Quality worked example

Inspection Sampling at 1% expected defect rate: a worked example in quality

Here is what the math looks like when conditions slip. We hold every other input steady and drop expected defect rate to 1%, then walk the calculation through step by step. Estimate inspection load and the probability of detecting at least one defect in a sampled lot.

The inputs for this scenario

  • Lot size: 5,000 units (held at the documented default)
  • Sample size: 125 units (held at the documented default)
  • Expected defect rate: 1 % (the input this scenario stresses; the baseline uses 1.2)
  • Inspection time: 18 sec / unit (held at the documented default)

Working through the calculation

  • The calculation starts from the formula this tool documents: Sampling rate = sample size รท lot size.
  • Detection probability works out to 71.53 % at these inputs, and this is the headline figure for the scenario.
  • Sampling rate works out to 2.5 % at these inputs.
  • Inspection hours works out to 0.63 hr at these inputs.
  • Expected defects in sample works out to 1.25 defects at these inputs.

How this compares with the baseline

  • Against the tool's baseline example, where expected defect rate sits at 1.2% and the headline result is 77.89 %, this scenario comes in 8.16% below the baseline at 71.53 %.
  • The practical read: the gap between this scenario and the baseline is entirely attributable to expected defect rate, so recovering it is worth quantifying in dollars before considering equipment or staffing changes. It models simple attribute sampling as independent draws and does not replicate the exact accept/reject logic of ANSI/ASQ Z1.4 or a specific AQL table.

Results at a glance

  • Detection probability: 71.53 % (headline result)
  • Sampling rate: 2.5 %
  • Inspection hours: 0.63 hr
  • Expected defects in sample: 1.25 defects

Run it with your numbers

  • To rerun this with your own numbers, open the live Inspection Sampling calculator, set expected defect rate to your actual value, and adjust the remaining inputs to match your operation.

Last reviewed 2026-05-12.