Acceptance Number (AQL) Calculator

Work out acceptance number (aql) instantly with clear inputs, formula shown and shareable results.

About Acceptance Number (AQL) Calculator

The operating characteristic curve of a single sampling plan gives the probability of accepting a lot of given quality: the Poisson sum of P(k defects) for k up to the acceptance number, with mean sample size x defect rate. A plan is defined by that curve, not by its AQL alone.

Formula

Probability of acceptance

Pa = sum from k=0 to c of e^-(np) x (np)^k / k! where np = sample size x defect rate

Worked example

With the default values below, Acceptance Number (AQL) Calculator returns Probability Of Acceptance of 91.608%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sample Sizeminimum 1: 200
Acceptable Quality Limitaccepts 0.01–20 %: 1 %
Actual Lot Defect Rateaccepts 0–100 %: 1.5 %
Acceptance Numberaccepts 0–1,000: 5

Results

Probability Of Acceptance: 91.608%
Expected Defects At AQL: 2.000
Expected Defects At Actual Quality: 3.000
Probability Of Rejection: 8.392%

Step by step

1Values used
2Probability of acceptance
3Probability Of Acceptance= 91.608
4Expected Defects At AQL= 2.000
5Expected Defects At Actual Quality= 3.000
6Probability Of Rejection= 8.392

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is a c = 0 plan not stricter in every sense?

Zero-acceptance plans have a steep OC curve near zero defects but often use smaller samples, so they can accept moderately bad lots with surprising frequency. Compare full OC curves, not acceptance numbers.

What are producer and consumer risk?

Producer risk is rejecting a lot at AQL quality, conventionally about 5%. Consumer risk is accepting a lot at the rejectable quality level, conventionally about 10%.