Acceptable Quality Level (AQL) Sample Size Calculator
Determine the required sample size and acceptance/rejection numbers for lot inspection using the ANSI/ASQ Z1.4 standard (attribute sampling).
Formula & Method
This calculator implements ANSI/ASQ Z1.4 (ISO 2859-1) single-sampling plans for attributes.
Step 1 — Find Sample Size Code Letter:
Use Table I of ANSI/ASQ Z1.4 with the lot size N and chosen General Inspection Level (I, II, or III) to obtain a code letter (A–R).
Step 2 — Find Sample Size n and Ac/Re:
Use Table II-A (Normal), II-B (Tightened), or II-C (Reduced) with the code letter and AQL to obtain:
• n = sample size
• Ac = acceptance number (max defects to accept lot)
• Re = rejection number = Ac + 1
Step 3 — Arrow Rule:
If no plan exists at the intersection, follow the arrow: ↓ use the first plan below (larger sample size).
Producer Risk (α):
P(reject | p = AQL) = 1 − P(X ≤ Ac | λ = n × AQL)
where X ~ Poisson(λ). Typically α ≈ 5%.
Consumer Risk (β):
P(accept | p = RQL) = P(X ≤ Ac | λ = n × RQL)
RQL (Rejectable Quality Level) ≈ 10 × AQL. Typically β ≈ 10%.
Max Allowable Defects in Lot:
= floor(N × AQL / 100)
Assumptions & References
- Based on ANSI/ASQ Z1.4-2008 (equivalent to ISO 2859-1) — the international standard for attribute sampling inspection.
- Applies to single-sampling plans only (not double or multiple sampling).
- Assumes lots are drawn from a continuous production process and are homogeneous.
- AQL is the maximum percent defective (or defects per 100 units) that can be considered satisfactory as a process average.
- Level I is used when less discrimination is needed (smaller samples); Level II is the default; Level III provides greater discrimination (larger samples).
- Normal inspection is the default. Switch to Tightened after 2 of 5 consecutive lots are rejected; switch to Reduced after 10 consecutive lots accepted under normal inspection.
- Producer Risk (α) and Consumer Risk (β) are approximated using the Poisson distribution, which is valid when n is large and p is small (np < 5 rule of thumb).
- Lot sizes below 2 or above 500,000 are outside the standard table range.
- This calculator does not cover variables sampling (ANSI/ASQ Z1.9) or continuous sampling plans.
- Reference: ANSI/ASQ Z1.4-2008, Sampling Procedures and Tables for Inspection by Attributes, ASQ Quality Press.