Quality worked example

Inspection Sampling at 1.38% expected defect rate: a worked example in quality

Push expected defect rate up to 1.38% and the picture changes. This example computes every intermediate figure at that operating point. Use when choosing sample size for receiving inspection, containment, or process verification.

The inputs for this scenario

  • Lot size: 5,000 units (unchanged)
  • Sample size: 125 units (unchanged)
  • Expected defect rate: 1.38 % (raised for this scenario; the documented default is 1.2)
  • Inspection time: 18 sec / unit (unchanged)

Working through the calculation

  • Applying the documented formula (Sampling rate = sample size รท lot size) to the inputs above produces each figure below.
  • At this operating point the engine returns 82.4 % for detection probability, the number this scenario is built around.
  • At this operating point the engine returns 2.5 % for sampling rate.
  • At this operating point the engine returns 0.63 hr for inspection hours.
  • At this operating point the engine returns 1.73 defects for expected defects in sample.

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 5.79% above the baseline at 82.4 %.
  • It computes the probability of finding at least one defect in the sample, the sampling rate versus lot size, expected defects in the sample, and inspection labor hours. The value of this scenario is the size of the gap it exposes: that gap, priced out over a year, is the budget you can justify spending to close it.

Results at a glance

  • Detection probability: 82.4 % (headline result)
  • Sampling rate: 2.5 %
  • Inspection hours: 0.63 hr
  • Expected defects in sample: 1.73 defects

Run it with your numbers

  • Every input above is editable in the live Inspection Sampling calculator, which recalculates instantly and can be shared with the inputs intact.

Last reviewed 2026-05-12.