First-Pass and Rolled Throughput Yield: Track Repairs Across Garment Stages

A factory can ship every garment in an order and still spend many hours repairing it. Final acceptance records what eventually became usable. First-pass yield records what met the agreed requirements without another attempt. Both measures matter, but they answer different questions.

The distinction becomes harder when work crosses several departments. A garment may pass sewing, fail finishing, and pass packing after a repair. The three department rates may hide an important fact. How many garments crossed the whole route without repair? That answer needs linked records for the same pieces.

This guide builds one original garment example from those records. All quantities, times and acceptance outcomes are invented for the calculation. They are not factory benchmarks, sampling plans or suggested targets.

Define the first pass before counting it

First-pass yield is often shortened to FPY. It measures the share of entering units that complete a defined process correctly on the first attempt. The ASQ quality glossary sets out what the first-pass numerator excludes. Its list includes scrap, rerun, retest, return and repair. A successful repair does not change the original attempt into a first-pass success.

For a fully observed group at one checkpoint:

First-pass yield = units passing on their first attempt ÷ units entering the defined process × 100.

State what counts as a unit. It could be a garment, panel, inspected roll or production batch. Do not put failed batches over a denominator of garments. The percentage would mix two different kinds of observation.

Right first time, or RFT, is also used for process quality. When a factory uses that name, write down its exact rule. Does it mean passing the first recorded check? Does it cover every requirement without repair, or use some other rule? A label on a dashboard cannot settle that difference.

An inspection record also has a limit. A first recorded pass does not prove that no earlier repair occurred. Operators may correct faults before the formal check. A strict no-rework measure needs to capture that work too. Otherwise, describe the result as first-check acceptance within the recorded boundary.

Define the start, end and requirements for each stage. Sewing exit may cover seam and assembly checks. Finishing may add appearance and measurements after the specified treatment. Packing may check identity, labels and packing requirements. A later failure need not mean that an earlier check was wrong. The stages may test different features.

Keep final acceptance beside first-pass yield

Final acceptance measures units that eventually meet the defined release requirements. It can include pieces that failed earlier and then passed after an approved repair. A report that uses only this figure can hide substantial repeat work.

Neither measure should replace the other. A high first-pass result cannot clear a shipment on its own. Any required final check must still be complete. A high final acceptance result does not show that the process was right first time.

The same applies to scrap. A scrapped piece may never reach packing. It still belongs to the original entering group. Record its exit and reason. Give any later replacement garment its own identity. Show how the report treats that new entry.

A useful report keeps three views. It shows first-attempt quality and what finally happened to each piece. It also records the work needed between those points. These views connect quality to the actual production route without erasing its history.

Follow one closed garment cohort

Consider a cohort of 1,000 distinct garments. A cohort is a named group followed through the same reporting route. Here every garment reaches three checkpoints: sewing exit A, finishing B and packing C.

The example records each garment's first attempt at each checkpoint. Any failed garment is repaired and checked again before moving onward. No piece is scrapped, lost or left unresolved. At the end, all 1,000 are accepted. These assumptions keep the example closed and make the denominators easy to inspect.

The table groups garments by their three first-attempt results. P means pass and F means fail. Each garment belongs to exactly one row. Later repairs do not change the letters.

The rows total 1,000. There are 885 garments with no first-attempt failure on the defined route. The other 115 fail at least one checkpoint. Some fail at more than one.

The three stage results are:

These stage percentages include all 1,000 garments at each checkpoint. A garment repaired after A can still pass its first attempt at B. The separate rates show each stage on its own. They do not reveal the number that passed all three first attempts.

Calculate yield through the whole route

Rolled throughput yield, often called RTY, concerns success through a sequence of processes. Minitab's throughput-yield guidance describes throughput without rework or scrap. It calculates rolled yield by multiplying process yields. Its worked route follows the surviving first-pass group from one step to the next.

Our cohort lets us calculate the observed route result directly:

Observed route first-pass yield = 885 ÷ 1,000 × 100 = 88.50%.

We can also build a matching multiplication from nested groups. First, 920 of the original 1,000 pass A. Among those 920, exactly 900 also pass B. Among those 900, exactly 885 also pass C.

The corresponding conditional fractions are:

A first pass: 920 ÷ 1,000.

B first pass among garments that passed A first time: 900 ÷ 920.

C first pass among garments that passed both earlier stages first time: 885 ÷ 900.

Multiplying gives:

Route yield = (920 ÷ 1,000) × (900 ÷ 920) × (885 ÷ 900) = 0.885.

The middle counts cancel, leaving 885 ÷ 1,000. This calculation uses the actual linked groups. It does not assume that the three first-attempt results are independent.

This uses the conditional multiplication rule. Emory University's probability notes explain the rule. Applying it through three events gives the chain used here. Each later fraction must refer to the group that satisfied the earlier conditions.

The B and C conditional percentages are about 97.83% and 98.33%. They differ from the department rates of 95.00% and 97.00% because their denominators differ. Keep the original fractions in the calculation and round only the displayed result.

Do not rename the conditional B result as the whole finishing department's FPY. It describes a selected subset: garments with an earlier first-pass success. Both figures can be useful if their labels explain who is included.

Check what a product of department rates means

Multiplying the three whole-cohort stage rates gives another number:

Stage-rate product = 0.92 × 0.95 × 0.97 = 0.84778, or about 84.78%.

That is 3.72 percentage points below the observed 88.50% after rounding. The difference is not an arithmetic error. The two calculations use different information.

The stage-rate product uses three separate shares. The observed route result uses the joint history of individual garments. In this example, failures overlap across stages. The pattern table supplies that overlap; the three department totals do not.

Some organizations define their RTY indicator as the product of stage FPYs. If that is the agreed convention, retain it and label it clearly as the stage-rate product. Show the directly observed route yield beside it when linked data are available. Do not present both as though they were the same measured count.

Using separate stage probabilities to predict a joint outcome needs suitable assumptions. NIST's definition of statistical independence explains the product relationship for independent events. Independence should not be assumed merely because different departments perform the work. Shared material, earlier faults and repair history can connect their outcomes.

The conditional chain avoids that assumption. For a route with several stages, it needs complete linked counts. Where data are incomplete, state the model and its limits. A precise spreadsheet result cannot recover missing garment histories.

Separate failed units, failed stages and defects

The cohort contains 80 first failures at A, 50 at B and 30 at C. Added together, these give 160 failed garment-stage records.

They do not mean 160 different garments failed. The pattern table shows only 115 distinct garments with at least one first failure. A garment failing both A and B contributes two stage records but remains one garment.

The 160 records are not necessarily 160 defects either. One failed inspection can reveal several faults. A single garment might have a seam fault, a label fault and an appearance fault at the same visit. Store the verdict and the defect details separately.

NIST's guidance on attribute charts separates two kinds of measure. One counts nonconformities. The other measures the fraction of units that do not conform. That distinction matters before any chart is chosen. There can be more defects than inspected garments. The count of distinct failed garments cannot exceed its defined group.

For decisions about which faults to tackle, use the separate defect records. ApparelDiary's Pareto chart guide develops that ranking. Keep the garment IDs. A later review can then distinguish frequent defects from widely affected pieces.

Record repeat visits without changing the first pass

Now examine repairs at sewing checkpoint A. Its 80 first failures all enter repair. Suppose 60 pass the first recheck. The remaining 20 need a second repair and then pass the second recheck.

There are 100 repair cycles at A: 80 first repairs plus 20 second repairs. There are also 100 rechecks. The original 1,000 first checks and those rechecks create 1,100 inspection visits.

Successful inspection events total 1,000. These comprise 920 initial passes, 60 passes at the first recheck and 20 at the second. Dividing successful events by visits gives:

Visit pass percentage = 1,000 ÷ 1,100 × 100 = about 90.91%.

That is not A's first-pass yield of 92.00%. It is also not its final acceptance of 100%. It answers a third question about inspection events.

Keep an attempt number within each garment and checkpoint. A second visit at A is not a new garment and does not reset its first-attempt result. Nor should a repeated scan of the same visit create an extra event. The record needs enough detail to tell a duplicate scan from a real reinspection.

When a repair sends work backward to an earlier stage, retain the route link. Define what the return means. Is it another attempt within the same process, or entry into a separately named process? Choose the rule before comparing results across weeks.

Convert repair history into a visible workload

Assume every first failure at B and C is repaired successfully in one cycle. The total repair cycles are then 100 at A, 50 at B and 30 at C: 180 cycles across 115 affected garments.

Use illustrative handling times of six minutes per A repair cycle, four per B cycle and three per C cycle. The resulting repair work is:

Repair minutes = (100 × 6) + (50 × 4) + (30 × 3) = 890 minutes.

If each of the 180 rechecks takes two minutes, reinspection adds 360 minutes. The combined repair and recheck workload is 1,250 minutes, or about 20.83 hours.

These invented times cover only the stated repair and recheck tasks. They exclude queues and any travel outside the task times. Management effort and other losses are also outside this total. They are not automatically overtime savings or extra shipment capacity.

ASQ's cost-of-quality framework places pre-delivery rework within internal failure costs. Turning minutes into money still needs an agreed costing basis. Avoid multiplying every minute by a wage and calling the result cash saved.

Resource limits need a separate review. ApparelDiary's rework loops and inspection capacity calculation explains that next step. The cohort history provides the workload inputs. The capacity review adds the resource and time boundaries.

Build records that can reproduce the report

Start with a stable garment identity. A bundle number can support handling. Yet bundles may split, merge or exchange pieces. The number may then fail to preserve each garment's history. Choose identification that matches the claims the factory wants to make.

Keep the unit record separate from its event records. Each event should identify the garment, checkpoint, attempt, time, verdict and requirement version. Name the inspector or system that made the decision. Add any repair link and the later disposition.

The GS1 traceability framework organizes traceability around events and their key data. That general principle is useful here. The proposed factory fields form an application design. They do not establish that the report meets every GS1 requirement.

Protect the first result from silent overwriting. If someone entered a wrong verdict, keep the correction and reason. Record its date and the person who made it. Correcting a wrong record changes the data. A physical repair changes the garment. Keep those actions distinct.

Reconcile the report from the event log. Give each cohort member a known status at every required stage. Use first pass, first failure, not yet assessed or a documented exit. The sums should account for the original group. Missing records belong in an exception list, not in the pass total.

Before release, select several garment histories and rebuild their reported paths by hand. Include a clean pass, a repeated repair, a return to an earlier stage and an unresolved case. This checks whether the software implements the intended definitions.

Handle open work and reporting cutoffs

A shift ends while production continues. Some garments have passed A but have not reached C. Others remain in repair. Counting only completed pieces can favor the fast, simple routes. It may hide the work that needs most attention.

Give the cohort a clear entry rule and a reporting cutoff. Show how many members have completed the whole route and how many remain open. Do not assign an unobserved packing result to pieces that have not been packed.

A provisional report may show stage results for the pieces actually assessed there. Label each denominator and keep the pending count visible. When the full cohort closes, calculate its final route result. Use the original membership and documented exits.

Daily stage reports can still help supervisors respond quickly. They simply answer a different question from a cohort followed across several days. Sewing's Tuesday output and packing's Tuesday output may contain different garments. Multiplying their rates does not create a linked Tuesday cohort.

If the business needs a fixed reporting deadline, agree how open cases are shown. Do not let the dashboard silently drop them or count them as good. A clear incomplete result is more useful than a misleading complete percentage.

Check the inspection system before claiming improvement

Yield depends on what is inspected and how verdicts are assigned. A changed defect definition or weaker check can raise reported yield. Different sampling coverage can do the same. The garments may not have changed at all.

Maintain clear examples of acceptable, unacceptable and borderline work. Resolve disagreements against the approved requirement. Record the conditions that affect judgement. Include lighting, garment state and the measurement method.

Minitab's attribute-agreement guidance recommends repeated ratings in random order. Compare them with known reference ratings where those are available. It also calls for representative appraisers and samples. Use a properly designed agreement study when the inspection system needs formal assessment.

Keep that study separate from the production-yield calculation. Agreement among inspectors does not itself prove a defect rate. A high production pass rate does not prove that inspectors agree. Both questions need evidence.

Combine lots with the correct weight

Consider a separate example with two lots at one checkpoint. A small lot has 90 first passes from 100 entrants. A large lot has 720 from 900.

The combined first-pass yield is:

Pooled FPY = (90 + 720) ÷ (100 + 900) × 100 = 81%.

The simple mean of 90% and 80% is 85%. That gives the small lot the same weight as the large one. It does not answer the question about the share of all entering garments that passed first time.

Pool counts when the units, inspection rules and boundaries are compatible. Keep useful breakdowns by style, line or material family beside the total. A change in product mix can move the factory percentage. No individual process may have improved.

For a comparison over time, examine both the mix and each group's result. Do not reward a department merely for receiving easier work. Explain changes to inspection scope or product requirements alongside the figures.

Use the result to choose the next action

In the main cohort, A has the lowest stage FPY and the most repair cycles. That makes it a sensible place to investigate, but it does not prove the cause lies within sewing. Incoming material, approved construction and prior handling may contribute.

Trace repeated failures through the individual paths. Ask whether pieces failing A also tend to fail later stages. Review their repairs. Was the later fault already present at an earlier check? The linked records can guide this investigation; the percentage alone cannot establish cause.

Test a proposed change under comparable conditions. Keep the acceptance rule, observation coverage and first-attempt definition stable. Review both first-pass performance and final quality. Check that the apparent gain does not come from passing unsuitable work.

The NIST discussion of proportions treats sampled defect fractions within a statistical framework. Our fully tracked cohort describes its own observed outcome. It does not guarantee the same result for the next order or establish a process change by itself.

Questions that often cause reporting errors

Can a repaired garment count as first pass at the next stage?

Yes, if it meets that next stage's requirements on its first attempt there. It still fails the route-wide no-repair measure because its earlier repair remains in the history. Keep local and route results distinct.

Is a final acceptance rate of 100% evidence of perfect production?

It shows the defined group's final disposition. In the example, all garments are accepted after 180 repair cycles. The final rate alone says nothing about how much repeat work was needed.

Can department totals replace garment-level links?

They can support each department's own yield and an explicitly defined product index. They do not generally show which garments passed every stage first time. That joint result needs linked histories or a stated model with defensible assumptions.

Should every defect lower yield more than once?

Within a unit-based first-pass calculation, one garment either passes or fails that first attempt. Several defects do not create several failed garments. Retain all defect details for diagnosis while counting the unit once.

Make every percentage traceable to its group

A useful yield report can explain its numerator, denominator, first-attempt rule and reporting cutoff. It keeps repairs and pending work visible. The final disposition does not overwrite the original history.

For the example, the essential results are 92.00%, 95.00% and 97.00% at the three stages, 88.50% observed first pass through the route, and 100% final acceptance after repair. The separate stage-rate product is 84.78%. Each figure has a clear purpose. Keep those meanings visible, then use the underlying histories to improve the work.

References

• ASQ: Quality Glossary, first-pass yield definition.

• Minitab: Throughput yield and rolled throughput yield.

• Emory University: Conditional Probability.

• NIST: Statistically Independent Events.

• NIST/SEMATECH: Attribute Charts.

• ASQ: Cost of Quality.

• GS1: Global Traceability Standard framework.

• Minitab: Data considerations for Attribute Agreement Analysis.

• NIST/SEMATECH: Comparing a proportion with a stated value.