In this chapter, we will cover the rolled through yield calculation or RTY. RTY is much more useful to us as a metric than first time yield. So for example, if we have 1,000 units and 100 of them have to be scrapped, then we are left with just 90, which calculates as 0.9, or 90% first time yield. Then we’d lose another 50 units at step 2, leaving us with about 94% first time yield. If we imagine that this is a multi-step process, we can skip some steps in between and resume at step 10. At this point, we were down to 795 units entering the final process, and 690 units exiting as good acceptable units at the end. The last step would have 87% first time yield. At a glance, none of these steps are particularly bad, with first time yield percentages in the high 80s to 90s percentile. But there’s more to the story. The formula for rolled throughput yield, or RTY, is the product of the first time yields of each step of the process. The FTY of each step is successively multiplied by the next through a series. Let’s evaluate some actual data. The first time yields of the first three steps of a process are 0.987, 0.958, and 0.996. While these numbers are quite good on their own, when we multiply them we get a product of 0.942. We multiply this times 100, giving us a rolled through yield percentage of 94.2%. Let’s examine this process a bit closer.
Each step in this three-step process has a first time yield well above 90%. So looking solely at these numbers might lead us to think that this overall process is doing pretty well. However, by rolling the yield through from one step to another in the process, we can reveal a very different picture. We calculate that roll through yield that’s only 84.9%. Now, that’s a big deal. When we think about the whole process end-to-end, it isn’t running at all like the 95 or 93 or 96 that we were achieving at the step level. We are experiencing about 15% of everything going through this process being scrapped. So the correct way to assess yield is by using this continued calculation. Again, remember that yield is a percentage of product that has no defect. If we take 1 minus the yield number, we get the percentage of the end product that is defective, or the P(d), for the small d here in the parentheses. So, for example, if we had a first pass yield of 0.9345, and we did the calculation of 1 minus that number, we would find that our probability of a defect factor is 0.055. You and your team may find it helpful to keep a Six Sigma conversion table on hand.
Using a table such as the yield and sigma level, we can take a probability of defect calculation number and quickly find the sigma that it correlates to. In our previous example, where our probability of defect factor was 0.0655, we can determine that we were actually only operating at about 1.5 sigma. In other words, we are operating at only 1.5 standard deviations to the left and to the right of the goal for this particular process. So that particular example shows us that maybe we’re not doing so well, and there’s quite a bit of room for improvement. Another helpful conversion table might show us that if our yield is 30.9%, or if our defects per million is 690,000, then we are operating at a 1.0 sigma, and so on. So, for example, with that 93.3% yield, we’re going to experience 66,800 defects per million. Which is definitely not a good thing for our customers. Metrics such as rolled throughput yield are very helpful in showing the actual performance of our overall process from end to end. With that data, we can determine where we stand in terms of Six Sigma performance.