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[n1] 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: Statistics & Experimental Design
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 — 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.
Notes¶
[n1] An operating-characteristic (OC) curve plots, for a given sampling plan, the probability of accepting a lot against the lot's true defect rate. It makes the plan's producer's risk (rejecting good lots) and consumer's risk (accepting bad lots) explicit before any sampling occurs, which is what turns "we sampled some" into a decision with known error rates. ↩