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## Six Sigma–Rolled Throughput Yield and Normalized Yield

In the last post, the authors Mikel Harry, Ph.D., and Richard Schroeder of the book Six Sigma:  The Breakthrough Management Strategy Revolutionizing the World’s Top Corporations, discussed the fact that first-time yield (the percentage of units that are defect-free) is a crude measure of quality, whereas throughput yield (the percentage of defects per defect opportunity) is a better measure of quality.

However, both first-time yield and throughput yield are terms that apply to a single step of the manufacturing process.   What are the equivalent concepts for multiple-step manufacturing processes.     The final yield is the multiple-step version of the first-time yield.    If out of 100 units that go into the assembly line, 90 units come out of the final step of the assembly process defect-free, then the final yield is 90%.    Now the multiple-step version of throughput yield is called the rolled throughput yield.

If a product goes through four steps in the manufacturing process, and at each step the throughput yield is 50%, then the rolled throughput yield will be 50% x 50% x 50% x 50% = 6.25%.    However, it is unlikely that each step of the process will have a throughput yield that is the same; they will likely all differ.    If you have four throughput yields of 100%, 50%, 25%, and 50%, this will also create a rolled throughput yield of 6.25%.

If you have a rolled throughput yield and you want to find out what the “normalized” yield is of each process, what you are doing is computing the throughput yield that each process would have to have, on average, to create that rolled throughput yield.   To do this, if you have n steps in the manufacturing process, then the normalized yield will be the nth root of the rolled throughput yield.  In the example given on pp. 88-89 of the book, a rolled throughput yield of 36.8% for a process with 10 steps has a normalized yield of 90.5%.    This is because 90.5% multiplied by itself 10 times would create a rolled throughput yield of 36.8%.

In the same way that throughput yield is a more accurate metric than first-time yield, rolled throughput yield is a more accurate metric than final yield.    Using the more accurate metric is a way of really getting a handle on the quality of one’s products.   So a metric is essentially a type of mathematical tool for creating change.   But creating change that improves quality takes more than the right tool; it takes the right strategy, which is the subject of the next chapter “The Breakthrough Strategy”.  It is this chapter which is the subject of the next series of posts.

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