Rolled Throughput Yield
Also known as RTY · rolled yield · first pass yield chain · hidden factory · cumulative yield · yield through n steps
Worked example: five steps at 99% each → 95.099% rolled yield — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
Rolled Throughput Yield explained
Rolled throughput yield is what actually gets through a chain of steps with no rework at all: when every step has the same first-pass yield. Five steps at 99% each is not 99% and not 95% by subtraction, it is . One unit in twenty is touched twice somewhere along the way.
Extend it and the arithmetic turns unforgiving. Twenty steps at 99% is 81.8%. Fifty steps at 99% is 60.5%. This is why long processes with individually impressive stations still disappoint, and why the phrase "hidden factory" was coined: the rework loops that produce the difference between 100% and RTY are staffed, floored and paid for, but they appear on no process map because each one is small.
Turn the formula around and it becomes a specification tool. To hold 95% overall across twelve steps, each step needs , so 99.57% per step. Anyone who has quoted a 95% target on a twelve-step process without doing that division has promised something quite different from what they think.
Rolled Throughput Yield formula
- = Rolled throughput yield
- = First-pass yield of each step
- = Number of steps (steps)
Missing one of these? Work it out first, then come back
- Number of steps — Economic Order Quantity (Wilson EOQ), Reorder Point