AOQ and AOQL: Average Outgoing Quality

AOQ (Average Outgoing Quality) measures the average fraction defective in accepted lots, accounting for the fact that rejected lots are 100% inspected and defects replaced. The AOQL is the worst-case AOQ — the peak of the AOQ curve.

The AOQ formula

AOQ = (Pa × p × (N − n)) / N Where: Pa = probability of lot acceptance at incoming defect rate p p = incoming defect fraction N = lot size n = sample size Simplified (when n << N): AOQ ≈ Pa × p

Why AOQ goes to zero at both extremes

When p → 0: almost no defects in the lot, so outgoing quality is excellent.
When p → 1: nearly every lot is rejected and 100% inspected, so defects are removed — outgoing quality is again excellent.
The worst case (AOQL) is in the middle, where enough defects exist to pass and sampling misses some.

Worked example

N = 1000, n = 80, Pa at p = 0.02 is 0.85 AOQ ≈ 0.85 × 0.02 = 0.017 (1.7%) At a different p = 0.05, Pa drops to 0.30: AOQ ≈ 0.30 × 0.05 = 0.015 (1.5%) AOQL is approximately 0.018 at p ≈ 0.03 for this plan.

CQE exam tips

AOQL is a guarantee: regardless of incoming quality, average outgoing quality will never exceed AOQL.
AOQ is always ≤ p (sampling + rectification never makes outgoing quality worse than incoming).
AOQL plans are available in Dodge-Romig tables.

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