Cumulative Yield
Cumulative yield is the overall fraction of good product that actually results from the total manufacturing investment, calculated as the product of every individual yield stage along the entire flow — line yield through the fab, die yield on the wafers that survive, package yield through assembly, and test yield at final electrical test — multiplied together rather than simply averaged. Because these stages multiply rather than add, even individually strong yields at each stage compound into a meaningfully lower overall number, which is exactly why cumulative yield functions as the true bottom-line metric for manufacturing economics.
Cumulative yield is built from four genuinely distinct stages, each measuring a different kind of survival at a different physical point in the manufacturing flow — [line yield](line-yield) measures wafer survival through the fab, die yield measures the fraction of functional die on wafers that do survive, package yield measures die survival through assembly, and test yield measures the fraction of packaged devices that pass final electrical test. Because each stage is measuring something physically different — wafers lost to breakage versus die lost to defects versus packages lost to assembly damage versus units lost to electrical failure — improving one stage does essentially nothing for the others, which is exactly why yield-improvement programs have to attack each stage with a genuinely different toolkit rather than treating "yield" as one undifferentiated target.
Die yield — the fraction of die on a surviving wafer that actually turn out functional — is typically the dominant component of cumulative yield by a wide margin, because die-level defects (random, systematic, and parametric combined) are usually responsible for a far larger fraction of total loss than wafer breakage, package failures, or test escapes individually. This dominance is exactly why most yield-engineering effort concentrates on die-level yield mechanisms — the random, systematic, and parametric yield-loss categories — rather than spreading evenly across all four stages: die yield is both typically the lowest of the four numbers and the one with the most room for meaningful improvement.
The multiplicative relationship between stages means that cumulative yield is always lower than even the lowest individual stage yield, and the gap between cumulative yield and that lowest stage grows larger as more stages are chained together — a mathematical consequence that makes cumulative yield look worse than any single stage would suggest in isolation. Four stages each individually running at a respectable 95-99% can still compound down to a cumulative number well below 90%, simply because multiplying four numbers each slightly less than 100% compounds that shortfall rather than averaging it out — which is exactly the trap that looking at any single stage's yield number in isolation can hide.
Identifying which single stage is the current bottleneck — the lowest-yielding stage in the chain — is the single highest-leverage piece of information cumulative yield analysis provides, because improving the bottleneck stage moves the overall cumulative number proportionally more than equal improvement effort spent on any already-strong stage. A die yield of 80% sitting alongside line, package, and test yields all above 97% means essentially all of the improvement opportunity available to that cumulative yield chain lives specifically in die yield — pushing package yield from 99% to 99.5% barely moves the overall number, while pushing die yield from 80% to 85% moves it substantially, which is exactly the kind of prioritization cumulative yield decomposition is meant to surface.
Cumulative yield determines the true cost per good die, because every manufacturing cost incurred along the entire flow — wafer processing, die fabrication, packaging materials and labor, test time — gets absorbed collectively by only the fraction of units that actually survive every single stage to become sellable product. A product with 74% cumulative yield effectively has to recover the full cost of processing roughly 1.35 wafers' worth of input for every one wafer's worth of good shippable output, which is exactly why even a modest improvement at any stage in the chain — but especially at the current bottleneck stage — translates directly into a meaningfully lower cost per good die across the entire product.