Quality calculator
Inspection Detection Probability Calculator
Estimate detection probability and inspection effort for independent observations with an assumed constant nonconforming probability.
What this calculator does
- Estimate detection probability and inspection effort for independent observations with an assumed constant nonconforming probability.
Formula used
- Detection probability = [1 − (1 − nonconforming probability)^sample size] × 100
- Inspection share = sample size ÷ planned batch size × 100
- Inspection hours = sample size × seconds per inspection ÷ 3,600
- Expected nonconforming sample units = sample size × nonconforming probability
Inputs explained
- Planned Batch Size: Whole units in the planned batch used for inspection share.
- Planned Inspections: Distinct whole units to inspect from the planned batch.
- Assumed Nonconforming Probability: Constant independent nonconforming probability supported by process records.
- Inspection Time per Unit: Observed inspection effort excluding setup and queue time.
How to use the result
- Best suited to lower assumed defect Probability, higher assumed defect probability.
- The probability is unconditional on a fixed number of defects in a finite lot. Inspection effort excludes setup, waiting and retests.
Current U.S. benchmarks
- U.S. manufacturing runs at 75.7% of capacity (Federal Reserve, Aug 2026). New factory orders are up 8.5% year over year (Census).
Common questions
- Does inspecting the whole batch guarantee finding a defect? Only if a detectable defect exists. This model also includes batches with no defects, so its unconditional detection probability can remain below one hundred percent.
- Can I enter a known number of bad lot units? No. A known finite defect count requires a without-replacement model. Here the input is a constant probability for independent unit outcomes.
- Is the expected defect count an actual count? No. It is an average across repeated samples under the assumed model. An individual sample always contains a whole number of nonconforming units.
- What happens with zero planned inspections? Detection probability, expected nonconforming count and inspection effort are all zero. The model does not silently add a minimum sample.
Related guides
Last reviewed 2026-10-06.