AQL and acceptance sampling plans, explained

Short answer: an acceptance sampling plan says: take a random sample of n units from the lot, and accept the lot if you find c or fewer defectives. The AQL (acceptable quality level) is the worst average quality the plan is designed to accept most of the time. Sampling standards such as ANSI/ASQ Z1.4 use tables that pick n and c from the lot size, inspection level and AQL. This page covers the ideas behind those tables and does not reproduce them.

• Producer's risk (α): the chance of rejecting a lot that is at the AQL. It's typically around 5%.
• Consumer's risk (β): the chance of accepting a lot at the LTPD (lot tolerance percent defective, sometimes called RQL). It's typically around 10%.
• OC curve: a plot of the probability of acceptance (Pa) against the lot's true percent defective. It shows how well the plan separates good lots from bad ones.

Worked example

The plan is n = 50, c = 1. For a large lot, the number of defectives in the sample is binomial.

What it means: a lot that is 1% defective passes about 91% of the time, so the producer's risk at 1% is about 9%. A lot that is 5% defective still passes about 28% of the time. That's the uncomfortable truth about small samples: they let a lot of bad lots through. To make the OC curve steeper, increase n.

Common exam traps

• Thinking AQL means "we accept this many defects." It describes how the plan behaves. It isn't a quality target or a license to ship defects.
• Thinking lot size drives protection. Sample size, not lot size or percent sampled, mostly determines the OC curve.
• Forgetting switching rules. Standard schemes move between normal, tightened and reduced inspection based on recent lot history.
• Treating sampling as quality control. Inspection sorts lots; it doesn't improve the process. Use it alongside process control, not instead of it.

More: 5 Whys · 8D problem solving · AOQ & AOQL · APQP & PPAP · AQL sampling plans · Attribute agreement & kappa · Attribute control charts · Availability & maintainability · Benchmarking types · Binomial vs Poisson · Blocking & randomization · Calibration & traceability · Capability: non-normal · Chi-square test · Confidence intervals · Control chart selection · Control plan · CA effectiveness · Cost of quality · Cp vs Cpk vs Cpm · Cpk vs Ppk · CQE exam day tips · CQE study plan · CQE vs CQA vs CSSBB · Is the CQE worth it? · CUSUM & EWMA · Design reviews · Design V&V · Destructive testing · DFMEA vs PFMEA · Document control · Fault tree analysis · First article inspection · Fishbone diagram · FMEA: RPN vs AP · Full vs fractional factorial · Gage R&R · GD&T basics · Hazard vs risk vs harm · Hypothesis test selection · I-MR chart · Interaction plots · ISO 14971 · ISO 9001 clauses · Kaizen event planning · Kano model · Lean wastes (TIMWOODS) · Linear regression · Management review · MRB dispositions · MSA: bias, linearity & stability · NCR, CAPA & PA · Nonparametric tests · Normal distribution & z-table · One-way ANOVA · p-value explained · Pareto chart · PDCA vs DMAIC · Poka-yoke · QFD / House of Quality · Quality audits · Quality mgmt principles · Quality manual vs procedures · Quality plan vs control plan · Redundancy: parallel & standby · Reliability allocation · Bathtub curve & MTBF · Response surface methods · Risk-based thinking · Risk matrix vs FMEA · 7 mgmt & planning tools · Short-run SPC · Six Sigma certifications · Sigma level & DPMO · Six Sigma DMAIC · Supplier quality scorecards · Switching rules (sampling) · Taguchi loss function · Theory of constraints · Tolerance stackup · Traceability & lot control · Type I vs II error · Value stream mapping · Variables vs attributes · Weibull analysis · Western Electric rules · X-bar R vs X-bar S · CQE calculators · Study planner · Section quiz

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