How do you calculate detection probability in sampling?

Detection probability = 1 - (1 - defect rate)^sample size. With a 1.2% defect rate and a sample of 125, that is 1 - 0.988^125 = about 77.9% chance of catching at least one defective unit.

Why does a 2.5% sample only catch 78% of the time?

Because the defect rate is low. Sampling 125 of 5,000 units at a 1.2% defect rate means you expect only 1.5 defects in the sample, so roughly one lot in five slips through with zero defects found even when defects exist.

What sample size do I need for higher detection?

Raise the sample size until 1 - (1 - defect rate)^n hits your target. To reach ~95% detection at a 1.2% defect rate you need about 250 units - double the current sample - which is why AQL plans trade cost for confidence.

What is sampling rate?

Sampling rate is sample size divided by lot size. Here 125 of 5,000 is 2.5%. It tells you inspection coverage but, on its own, says nothing about detection power - the defect rate drives that.

How much inspection labor does a sample cost?

Multiply sample size by seconds per unit and divide by 3,600. At 125 units and 18 seconds each, that is 0.625 hours - about 38 minutes per lot, useful for staffing incoming inspection.

Sampling vs 100% inspection - when should I switch?

Switch to 100% (or automated) inspection when detection probability is too low for the risk, or when the cost of an escape exceeds the extra inspection labor. Low defect rates plus high consequence usually justify full inspection or a poka-yoke.

Quality calculator

Inspection Sampling Calculator

Inspection Sampling estimates how likely a sampling plan is to catch at least one defect in a lot, given the sample size and the expected defect rate. Incoming-quality and QA engineers use it to sanity-check AQL plans and to see the real detection power behind a sample they thought was safe. It also converts the plan into labor hours so you can weigh inspection cost against risk. The uncomfortable truth it exposes is that small samples against low defect rates catch far less than people assume.

What this calculator does

Estimate inspection load and the probability of detecting at least one defect in a sampled lot.
Use when choosing sample size for receiving inspection, containment, or process verification.
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.

Formula used

Sampling rate = sample size ÷ lot size
Detection probability = 1 − (1 − defect rate) ^ sample size
Inspection hours = sample size × seconds per inspection ÷ 3,600

Inputs explained

Lot size: undefined
Sample size: undefined
Expected defect rate: undefined
Inspection time: undefined

How to use the result

Use it when designing or auditing a sampling plan, justifying sample size to a customer, or estimating inspection labor for a lot.
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.

Current U.S. benchmarks

U.S. manufacturing runs at 75.6% of capacity (Federal Reserve, May 2026). New factory orders are up 2.3% year over year (Census).

Common questions

How do you calculate detection probability in sampling? Detection probability = 1 - (1 - defect rate)^sample size. With a 1.2% defect rate and a sample of 125, that is 1 - 0.988^125 = about 77.9% chance of catching at least one defective unit.
Why does a 2.5% sample only catch 78% of the time? Because the defect rate is low. Sampling 125 of 5,000 units at a 1.2% defect rate means you expect only 1.5 defects in the sample, so roughly one lot in five slips through with zero defects found even when defects exist.
What sample size do I need for higher detection? Raise the sample size until 1 - (1 - defect rate)^n hits your target. To reach ~95% detection at a 1.2% defect rate you need about 250 units - double the current sample - which is why AQL plans trade cost for confidence.
What is sampling rate? Sampling rate is sample size divided by lot size. Here 125 of 5,000 is 2.5%. It tells you inspection coverage but, on its own, says nothing about detection power - the defect rate drives that.
How much inspection labor does a sample cost? Multiply sample size by seconds per unit and divide by 3,600. At 125 units and 18 seconds each, that is 0.625 hours - about 38 minutes per lot, useful for staffing incoming inspection.

Last reviewed 2026-05-12.