KEVOS® MAKEOS · Quality
Acceptance Sampling Plan (n and c for Producer and Consumer Risk)
What sample size and acceptance number protect both me and my customer at these quality levels, and does my current plan do it?
Design of a single attributes sampling plan: the smallest sample size and acceptance number whose operating characteristic accepts lots at the acceptable quality level with at least 1 − α probability and accepts lots at the rejectable quality level with at most β probability (binomial, as the sampling OC tool), its average outgoing quality limit, and the same checks for a plan you choose.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Acceptable quality level (AQL) | % defective | Defect level that should be accepted nearly always. |
| Rejectable quality level (LTPD) | % defective | Defect level that should be rejected nearly always (lot tolerance percent defective). |
| Producer’s risk α | % | Largest chance of rejecting a good lot at the AQL. |
| Consumer’s risk β | % | Largest chance of accepting a bad lot at the RQL. |
| Your sample size (0 = use the designed plan) | Sample size of a plan you want to check (0 checks the designed plan). | |
| Your acceptance number | Acceptance number of that plan (accept if the sample has this many defectives or fewer). |
Method and formulas
- Probability of acceptance P_a(p) = Σ_{k≤c} C(n, k) p^k (1 − p)^(n−k) (as the sampling OC tool).
- For each c from 0 upward, find the smallest n with P_a(RQL) ≤ β; the first such plan with P_a(AQL) ≥ 1 − α is the design.
- Average outgoing quality limit = largest p × P_a(p) over p.
- Example: sample 132 and accept on 3 or fewer defectives: P_a is 95.575% at the AQL and 9.9228% at the RQL.
Limitations
- Binomial model for large lots; small lots need the hypergeometric model.
- Single sampling only; double and sequential plans need fewer samples on average.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design an incoming inspection plan
- Check whether a supplier’s plan protects you
- Trade inspection cost against risk
Who it is for
- Quality engineers
- Supplier quality engineers
- Inspectors
What you get
- Designed sample size and acceptance number
- Acceptance probabilities and AOQL
- Check of your plan
Interpreting the result
- The closer the AQL and RQL, the larger the sample must be to tell them apart.
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.
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