KEVOS® MAKEOS · Quality
Acceptance Sampling Probability (OC Curve)
What is the chance this sampling plan accepts a lot with a given defect rate?
Probability of accepting a lot for a single sampling plan (sample size n, acceptance number c) at a given fraction defective, with average outgoing quality and the operating characteristic at several defect levels.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Sample size | items | Number of items inspected from the lot. |
| Acceptance number (max defects allowed) | defects | Largest number of defectives that still accepts the lot. |
| Lot fraction defective | % | True percentage defective in the lot to evaluate. |
Method and formulas
- Pa = Σₖ₌₀..c C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ (binomial).
- Average outgoing quality ≈ p × Pa when rejected lots are fully sorted.
- Example: n = 50, c = 1 accepts a 2% defective lot 73.577% of the time.
Limitations
- Binomial model (lot much larger than the sample); small lots need the hypergeometric distribution.
- Assumes random sampling and perfect inspection.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Understand what a sampling plan really protects against
- Compare sampling plans
- Explain risk to customers and suppliers
Who it is for
- Quality engineers
- Process engineers
- Production supervisors
What you get
- Probability of acceptance
- Average outgoing quality (rectifying inspection)
- Operating characteristic table
Interpreting the result
- Read the table to see the defect levels the plan reliably rejects, not just the AQL.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–133. Topic reference; no source tables or recommended settings are reproduced.
- ISO 2859-1 Sampling procedures for inspection by attributes
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Acceptance Sampling Probability (OC Curve) calculator
