AQL Sample Size Calculator

Choose your AQL, risks, and plan fast. See the smallest sample meeting acceptance probability targets. Download clear reports for audits, suppliers, and teams now.

Calculator Inputs
Designed for single-sampling acceptance plans using an OC-curve approach.
Total units in the submitted lot.
Quality level you want to accept with high probability.
Poor quality level you want to reject with high probability.
Probability of rejecting a lot at the AQL.
Probability of accepting a lot at the RQL.
Choose hypergeometric for small lots or strict sampling without replacement.
Higher values can find plans that were missed.
Search c from 0 up to this value.
Use this when your audit program requires a specific c.
Reset
Tip: If no plan is found, increase Max sample size or relax α/β slightly.
Example Data Table
Illustrative scenarios for quick comparison.
Lot Size (N) AQL (%) RQL (%) α β Model Suggested n Suggested c
150 1 4 0.05 0.1 binomial 80 2
1200 0.65 3 0.05 0.1 binomial 125 2
5000 1 4 0.05 0.1 binomial 200 3
20000 0.4 2 0.05 0.1 binomial 315 2
800 1.5 6 0.1 0.1 hypergeometric 110 3
Examples are illustrative. Always confirm your acceptance sampling policy before use.
Formula Used
Acceptance probability drives the recommended plan.

The calculator designs a single-sampling plan by searching for the smallest sample size n and acceptance number c that satisfy two risk constraints.

Binomial model (common)
Pa(n,c,p) = Σk=0..c C(n,k) · pk · (1−p)n−k
Where p is the assumed defect rate, and Pa is the probability of accepting the lot.
Risk targets
  • Pa(AQL) ≥ 1−α (protects the producer)
  • Pa(RQL) ≤ β (protects the consumer)

Hypergeometric mode replaces the binomial probability when sampling without replacement from a finite lot.

How to Use This Calculator
A practical workflow for inspection planning.
  1. Enter the lot size and select a probability model.
  2. Set AQL to the quality you want to accept often.
  3. Set RQL/LTPD to the quality you want to reject.
  4. Choose α and β to match risk appetite.
  5. Click Calculate to get the plan and decision rule.
  6. Download CSV or PDF for audits, suppliers, and records.
Interpretation: Inspect n units. Accept if defectives ≤ c. If rejected, follow your escalation policy.

Setting AQL and RQL Targets

AQL represents the defect level a process can routinely achieve while still being acceptable. RQL (often called LTPD) represents an unacceptable level you want to catch. A practical pairing keeps RQL at least 3× to 6× higher than AQL. For example, an AQL of 1.0% with an RQL of 4.0% creates clear separation between “good” and “bad” lots and supports supplier agreements and contracts.

Risk Parameters and Decision Strength

Producer risk α is the chance of rejecting a lot that is truly at the AQL. Consumer risk β is the chance of accepting a lot that is truly at the RQL. Many programs start near α = 0.05 and β = 0.10, which translates to Pa(AQL) ≥ 0.95 and Pa(RQL) ≤ 0.10. Tightening α or β increases inspection effort because the plan must discriminate more strongly. Loosening targets reduces sample size but can raise dispute risk.

Sample Size Drivers in Real Lots

The calculator searches a single-sampling plan (n, c) that meets both risk limits. Larger lots do not always require proportionally larger samples, because the probability model focuses on defect rate rather than count. When the inspection fraction n/N becomes high, switching to the finite-lot model helps prevent overconfidence. For small lots, hypergeometric probabilities can be noticeably stricter than binomial. Check that the recommended n fits your receiving window.

Acceptance Number and Defect Classification

The acceptance number c is the maximum defectives allowed in the sample. Holding n constant, a lower c reduces acceptance probability and protects the customer, but it can raise false rejections. Many teams set different plans by defect class: critical defects often use c = 0, major defects allow small c values, and minor defects may permit higher c with larger n. Keep defect definitions consistent across sites.

Using Results for Supplier and Process Control

A sampling plan is most useful when combined with process data. Track actual defectives found per lot, the observed sample defect rate, and the decision outcome. If repeated lots fail near the same RQL, trigger containment and corrective action rather than simply increasing n. Exported CSV/PDF results support audits, supplier reviews, and clear risk communication.

FAQs
Quick answers for common sampling questions.
1) What is the difference between AQL and RQL/LTPD?
AQL is the quality level you want to accept most of the time, while RQL/LTPD is a poor quality level you want to reject. Setting RQL higher than AQL creates discrimination between good and bad lots.
2) When should I use binomial versus hypergeometric?
Use binomial for large lots or when sampling without replacement has minimal impact. Use hypergeometric for smaller lots or when you want finite-lot accuracy, especially when n is a sizable fraction of N.
3) What do producer risk α and consumer risk β mean?
α is the chance you reject a lot that is truly at the AQL. β is the chance you accept a lot that is truly at the RQL. Lower α or β increases required sample size or tightens c.
4) Why do I get “No plan found within limits”?
The search may be constrained by your max sample size or max c, or your risk targets are very strict. Increase the maximum search limits, widen the AQL–RQL gap, or relax α/β slightly.
5) Does this match standard sampling tables exactly?
No. This tool designs a single-sampling plan to meet your chosen risk targets, which may differ from published tables that use predefined inspection levels. If you must comply with a specific standard, verify the plan against that standard.
6) How do I apply the acceptance number c?
Inspect n units chosen per your sampling method. Count defectives by the same defect definition used to set AQL/RQL. Accept the lot if defectives are ≤ c; otherwise reject or follow your escalation workflow.
Quality note
This tool provides statistically designed plans. If you must follow a specific standard table, verify that its plan satisfies your required α/β at the chosen AQL/RQL.
Good practice
Combine sampling with supplier history, process capability, and corrective actions.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.