# How to Link Yield and Defect Rate for Six Sigma

Yield and defect rate aren’t completely independent of each other for Six Sigma. When you have an overall process with a relatively low defect rate — say, a process that produces units with a *DPU* less than 0.10 (or 10 percent) — you can mathematically link the process defect rate to the overall process yield with the following equation:

where e in the equation is a mathematical constant equal to 2.718.

You can find a function or key for raising e to a power on any scientific calculator or computer spreadsheet program. (Look for the e* ^{x}* key on your calculator.)

The actual value of the constant e is 2.71828182845905. . . . The decimal digits of e go on forever, never repeating. But you don’t need to know the details of this curious constant called* *e to excel at Six Sigma.

The power of this mathematical link between yield and defects is that if you can only measure or have only measurements of the defect rate of a process, you can still calculate its rolled throughput yield. A little bit of algebraic contortion provides an equation to calculate *DPU* based only on the rolled throughput yield of a process:

DPU= –ln(RTY)

where ln is the natural logarithm.

Every scientific calculator has an ln button.