Free Rolled Throughput Yield (RTY) Calculator

Step 1: Batch Volume, Process Stages, Step Yield %, Material/Labor & Rework/Scrap Costs

Multi-Stage Quality & Process Parameters

⚙️ Process Flow & Step Yields

Annual Units Started (Batch Size)

Number of Process Steps

Average First Pass Yield per Step (%)

💵 Cost Structure & Hidden Factory Waste

Material Cost / Unit ($)

Direct Labor / Unit ($)

Rework Cost / Defect ($)

Scrapped Defect Ratio (%)

Rolled Throughput Yield

85.9% RTY

85,907 / 100,000 units first-pass defect-free across 6 stages

Hidden Factory Waste

$364.7K/yr

Hidden Factory Waste (11,480 reworks + 3,827 scraps)

True Unit Cost

$67.14

+6.6% inflation over nominal $63.00 bill of materials

Process Capability

~3.5σ Level

Good Industrial Control (RTY 85%-95%)

Defect Cascade Matrix: Process Steps vs. Step Yield (%)

Simulates Rolled Throughput Yield (RTY %) and Total Annual Hidden Factory Waste ($K/yr) across process lengths and step yields.

Process Steps	92% Step Yield	95% Step Yield	97% Step Yield	98.5% Step Yield	99.5% Step Yield

Lean Six Sigma Principles

Understanding RTY & The Hidden Factory

Key operational quality principles governing multi-stage process yield:

The Illusion of Final Inspection: A high final-test pass rate (e.g. 98%) often masks the fact that 25% of products required multiple rework loops before passing.
Multiplicative Compounding: Total yield decreases exponentially with the number of process steps: $RTY = prod Y_i$. Adding inspection or touch-up steps without fixing root causes reduces true throughput.
The Hidden Factory Cost: Rework consumes skilled technician hours, slows production cycle times, creates buffer inventory WIP, and increases field warranty failure rates.
Poisson Defect Modeling: In complex operations, Defects Per Unit ($DPU = -ln(Y)$) captures the true occurrence rate of multiple defects on single units.

Evaluate defect rates in the Six Sigma DPMO Lab.

Mathematical Formulation

RTY & defect cascade equations

RTY = Y_1 × Y_2 × dots × Y_n = ( Step_Yield )^{Steps}

DPU_i = -ln( Y_i )

Total_DPU = sum_{i=1}^n DPU_i = n × [ -ln( Step_Yield ) ]

Total_Defect_Occurrences = Units_Started × Total_DPU

Scrapped_Units = Total_Defects × Scrap_%

Hidden_Factory_Waste = ( Scrapped_Units × Scrap_Cost ) + ( Reworked_Units × Rework_Cost )

True_Unit_Cost = ( Total_Spend + Rework_Cost ) / Good_Units_Delivered

Calculate statistical capability in the Process Capability (Cpk) Lab.

FAQ

Rolled throughput yield questions

What is Rolled Throughput Yield (RTY)?

Rolled Throughput Yield (RTY) is the probability that a unit will pass through all sequential stages of a multi-step manufacturing or service process without requiring rework or producing defects: RTY = Y_1 * Y_2 * ... * Y_n.

How does RTY differ from traditional First Pass Yield (FPY)?

Final-stage or aggregate FPY often hides intermediate defects that were repaired along the way. RTY measures true first-time-right quality, exposing the 'hidden factory' of costly rework loops.

What is the 'Hidden Factory' in Lean Six Sigma?

The hidden factory refers to the unbudgeted labor, machine time, floor space, and scrap materials consumed solely to fix, re-inspect, and test defective items produced during upstream manufacturing operations.

Why does RTY drop drastically as process steps increase?

Because yields compound multiplicatively. A 10-step process where each step has a 98% yield results in an overall factory RTY of 0.98^10 = 81.7%, meaning nearly 1 in 5 units requires rework or is scrapped.

Can I export the RTY and hidden factory audit to CSV?

Yes. You can export complete multi-stage yield breakdowns, defect cascades, rework and scrap waste valuations, and 6x5 sensitivity tables as a UTF-8 CSV spreadsheet with formula defense.

Continue Exploring Lean Quality & Operations Tools

Explore our Operations & Quality Hub, evaluate process capability in the Process Capability (Cpk) Lab, analyze defect rates in the Six Sigma DPMO Lab, calculate plant equipment efficiency in the OEE Lab, or calculate quality prevention costs in the Cost of Quality Lab.