Statistical Acceptance Sampling Plan¶
Offline sampling plan — instantiates Inline vs. Offline Inspection Trade-Off
Samples completed lots using predefined sample sizes and accept/reject numbers to decide, with quantified risk, whether a lot can be released.
Statistical Acceptance Sampling Plan decides whether to accept or reject an entire completed lot by inspecting only a defined sample of it — and, crucially, it makes that decision with the sampling risk quantified in advance. Its defining move is the accept/reject rule: draw a sample of size n, count the defectives, accept the lot if the count is at or below an acceptance number c and reject otherwise. Because the sample is chosen and the numbers computed to hit a stated confidence — a known chance of wrongly accepting a bad lot and of wrongly rejecting a good one — the plan converts "we checked some and they looked fine" into a defensible release decision with its error rates on the record. It is the mechanism for releasing lots you cannot or need not inspect 100%, on a budget of inspection you choose against a risk you state.
Example¶
A garment importer receives a lot of 10,000 shirts and must decide whether to accept it without inspecting all 10,000. It applies a published attribute sampling plan indexed to an Acceptable Quality Limit: at the chosen inspection level the standard prescribes drawing a sample of 200 shirts, with an acceptance number of 5 and a rejection number of 6. Inspectors pull the 200, tally defects — loose seams, misaligned prints, missing buttons — and find 4. Four is at or below 5, so the lot is accepted and released; had they found 6 or more, the whole lot would be rejected back to the supplier. The plan's operating-characteristic curve tells the importer, before a single shirt is pulled, the probability that a lot of any given true defect rate will pass — so the release decision comes with its risk already priced in, not discovered after a customer complains.
How it works¶
- Fix the plan before sampling. Sample size n, acceptance number c, and rejection number are set in advance from the lot size, inspection level, and target quality — never chosen after seeing results.
- Sample and count against the rule. Inspect n units, count defectives, and apply the accept-if-≤-c rule mechanically. The output is a lot-level accept/reject, not a per-unit disposition.
- Design to an operating-characteristic curve. The plan is selected so its OC curve gives acceptable producer's and consumer's risk — the plan is its risk profile.
- Escalate on rejection. A rejected lot is returned, screened 100%, or renegotiated; the plan sets the release gate but hands off what happens to a rejected lot.
Tuning parameters¶
- Acceptable Quality Limit (AQL) — the defect level the plan is built to routinely pass. Tighter AQL protects the customer but rejects more lots and inspects harder.
- Sample size / inspection level — how many units are drawn. Larger samples sharpen the OC curve (steeper discrimination) at higher inspection cost.
- Single vs. double vs. sequential — whether one sample decides, or a small first sample can defer to a second. Multi-stage plans cut average inspection when lots are clearly good or bad, at procedural complexity.
- Acceptance number c — how many defectives are tolerated in the sample. Raising c passes more lots (lower producer's risk) but admits worse lots (higher consumer's risk).
When it helps, and when it misleads¶
Its strength is quantified, economical release: it lets a completed lot be accepted or rejected on a fraction of the units while stating exactly how much protection that buys, via the operating-characteristic curve[1] and its producer's/consumer's risk. It is the disciplined answer to "how much is enough to sample?" — and it makes a release decision auditable and negotiable between buyer and supplier.
Its failure mode is that acceptance sampling detects bad lots; it does not improve them. A plan can only sort incoming lots into accept/reject piles — it does nothing to make the process produce fewer defects, and leaning on it invites a "test quality in" posture that mature quality thinking warns against. It also assumes the sampled units represent the lot; a stratified or clustered defect (all bad units in one carton) can slip through a plan that draws unluckily. The classic misuse is reading "lot accepted" as "lot is defect-free" — it means only that the sample cleared the bar at the stated risk. The guarding discipline is to treat the plan as a risk-quantified gate feeding process improvement, and to reduce reliance on it as the source proves capable.
How it implements the components¶
sampling_confidence_plan— this is its heart: the sample size, acceptance number, and OC-curve risk that make the lot decision statistically defensible.coverage_strategy_choice— it selects the lot-sampling option on the coverage menu (rather than 100% or inline) for lots where sampled release is adequate.
It does not compute a plan for tests that destroy the unit (detectability_and_test_latency_assessment driving destructive sampling — that's destructive_test_sampling, a sibling it is easily confused with: destructive sampling is forced by a consuming test, whereas this plan samples non-destructive checks by statistical choice). It also does not gate every finished unit at a full exit test (inspection_placement_map as a 100% end-gate — that's end_of_line_batch_release_test), and it does not permanently reduce inspection on a proven source (inspection_policy_revision_loop — that's skip_lot_or_reduced_inspection_rule).
Related¶
- Instantiates: Inline vs. Offline Inspection Trade-Off — it is the risk-quantified offline sampling gate.
- Consumes: feeds rejected lots to containment_hold_and_sort for 100% screening.
- Sibling mechanisms: destructive_test_sampling · end_of_line_batch_release_test · skip_lot_or_reduced_inspection_rule
Editorial Notes¶
Form Classification¶
Form family: Assessment, Review & Assurance
Rationale: Statistical Acceptance Sampling Plan operates by samples an existing lot under a fixed plan and issues the lot-level acceptance finding. That concrete deployed or enacted form is Assessment, Review & Assurance under the frozen taxonomy.
Nearest alternative: Decision, Gate & Allocation — Although Decision, Gate & Allocation can support this mechanism, the frozen evidence makes its operative form the act that samples an existing lot under a fixed plan and issues the lot-level acceptance finding; the alternative is therefore secondary rather than defining.
Review outcome: Adjudicated after independent review; high confidence.
Origin Attribution¶
Primary origin: Experimental Design & Statistics
Origin pattern: Single lineage
Present-day reach: Specialized
Rationale: Sample-size and accept-number lot release is canonical acceptance sampling.
Related originating lineages:
- Data Science & Analytics — Data science, analytics, and operational monitoring supplies a parallel or contributing lineage for the mechanism's defining operation: samples completed lots using predefined sample sizes and accept/reject numbers to decide, with quantified risk, whether a lot can be released.
- Engineering & Design (beyond software) — Quality control applies it.
- Logistics & Supply Chain Management — Incoming lots are inspected.
- Mathematics — Mathematical modeling, proof, and abstract-structure practice supplies a parallel or contributing lineage for the mechanism's defining operation: samples completed lots using predefined sample sizes and accept/reject numbers to decide, with quantified risk, whether a lot can be released.
Review resolution: The blind reviewers agree that statistics_experimental_design is the primary origin and differ only on alternate origin disagreement. I preserve every independently explained alternate from both records rather than imposing a numeric cap. I retain single_lineage because the combined evidence shows one traceable formative lineage. The broader reach of specialized records portability separately from historical provenance; encyclopedia_synthesis=false preserves the affirmative synthesis judgment where either reviewer identified one.
Review outcome: Reconciled after independent review; high confidence.
References¶
[1] International Organization for Standardization. “ISO 2859-1:2026 Sampling Procedures for Inspection by Attributes—Part 1: Sampling Schemes Indexed by Acceptance Quality Limit (AQL) for Lot-by-Lot Inspection”. International Organization for Standardization. 3rd edition (2026). Defines sample-based lot acceptance and rejection plans whose operating-characteristic behavior and producer and consumer risks quantify the protection obtained without inspecting every unit. registry ↩