Acceptance Sampling

Acceptance Sampling designs sampling plans for accepting or rejecting lots based on inspecting a sample. Balances risk of rejecting good lots against accepting bad lots.

Step 1 — Provide plan parameters

  • Lot Size — total items in lot
  • AQL — acceptable quality level (e.g. 0.01 = 1%)
  • LTPD — lot tolerance percent defective (e.g. 0.05 = 5%)
  • Producer's Risk (alpha) — P(reject good lot), typically 0.05
  • Consumer's Risk (beta) — P(accept bad lot), typically 0.10

Step 2 — Results

Sampling plan:

  • Sample size (n) — items to inspect
  • Acceptance number (c) — max defects to accept

Risk verification:

  • P(accept) at AQL (should be >= 1-alpha)
  • P(accept) at LTPD (should be <= beta)

OC Curve — P(accept) vs true defect rate

Average Total Inspection (ATI) at AQL and LTPD

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Statistical methods used

Binomial model:

P(accept | p) = sum(C(n,i) * p^i * (1-p)^(n-i)) for i = 0 to c.

Plan search: Find smallest (n, c) satisfying both:

  • P(accept | AQL) >= 1 - alpha
  • P(accept | LTPD) <= beta

OC Curve: Plots P(accept) across all defect rates.

ATI: n * P(accept) + N * (1 - P(accept)) under rectifying inspection.

Two risks:

  • Producer's risk (alpha) = Type I error
  • Consumer's risk (beta) = Type II error