Acceptance Sampling Calculator (Single Sampling Plan, OC Curve Point)
Chance that a lot passes inspection for a plan of n items checked and c defects allowed, with the average outgoing quality and the average number of items inspected.
Results
The dashed line marks the value you entered.
What this tool does
In a single sampling plan you inspect n items from a lot and accept it if there are no more than c defective ones. The chance of acceptance depends on the true defect rate: the operating-characteristic (OC) curve, drawn in the chart, falls from 100 % for perfect lots to nearly 0 for bad ones, and a stricter plan makes the fall steeper. The calculation uses the binomial distribution, a good approximation when the sample is small compared with the lot, say under about a tenth. The average outgoing quality assumes that rejected lots are fully screened and the defects replaced. Standards such as ISO 2859-1 tabulate ready-made plans.
Formula
Pa = Σ C(n,k) pᵏ (1−p)ⁿ⁻ᵏ for k ≤ c · AOQ = p × Pa × (N − n) ÷ N
Variables
| Symbol | Meaning | Unit |
|---|---|---|
lz | Lot size | — |
sz | Sample size inspected | — |
ac | Acceptance number (most defects still accepted, 0 to 3) | — |
p | Share of defective items in the lot | % |
PA | Chance the lot is accepted | % |
PR | Chance the lot is rejected | % |
AQ | Average outgoing quality (defective share after screening rejects) | % |
TI | Average items inspected per lot | — |
Worked example
- Lot size1000
- Sample size inspected50
- Acceptance number (most defects still accepted, 0 to 3)1
- Share of defective items in the lot2 %
- Chance the lot is accepted73.58 %
- Chance the lot is rejected26.42 %
- Average outgoing quality (defective share after screening rejects)1.398 %
- Average items inspected per lot301.0
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.