Enter the total number of rejections and the total number of units into the calculator to determine the rejection percentage. This calculator can also evaluate either the number of rejects or total units when provided the other variables.
- All Math and Numbers Calculators
- Failure Rate Calculator
- Defect Rate Calculator
- Rate Per 1000 Calculator
- System Reliability Calculator
- Defect Density Calculator
Rejection Percentage Formula
The following formula is used to calculate a rejection percentage.
R = (TR / TU) * 100
- Where R is the rejection percentage (%)
- TR is the total number of rejected units
- TU is the total number of units inspected or produced
To calculate rejection percentage, divide the total number of rejects by the total units in the lot, then multiply by 100. The result cannot exceed 100% because the number of rejects can never surpass the total units produced.
Rejection Percentage vs. Defect Rate vs. Scrap Rate
Rejection percentage is often confused with defect rate and scrap rate, but these metrics measure different things. Defect rate is the broadest metric and captures all non-conforming units, including those that can be reworked and salvaged. Rejection percentage (sometimes called reject rate) specifically measures units that fail inspection and are removed from a production lot. Scrap rate is the narrowest metric and counts only units that are completely unrecoverable and must be discarded.
A related metric is the rework rate, calculated as (Total Parts Reworked / Total Parts Produced) x 100. The relationship between these metrics is: Defect Rate = Rejection Rate + Rework Rate. A high rework rate suggests fixable process drift, while a high rejection rate points to fundamental process failures.
Industry Benchmark Rejection Rates
Acceptable rejection rates vary dramatically across industries, and most modern manufacturers express targets in parts per million (PPM) rather than percentages. The global manufacturing average hovers around 75 PPM (0.0075%). Below are typical targets by sector:
| Industry | Target Rejection Rate (PPM) | Equivalent Percentage |
|---|---|---|
| Medical devices (implantable) | 0 to 10 PPM | 0.000% to 0.001% |
| Automotive (safety-critical) | 0 to 50 PPM | 0.000% to 0.005% |
| Aerospace | 10 to 50 PPM | 0.001% to 0.005% |
| Electronics (consumer) | 100 to 500 PPM | 0.010% to 0.050% |
| Fastener/hardware | 200 PPM or less | 0.020% or less |
| Food and beverage | Below 10,000 to 20,000 PPM | Below 1% to 2% |
| General manufacturing | 75 PPM (global avg) | 0.0075% |
| World-class suppliers | Below 25 PPM | Below 0.0025% |
To convert between PPM and rejection percentage: PPM = Rejection Percentage x 10,000. A 0.5% rejection rate equals 5,000 PPM. Decades ago, 10,000 PPM (1%) was considered outstanding. Today, automotive OEMs and medical device companies routinely demand rates below 50 PPM.
Rejection Percentage and Six Sigma Levels
The Six Sigma framework maps rejection rates to process capability using sigma levels. Each sigma level corresponds to a specific defects-per-million-opportunities (DPMO) value, accounting for a standard 1.5-sigma long-term process shift:
| Sigma Level | DPMO | Rejection % | Yield |
|---|---|---|---|
| 1 | 691,462 | 69.15% | 30.85% |
| 2 | 308,538 | 30.85% | 69.15% |
| 3 | 66,807 | 6.68% | 93.32% |
| 4 | 6,210 | 0.62% | 99.38% |
| 5 | 233 | 0.023% | 99.977% |
| 6 | 3.4 | 0.00034% | 99.99966% |
Most manufacturing operations fall between 3 and 4 sigma. Reaching 6 sigma means only 3.4 defects per million units. If your rejection percentage is above 6.68% (3 sigma), the process has significant room for improvement through statistical process control.
Cost of Rejection
Every rejected unit carries both direct and hidden costs. Direct costs include material and labor already invested. Hidden costs include inspection labor, disposal, production downtime for root cause investigation, replacement runs, and late-delivery penalties. A useful estimation formula:
Cost of Rejection = (R / 100) * TU * C_unit
Where R is the rejection percentage, TU is total units produced, and C_unit is the fully loaded cost per unit (materials + labor + overhead). A facility producing 50,000 units per month at $12 per unit with a 2.5% rejection rate loses $15,000 monthly in rejected product alone. Industry research estimates that total quality failure costs typically range from 15% to 25% of total revenue when rejection rates are poorly managed.
Common Causes of High Rejection Rates
High rejection percentages in manufacturing typically trace back to a handful of root causes. Raw material variability is the most common, where incoming material properties fall outside specification due to supplier inconsistency. Machine wear and calibration drift cause dimensional deviations that worsen gradually over a production run. Environmental factors such as temperature and humidity fluctuations affect processes like injection molding, coating, and adhesive bonding. Operator error from inadequate training or fatigue accounts for a significant share of rejections in manual operations. Finally, inadequate process design, where tolerances are tighter than the process is capable of holding, creates a built-in rejection floor that no amount of operator vigilance can overcome.
Reducing Rejection Percentage
The most effective framework for reducing rejection percentage is Lean Six Sigma's DMAIC methodology (Define, Measure, Analyze, Improve, Control). In the Define phase, specific defect types are identified and prioritized using a Pareto chart, which typically reveals that 80% of rejections come from 20% of defect categories. The Measure phase establishes process capability (Cp and Cpk indices) and baseline rejection data. During Analysis, fishbone diagrams and 5-Why analysis trace rejections to root causes. The Improve phase implements countermeasures such as adjusted machine parameters, improved incoming inspection, or mistake-proofing (poka-yoke) fixtures. Control sustains gains through statistical process control (SPC) charts that trigger alerts before the process drifts out of specification. Published case studies have documented rejection rate reductions from above 10% down to below 1.5% through this approach.
Lot Rejection vs. Unit Rejection
Rejection percentage can be calculated at either the unit level or the lot level. Unit rejection percentage uses the formula above: rejected units divided by total units. Lot rejection percentage measures how many entire lots (batches) are rejected out of total lots inspected. Under the AQL (Acceptable Quality Limit) system defined in ISO 2859-1, an entire lot is accepted or rejected based on defective units found in a random sample. A lot can be rejected even if the vast majority of units conform, because the sample defect count exceeds the accept number for that AQL level. Lot rejection rates are typically higher than unit rejection rates for the same process. When reporting rejection percentage, always specify whether it refers to units or lots.
