Rolled throughput yield

Of 1,000 starts, 960 pass A first time, 912 of those also pass B first time, and 894 of those also pass C first time. Multiplying these conditional survivor ratios gives 89.4% end-to-end first-pass yield without assuming independence. If 86 failed units later recover, 980 finish acceptable, or 98% of original starts. Unlinked stage yields may count different populations.

Minitab defines rolled throughput yield as first-pass success across the route and multiplies step yields excluding rework and scrap. Check whether the factors follow the same units. Minitab throughput and rolled throughput yield

Define what “right first time” covers

Record the product, route revision, starting cohort, acceptance criteria and treatment of repair, retest, scrap and unresolved units.

ASQ's first-pass-yield definition excludes units scrapped, rerun, retested, returned or diverted into offline repair. Recovering a unit later does not erase its initial failure. Applied across a route, an observed right-first-time unit must satisfy the specified first-pass conditions at every required stage. ASQ quality glossary, “First pass yield”

Three different quantities can appear under a yield heading:

Keep these labels in exports and dashboards. A percentage without its basis cannot establish whether two reports disagree or simply answer different questions.

Conditional multiplication does not require independence

For two first-pass events A and B, the probability of passing both is P(A and B) = P(A) × P(B given A). If the events are independent, the conditional term can be replaced by P(B). Penn State's probability course distinguishes this conditional multiplication rule from the product of probabilities for independent events. The same reasoning extends to successive conditional stages. Penn State STAT 414, independent events

In production terms, the denominator for the next conditional yield must be the group that has already passed all earlier steps first time. Those units may be identified analytically even if repaired units physically continue alongside them. Do not mix repaired units into a conditional survivor denominator while continuing to interpret the product as an exact survivor fraction.

Original example: linked survivor counts

Assume an invented 1000-unit cohort follows three required stages. Of the original units, 960 pass A first time. Among those 960, 912 also pass B first time. Among those 912, 894 also pass C first time. Every unit's route status is resolved.

Using unrounded ratios, the product is (960/1000) × (912/960) × (894/912) = 894/1000 = 89.4%. The intermediate counts cancel. No independence assumption is needed. The failure groups also reconcile: 40 first fail at A, another 48 lose first-pass status at B, and another 18 lose it at C; 40 + 48 + 18 + 894 = 1000.

Suppose 86 of those 106 first-pass failures eventually become acceptable after approved recovery and the other 20 are scrapped. Final acceptable output is 894 + 86 = 980 units, or 98% final yield. The gap from 89.4% is 8.6 percentage points, representing recovered output relative to the original starts. It does not quantify recovery attempts or hours; a unit may need more than one attempt.

Original example: marginal yields are insufficient

Now take a different 100-unit cohort in which every unit reaches both stations after any required correction. Each station has ten initial failures, so each marginal station yield is 90%.

If the same ten units fail at both stations, 90 units pass the entire route first time. If the failure groups are disjoint, only 80 units do. Multiplying 0.9 × 0.9 gives 81%, which is neither observed result. The station percentages alone do not identify how failures overlap.

An 81% model may be justified under an independence assumption for a suitably defined population, but report that assumption. Direct unit histories can instead measure the intersection of first-pass successes. Shared material problems, common setups or other dependencies are reasons to investigate the assumption rather than declare stations independent merely because they are physically separate.

Defect models and complex routes

RTY terminology is not uniform across all quality methods. ASQ's published abstract for Spencer Graves's Six Sigma Rolled Throughput Yield, Quality Engineering, December 2001, volume 14(2), pp. 257–266, distinguishes Poisson defect-count formulations from binomial unit-count formulations. It also warns that parallel paths with different quantities can produce quality indices that are not literally proportions of units. This article's serial survivor example should not be substituted for every such model. ASQ publication abstract

For an assembly requiring multiple components, establish what a “unit” means and how many component instances are required. Minitab's Product Report documentation, for example, uses component complexity in computing a rolled yield for multiple required instances. That is a documented model with defined inputs, not permission to multiply unrelated department yields into an assembly acceptance rate. Minitab Product Report calculations

Use in planning and improvement

For an independent-yield planning model with fixed route yields of 0.95 and 0.96, predicted joint yield is 0.912. Delivering 456 first-pass good units would require 456/0.912 = 500 starts in expectation. That is an average-model calculation, not assurance that a particular 500-unit batch supplies 456. Variation, changing mix, recovery capacity and order-specific constraints require separate planning treatment.

Before combining shifts or products, preserve their counts and route differences. Do not take an unweighted average of percentages from unequal cohorts. Pending work and alternate routes need explicit treatment; an unfinished unit is not evidence of a first-pass failure. A zero denominator gives no estimate.

Use RTY with defect modes, stage counts, recovery effort, scrap and final delivery evidence. A high RTY does not prove that inspection detects every defect or that the product meets reliability requirements. The online definitions are undated living pages reviewed on 2026-11-02; the ASQ paper's December 2001 publication details are explicitly identified above, rather than inferred from a website footer.

Related reference

First-pass yield · Production planning guides