The manufacturing yield determination is based on the definition of the probability of obtaining a defect. The FTY is the percentage number of units produced without defects, prior to test or inspection. It is different than the traditional yield, which includes rework and repair.
The Poisson distribution, as discussed in the previous chapter, is a good basis for calculations of defects, especially when the number of possibilities or outcomes of defects is large and the probability of getting a defect at any time or region is small. In this case, the Poisson distribution can be simplified from Equation 3.7 as follows:
When an assembly is made from similar parts or operations, such as the transistors in an IC or soldering in a PCB, then the FTY for the assembly can be derived from the total DPUs of the individual operations. Sometimes, this yield is referred to as total yield (Yt) or assembly estimated yield (YA) to distinguish it from FTY. It can be derived a follows:
In six sigma quality, the DPUs are very small, and approximations can be performed without sacrificing the accuracy of the yield estimates. In this case, the general equation for yield can be further simplified by the power series expansion of exponential functions:
Since the DPU is small in six sigma quality (0.000034), we can ignore all the terms beyond the first two:
where n is the number of operations to be analyzed for defects.