’t underestimate the value in measuring RTY in complex processes, as it can uncover the true scale of the losses to the organization.

## Maximum allowed yield for a target RTY

You’re likely to want to have a target Rolled Through Yield so that you can improve your process. In the example above, the RTY of 28.4% would be costing the organization a huge amount of money.

Say you give yourself the medium term target instead of 90%, which would be a huge improvement. What are the yields for each process?

The 12 yields are multiplied together, so the target yield can be worked out from this:

Target Yield (N processes) = RTY1/N

To get to 90% for 12 processes, each of your processes should target:

Target Yield (12 processes) = 0.91/12 = 99.1%

If any of your processes come in below 99.1% yield, your other ones will need to be higher to compensate. If any of your yields are below 90%, it will be impossible for your RTY to hit your target, whatever the other yields are.

## RTY in the real world

The above works for a simple line process, but the real world doesn’t work like that. Different product lines and even the same product for different customers can have different steps. In the above example, some products might miss out processes 3 and 8, giving them a different RTY.

You have two real options when it comes to coping with this:

- Only calculate the Rolled Through Yield for one product type (the one that will have the biggest effect on your business), and work on improving that one.
- Calculate a weighted average RTY by averaging over the different product lines:

Weighted average = RTY1 x Product 1 % of total output + RTY2 x Product 2 % of total output etc. This will give you your Rolled Through Yield for your entire output, which can be more useful to target improvements on.

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