rolled throughput yield (rty)
**Rolled Throughput Yield (RTY)** is the **cumulative probability of passing all process steps without defects** — calculated by multiplying individual step yields, revealing true process capability better than final yield alone since it accounts for hidden rework.
**What Is RTY?**
- **Definition**: Product of all individual process step yields.
- **Formula**: RTY = Y₁ × Y₂ × Y₃ × ... × Yₙ
- **Purpose**: Measure true first-time-through capability.
- **Insight**: Reveals hidden rework and inefficiency.
**Why RTY Matters**
- **True Capability**: Shows actual first-pass success rate across entire flow.
- **Hidden Factory**: Exposes rework loops not visible in final yield.
- **Cost Impact**: Lower RTY means more rework, higher cost.
- **Bottleneck Identification**: Pinpoints weakest process steps.
- **Improvement Focus**: Guides where to focus improvement efforts.
**Calculation**
```python
def calculate_rty(step_yields):
rty = 1.0
for yield_value in step_yields:
rty *= yield_value
return rty * 100
# Example
steps = [0.98, 0.95, 0.97, 0.99, 0.96] # 5 process steps
rty = calculate_rty(steps)
print(f"RTY: {rty:.1f}%") # 85.7%
```
**RTY vs Final Yield**
- **Final Yield**: 95% (after rework)
- **RTY**: 85% (true first-pass)
- **Difference**: 10% hidden rework
**Improvement Strategy**: Focus on lowest-yield steps first for maximum RTY improvement.
RTY is **the truth teller** — revealing the real efficiency of manufacturing by accounting for all rework, making it essential for identifying true improvement opportunities.