Bill Smith, an engineer at Motorola, introduced his Rolled Through-put Yield theory in the late 80’s. He showed that process yield is very similar to product reliability. Process reliability can be calculated by multiplying the yields of the individual components of a process. Applying that to a sequential process….in order for an entire process to be successful, all the steps of the process must be successful. This is important because it allows us to prioritize our efforts for process improvements. And thus, the need to push processes to levels well beyond 3-sigma was realized, understood, and accepted.

The difference was important because Bill Smith had just completed a study at Motorola when the chairman demanded that the company needed to increase quality and also reduce the cost of manufacturing. Smith’s research showed that the product reliability was correlated to the number of times the part was repaired or reworked in the process. Thus a push was made to reduce the number of times a part was repaired. This meant that the part needed to be right the first time.

Some people confuse rolled throughput yield and first pass yield as one in the same. However, they are not the same. First pass yield is obtained by counting the number of good parts that make it through the process right the first time divided by the total number of parts that enter the process. Say that a product goes through a five-step process. Let’s further assume that each unit has 20 opportunities for a defect.

Suppose we put 100 parts through the process and we observed 5 defects in the 100 units. Further suppose that all five defects occurred on one unit. Thus, 99 parts made it through the process the first time, thus giving the FPY of 99%. Now let’s assume that the five defects occurred on 5 different parts. Now the first pass yield calculation is 95% since there were 5 parts of the 100 that was not right the first time. Thus, the FPY calculation is highly dependent on how the defects are distributed across the units.

On the other hand, the rolled through put yield will be 95% in both cases. If there are 100 units with 5 defects then the expected number of defects per unit is .05 (5defects/100 units). Thus we would expect 5 out of 100 parts to have at least 1 defect. This gives a rolled throughput yield of 95% regardless of where or when the defects occur. Thus the rolled throughput yield is a more consistent measure of the process than the first pass yield.

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