Mastering RTY Calculation for Six Sigma Success

The Six Sigma Training program was created using innovative quality improvement methods. The term “Six Sigma” is derived from a field of statistics known as process capability and refers to the ability of manufacturing processes to produce a very high proportion of output within specification. Processes that operate with “Six Sigma quality” over the short term are assumed to produce long-term defect levels below 3.4 defects per million opportunities. Six Sigma aims to improve overall processes to that level of quality or better.

Within Six Sigma, there are common measurements that help track the quality of a business process. Metrics are a vital part of the Six Sigma methodology, equipping project teams with the necessary data to identify problems and opportunities for improvement in organizational processes. One of the most important metrics is Rolled Throughput Yield (RTY), which quantifies a process or product’s overall quality by multiplying the Defects per Million Opportunities (DPMO) of each process step. 

This article will explain RTY, why it’s crucial to process optimization, and how to calculate it. We will also look at real-world scenarios demonstrating RTY calculation.

What is RTY?

RTY is a  measure of quality in a multi-step process. To distinguish it from first-time yield (FTY), FTY is the probability of going through a single step defect-free, while rolled throughput yield is the probability of going through a multi-step process defect-free. So, they’re very much related, but unless you have a process that’s one step (which is rare), roll throughput yield is probably the more high-level metric of process quality.

This formula uses a mathematical concept that people need help understanding. Statisticians and mathematicians, which many of us are not, use this mathematical constant E to calculate the yield of an individual process step. Oftentimes, people say, “Well, how do I get it (e)?” It’s important to note that you don’t need a deep understanding of ‘E’ to use it in a formula. For those without an extensive background in statistics and math, it often involves accepting that the formulas and software can handle the calculations without needing to comprehend every intricate detail.

Overall, RTY helps identify the weakest performing step, the weakest link in the chain, and also helps expose what they call our hidden factories. A hidden factory is a little hidden area of assembly in your factory. It’s extra process steps not documented within the process, but they have to occur to achieve process quality.

Let’s look at a few real-world examples illustrating the significance of RTY:

Example 1: RTY in Software Development

In software development, a product goes through several phases, including requirements gathering, design, coding, testing, and deployment. The RTY represents the probability that a software product moves through all these phases without any critical defects. If each step has a 95% success rate, the RTY would be 0.95^5, approximately 77%.

Example 2: RTY in Supply Chain Management

In supply chain operations, products may go through multiple processes, such as sourcing, manufacturing, quality control, and distribution. RTY could assess the probability that a product is delivered to the customer without any defects or delays based on the quality and efficiency of each process.

Example 3: RTY in Manufacturing

Each station on an assembly line in a factory contributes to the overall quality of the final product. The RTY would be the probability that a product goes through all the stations without defects. If there are ten stations, and each station has a 90% first-pass yield, the RTY would be 0.9^10, which is approximately 34%.

Calculating RTY

Before we explain the RTY formula, we want to emphasize the importance of accurate data in Six Sigma. One of the most common pitfalls of calculating RTY (or any Six Sigma metric, for that matter) is related to data collection. Ensuring data accuracy is crucial. As the saying goes, “garbage in, garbage out.” Now, onto the formula…

The Rolled Throughput Yield (RTY) is calculated by multiplying the First Pass Yield (FPY) or success rate of each step in a process. The formula for RTY is:

RTY = FPY1 * FPY2 * FPY3 * … * FPYn


RTY is the Rolled Throughput Yield.

FPY1, FPY2, FPY3, … FPYn are the First Pass Yields for each step in the process.

By multiplying these individual FPYs, you can calculate the overall probability that a unit will pass through all the steps in the process without defects. If any step has a low FPY, it significantly impacts the RTY, indicating you need to improve that specific area to increase the overall process efficiency and quality.

Fortunately, you don’t have to do this all with paper and pen. There are specialized softwares out there that you can use to calculate RTY. Microsoft Excel offers an add-in called Sigma Excel. There’s also standalone software known as Minitab, considered one of the top options. Another one worth mentioning is JMP. All three are reputable choices. While Minitab is considered top-tier, Sigma Excel provides essential functionality. These software tools cover the basics, including rolled throughput yield calculations, control charts, and most of what’s needed for Six Sigma.

Before we move on, let’s consider a real-life scenario to demonstrate how RTY is calculated: A Customer Service Support Process.

In a customer service call center, there is a multi-step process involved in resolving customer issues. The goal is to calculate the Rolled Throughput Yield (RTY) for the entire process. Here are the steps involved and their respective First Pass Yields (FPY):

Initial Contact and Issue Documentation (FPY1): When a customer initially contacts the call center and the agent documents the issue, there’s an 85% chance that the problem is documented accurately, so FPY1 = 0.85.

Troubleshooting and Resolution Attempts (FPY2): During the troubleshooting and resolution attempts by the customer service agent, 90% of the issues are resolved on the first try, so FPY2 = 0.90.

Escalation to a Senior Support Agent (FPY3): For more complex issues, there’s an 80% success rate of accurately escalating the matter to a senior support agent, so FPY3 = 0.80.

Final Resolution and Customer Satisfaction (FPY4): The final resolution and ensuring customer satisfaction have an 88% success rate, so FPY4 = 0.88.

To calculate the Rolled Throughput Yield (RTY), you multiply these FPY values:

RTY = FPY1 * FPY2 * FPY3 * FPY4

RTY = 0.85 * 0.90 * 0.80 * 0.88

Calculating the above expression:

RTY = 0.85 * 0.90 * 0.80 * 0.88 = 0.5256

So, in this customer service support process, the RTY is approximately 0.5256, or 52.56%. This means that there is a 52.56% probability that a customer’s issue will go through all the steps without any defects and will result in a satisfactory resolution.

Improving RTY for Process Optimization

In the example we provided above, the RTY assesses the overall efficiency and quality of the customer service support process. Based on the data, you can identify areas where improvements may be needed to increase customer satisfaction and issue resolution rates. There is a useful concept here to keep in mind: your process chain is only as strong as its weakest link. In multi-step processes, you often have several steps that perform well but one that underperforms. The key is to focus your efforts on improving the weakest step, as this is likely to yield the best overall results.

So, once you have an overall measure of your process’s efficiency and quality, it’s time to analyze the data. A lower RTY indicates areas in the process where defects or errors are likely occurring. If your RTY is significantly below your desired target or industry benchmarks, it indicates room for improvement. Review the FPYs for each step in your process, and identify which is the lowest. In the case above, FPY3 had the lowest. 

Once you know which critical step will likely have defects, you can use Lean Six Sigma tools and techniques to enhance RTY. For example, Value Stream Mapping (VSM) can help you visualize the entire process and identify areas of waste and inefficiency. 

Common Misconceptions and Pitfalls

There are common misconceptions about Rolled Throughput Yield (RTY) that can lead to incorrect interpretations and misapplications. Some people think it can only be applied to manufacturing, which, as you can see from the above scenarios and examples, is untrue. Also, RTY does not equal product quality. You can have defects in your process and still turn out a good product. RTY measures the cumulative success rate of a process, but it doesn’t consider the specific characteristics or critical-to-quality factors.

Remember: data accuracy is everything when calculating RTY. If you leave a step out and fail to calculate all FPYs, you won’t get the results you need. Do not assume FPY values; you need concrete data to get accurate results and make improvements. Finally, RTY is not a one-and-done measurement. You should monitor and review it regularly to make sure processes are consistently functioning optimally. 


RTY is a valuable tool for evaluating process performance, but it’s important to remember that the goal of Six Sigma is not just to fix immediate issues but to establish a culture of continuous improvement. Regularly monitoring RTY and being responsive to changes in performance will help you identify and address new areas for improvement as they arise.

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