Scenario
Process Integration Engineers saw in the quarterly report: Each station's yield was between 98-99%, which looked healthy. But the overall shipping yield was only 55%.
The manager asked: "Which station is causing the problem?"
No one could answer immediately, because everyone only looked at individual stations; no one had calculated the stacked yield.
Stacked Yield Formula
Stacked Yield = Y1 × Y2 × Y3 × ... × Yn
Multiply the yield of each station to get the final yield.
Mathematical Explanation:
- 40 stations, 99% yield per station
- Overall Yield = 0.99^40 = 0.669 = 66.9%
- 98% yield per station: 0.98^40 = 0.446 = 44.6%
- 99.5% yield per station: 0.995^40 = 0.819 = 81.9%
A 1% difference in yield results in an overall gap of over 37% after 40 steps. This is why improving the yield of each station is crucial.
The Difference Between FPY and RTY
FPY (First Pass Yield)
= The proportion that passes the first time without rework
RTY (Roll Throughput Yield)
= Stacked yield after considering rework
If your stations allow rework, FPY will be higher than RTY. But rework itself is waste—RTY is the true indicator of process efficiency.
Which Station's Improvement Offers the Greatest Benefit?
By using partial derivatives (differentiating with respect to each station's yield), one can determine which station's improvement is most effective:
Conclusion: Improving the worst-performing station by 1% yields the largest increase in overall yield.
Intuitive understanding: Overall Yield = Weakest Link × Other Links. Improving the weakest multiplier yields the highest benefit.
Practical approach:
- List the yields of all stations
- Identify stations that are more than 2 standard deviations below the average
- Prioritize resources to improve these stations
Reverse Calculation for Yield Target Setting
Given the overall yield target, reverse calculate the required yield for each station:
Target Overall Yield = 90%, Number of Stations = 40
Required Yield per Station = 0.90^(1/40) = 0.9974 = 99.74%
This calculation tells you how high the standard for each station needs to be to achieve an overall target of 90%.
Golden Quote
"Stacked yield is the process integration engineer's magnifying glass—a small problem at an individual station becomes a gaping hole at the output. Behind every 99% lies a 1% cost, and 40 such 1% losses add up to a 33% loss."