Quality & Metrology calculator

Zero-Acceptance Detection Sample Size Calculator

Size independent inspections to detect at least one nonconforming unit at a stated defect probability and detection target.

What this calculator does

  • Size independent inspections to detect at least one nonconforming unit at a stated defect probability and detection target.

Formula used

  • Required n = round up[log(1 − detection target) ÷ log(1 − defect probability)]
  • Detection probability at n = [1 − (1 − defect probability)^n] × 100
  • One-fewer detection uses n − 1 independent inspections
  • Capacity shortfall = max(0, required n − available inspections)
  • Capacity remaining = available inspections − required n

Inputs explained

  • Defect Probability to Detect: Assumed independent nonconforming probability at the design condition.
  • Required Detection Probability: Desired chance of observing at least one nonconforming unit.
  • Available Independent Inspections: Whole inspection capacity available for this detection study.

How to use the result

  • Best suited to a lower sample burden at two Percent, a higher sample burden at half a percent.
  • This is not an ANSI/ASQ or ISO AQL table lookup. A fixed finite lot sampled without replacement requires a different probability model. Targets extremely close to a sample-count boundary require higher-precision probability calculations; dependent results are withheld.

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

  • Is the defect probability an AQL? No. It is the probability at which this study must detect at least one nonconforming unit. A standards AQL plan requires additional rules.
  • What does zero acceptance mean here? The detection event is finding one or more nonconforming units. Operational lot disposition still follows your approved quality procedure.
  • Why show one fewer inspection? It demonstrates the minimum whole sample. At the same assumed defect probability, one fewer inspection misses the requested detection target.
  • Can I use this for a small fixed lot? Not as an exact finite-lot guarantee. Sampling without replacement from a known finite defect count requires a hypergeometric model.

Last reviewed 2026-10-06.