AQL Sampling Calculator

How does AQL acceptance sampling work?

Acceptable Quality Limit (AQL) sampling is a statistical method defined in ISO 2859-1 (ANSI/ASQ Z1.4) for deciding whether to accept or reject a production lot based on inspecting a random sample. The AQL value represents the worst tolerable defect rate that the consumer considers acceptable as a process average.

The sampling plan specifies three values: the sample size (n), the accept number (Ac), and the reject number (Re). If the number of defectives found in the sample is ≤ Ac, the lot is accepted; if ≥ Re, it is rejected. The plan balances producer's risk (α, rejecting good lots) and consumer's risk (β, accepting bad lots).

Inspection levels (I, II, III and special levels S-1 through S-4) control the relationship between lot size and sample size. Level II is the default; Level I reduces sample size for less critical items, while Level III increases it for greater discrimination.

Formula: Sample Code Letter = f(Lot Size, Inspection Level) Sample Size (n) = lookup(Code Letter, AQL) Accept if defectives ≤ Ac Reject if defectives ≥ Re = Ac + 1

Example Calculation

A lot of 5,000 units is inspected at AQL = 1.0%, General Inspection Level II. The code letter is 'L', giving a sample size of 200. Accept number Ac = 5, Reject number Re = 6. Draw 200 random units; if 5 or fewer are defective, accept the lot. If 6 or more are defective, reject it.

When to Use This Calculator

• When setting up incoming inspection plans for purchased components or raw materials from new or existing suppliers
• During supplier negotiations to agree on inspection levels and AQL values as part of the quality agreement
• When transitioning between normal, tightened, and reduced inspection based on recent lot history per the switching rules in ISO 2859-1
• Before a shipment decision to determine the correct sample size and accept/reject criteria for the specific lot size and quality level
• When designing inspection plans for different defect severity classes — critical, major, and minor — each with its own AQL level

Common Mistakes to Avoid

• Using the same AQL for all defect types — critical defects (safety) need much tighter AQL (0.065-0.15%) than minor defects (2.5-4.0%); using one level for all creates either over-inspection or quality risk
• Not following the switching rules — ISO 2859-1 requires switching to tightened inspection after 2 rejected lots in 5, and to reduced inspection after 10 consecutive accepted lots; ignoring these rules voids the statistical protection
• Drawing non-random samples — taking samples from the top of a box or from one area of the lot introduces bias; each unit in the lot must have an equal probability of selection
• Treating AQL passing as a quality guarantee — AQL is a risk management tool, not a quality certificate; a lot at exactly the AQL defect rate still has ~5% probability of rejection

How to Interpret Results

• The decision rule is binary with no middle ground: accept the lot if defectives found ≤ Ac, reject if ≥ Re (Re is always Ac + 1) — every inspected unit must be classified before deciding
• An accept number of 0 means a single defective rejects the entire lot — common with small samples or tight AQL values; verify this severity matches the defect class before committing to the plan
• Sample size grows with lot size but far less than proportionally — a falling Sampling % for large lots is correct, because statistical protection comes from the absolute sample size, not the percentage
• If Sampling % approaches or exceeds 50% for a small lot, the savings over 100% inspection are minimal — consider full inspection instead
• The same lot size and AQL give a larger sample at Level III (tightened) and a smaller one at Level I (reduced) — switch levels per the ISO 2859-1 rules based on recent lot acceptance history, not ad hoc

Related Standards & References

• ISO 2859-1 — Sampling procedures for inspection by attributes, the international standard defining AQL tables and switching rules
• ANSI/ASQ Z1.4 — The US equivalent of ISO 2859-1, widely used in commercial and military procurement
• ISO 2859-2 — Sampling plans indexed by limiting quality (LQ) for isolated lot inspection
• GB/T 2828.1 — Chinese national standard for acceptance sampling, technically identical to ISO 2859-1

Sampling Plan Reference — AQL 1.0%, Level II

Sample size and accept/reject numbers for AQL 1.0%, General Inspection Level II, across every ISO 2859-1 lot-size range. Figures are computed by this calculator.

Frequently Asked Questions

What AQL level should I use?

AQL 0.065-0.15% is used for critical defects (safety hazards). AQL 0.40-1.0% is typical for major defects (functional failures). AQL 1.5-4.0% is common for minor defects (cosmetic issues). The appropriate level depends on the consequences of defects reaching the customer and industry standards.

Does passing AQL inspection guarantee lot quality?

No. AQL sampling is a probabilistic method — it reduces risk but cannot guarantee zero defects. A lot at exactly the AQL defect rate has roughly a 95% chance of acceptance. Lots with higher defect rates have lower acceptance probability. For zero-defect requirements, 100% inspection or process capability control (Cpk) is necessary.