BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Sample size
- What it is
- The number of items drawn at random from the lot and inspected.
- Units and format
- Enter a number in items: a count of items. The form accepts 1 items to 5000 items. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 items as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger sample at the same acceptance number makes acceptance of a defective lot less likely.
- Get it right
- The sample must be drawn at random from the whole lot for the probabilities to hold.
What this means: Acceptance number (max defects allowed)
- What it is
- The largest number of defective items found in the sample that still allows the lot to be accepted.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 1000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher acceptance number raises the probability of acceptance.
- Get it right
- It must be less than the sample size. Take it from your sampling plan or standard.
What this means: Lot fraction defective
- What it is
- The true share of defective items in the lot being evaluated, used to find the probability that the plan accepts it.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher defect level lowers the probability of acceptance.
- Get it right
- Type the percentage (2 for 2 %), not a fraction.
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
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Accepting or rejecting a lot
In Accept or Reject by the Numbers
What it covers: Decide about lots by sampling: designing a plan for producer's and consumer's risk, operating characteristics, lot acceptance from process capability, and what a sample adds to prior data.
Method explained here · BIZOMAT original book
Charting and sampling defect counts
What it covers: Charting daily defect counts with c and u charts, why clustering between parts causes false alarms and how to widen the limits, how inspection misses defects, and planning sampling of outgoing parts.
Method explained here · BIZOMAT original book
Testing tubes and bars with encircling coils
In Eddy-Current Inspection by the Numbers
What it covers: Encircling-coil testing of tubes: fill factor, frequency for the wall, differential and absolute coils, line speed, reference tubes and end zones, and auditing a supplier with a sampling plan.
Method explained here · BIZOMAT original book
Capability and control of a leak test
In Production Leak Testing by the Numbers
What it covers: Why leak data are log-normal and mixed, why a Cpk misleads, p-charts of reject rates, charting the reference leak, what a customer audit can show, and a capability claim corrected.
Method explained here · BIZOMAT original book
Procedures, people, sampling and cost
In Ultrasonic Testing by the Numbers
What it covers: What a written ultrasonic procedure must fix, how inspectors are qualified, what a 10% weld sample really protects against, random selection, trustworthy records and what testing costs.
BIZOMAT 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