Statistical
Rolled Throughput Yield (RTY = PRODUCT) & Hidden Factory DPU formulas
Multiply sequential step First-Pass Yields with PRODUCT(B2:B5) to expose multi-step "Hidden Factory" rework loss and Poisson Defects per Unit (-LN(RTY)).
Combine first-pass yields with compatible denominators
Multiplying stage pass probabilities gives the all-stage first-pass probability when each stage probability is conditional on having passed all prior stages. If using unconditional stage rates, the product needs an independence assumption. Use consistent cohorts and denominators; rates from reworked entrants do not automatically satisfy these conditions. The supplied four rates multiply to 0.755136.
The complement 0.244864 is the modeled fraction failing at least one first-pass check, not a guaranteed fraction in every finite batch or a split between scrap and rework. Under an additional Poisson defect-count assumption, exp(-DPU) is the zero-defect probability, so -ln(RTY) is an implied DPU. It is not a measured defect rate without that model.
| Pipeline Stage | First-Pass Yield (B) | Cumulative RTY So Far | Six Sigma Interpretation |
|---|---|---|---|
| Stage 1: Machining | 0.95 (95.0%) | 95.00% | 5% fail the first-pass check |
| Stage 2: Welding | 0.92 (92.0%) | 87.40% | Compounded loss grows |
| Stage 3: Coating | 0.96 (96.0%) | 83.90% | |
| Stage 4: Final Test | 0.90 (90.0%) | RTY = 75.51% (0.7551) | Modeled first-pass failure = 24.49% | Poisson-implied DPU = 0.2809 |
Calculate multi-stage Rolled Throughput Yield (RTY)
Multiplies step-level First-Pass Yields across any number of sequential process steps.
=IF(OR(COUNT(B2:B5)<>4,MIN(B2:B5)<0,MAX(B2:B5)>1),"Invalid inputs",ROUND(PRODUCT(B2:B5), 4))Hidden Factory rework share (1 - RTY) and Poisson Defects Per Unit (-LN(RTY))
This is a Poisson-model-implied defect count per unit. At zero RTY no finite DPU gives exactly zero defect-free probability, so return No finite DPU. All four rates must be numeric fractions in [0,1].
=IF(OR(COUNT(B2:B5)<>4,MIN(B2:B5)<0,MAX(B2:B5)>1),"Invalid inputs",IF(PRODUCT(B2:B5)=0,"No finite DPU",ROUND(-LN(PRODUCT(B2:B5)), 4)))Try the example
Use the original values or change them to test your understanding.