Determine sample size and accept/reject numbers for incoming lot inspection based on AQL, lot size, and inspection level per ANSI/ASQ Z1.4.
Acceptance sampling inspects a random sample from a lot and decides to accept or reject the entire lot based on the number of defective items found. The plan defines three numbers: the sample size (n), the acceptance number (Ac), and the rejection number (Re). If defectives found ≤ Ac, the lot is accepted; if ≥ Re, the lot is rejected.
The key parameter is the Acceptable Quality Limit (AQL) — the maximum percent defective considered satisfactory as a process average. ANSI/ASQ Z1.4 (formerly MIL-STD-105E) provides tables that map lot size, AQL, and inspection level to the appropriate sample size and accept/reject numbers.
This calculator implements a simplified single-sampling plan lookup. Enter your lot size and desired AQL, and it returns the sample size and acceptance number. It uses the hypergeometric probability model to compute the probability of acceptance at the specified AQL, giving you confidence in the plan's discriminating power.
Acceptance sampling provides a statistically sound alternative to 100% inspection. It reduces inspection cost while maintaining a known level of quality protection. The AQL-based framework ensures consistency: both you and your supplier agree on what quality level is acceptable and what sampling plan enforces it. Consistent measurement creates a reliable baseline for tracking improvements over time and demonstrating return on investment for process optimization initiatives.
Sample size (n) and acceptance number (Ac) are determined by standard tables based on lot size, AQL, and inspection level. P(accept) = Σ [C(D,d) × C(N-D,n-d) / C(N,n)] for d = 0 to Ac where N = lot size, n = sample size, D = number of defectives in lot, d = defectives in sample, C = combinations. Re = Ac + 1
Result: n = 80, Ac = 2, Re = 3
For a lot of 1,000 units at AQL 1.0% under normal inspection (Level II), inspect 80 random units. Accept the lot if 0, 1, or 2 defectives are found. Reject if 3 or more defectives are found.
Acceptance sampling plans are designed using the hypergeometric or binomial probability distribution. For each combination of lot size, sample size, and acceptance number, the probability of accepting a lot with any given defect rate can be calculated. The Operating Characteristic (OC) curve plots this probability, visually showing the plan's discrimination.
Z1.4 includes switching rules: start with normal inspection, switch to tightened after poor results, switch to reduced after sustained good results. This dynamic adjustment automatically increases protection when quality deteriorates and reduces inspection burden when quality is consistently good.
Double and multiple sampling plans offer alternatives that inspect fewer units on average (when lots are very good or very bad) but require more complex administration. Sequential sampling inspects one unit at a time until a decision is reached. Choose the plan type based on inspection cost, administration complexity, and average sample number requirements.
Acceptable Quality Limit is the maximum percent defective that is considered satisfactory as a process average. A lot at the AQL defect level has approximately a 95% chance of acceptance. It is NOT a tolerance for individual lots but a long-run average.
AQL is the quality level the plan is designed to accept (producer's risk ≈ 5% of rejecting). LTPD is the quality level the plan is designed to reject (consumer's risk ≈ 10% of accepting). They define the two ends of the OC curve.
Switch to tightened when 2 out of 5 consecutive lots have been rejected under normal inspection. This increases sample size and lowers the acceptance number, providing stronger protection against deteriorating quality.
Yes — acceptance sampling is especially valuable for destructive testing, where 100% inspection is impossible. Keep sample sizes small enough to minimize destruction costs while maintaining statistical validity.
Z1.4 assigns a code letter (A through R) based on lot size and inspection level. The code letter then maps to the sample size and accept/reject numbers for each AQL. This two-step lookup provides flexibility in plan selection.
No. While many advocate for zero-defect processes, acceptance sampling remains essential for incoming material from external suppliers, destructive test situations, and early-stage supplier relationships. It's a practical quality tool.