The concept is analogous to Rolled Throughput Yield, i.e the output of process1 is the input of process2 while the output of process2 is the input of process3. If you have the yield of all three processes, the overall yield = output of process3/input process1 = Y1*Y2*Y3. You don't average as AVG(Y1,Y2,Y3).
The same goes with OEE, you can only utilize the fraction that is available, and %correctly utilized only makes sense from the fraction that is utilized. That is why you take their products