Acceptance Sampling Plans
Acceptance sampling is a quality control procedure where a batch of products is inspected to determine if it meets quality standards. This calculator helps you design and evaluate single sampling plans based on your quality requirements.
Where:
- Pₐ = Probability of acceptance
- n = Sample size
- c = Acceptance number
- p = Proportion defective
- d = Number of defectives in sample
Design a Sampling Plan
Design a single sampling plan based on your quality requirements (AQL, LTPD, α, and β).
Recommended Sampling Plan
Sample Size (n)
Acceptance Number (c)
Rejection Number (r)
Plan Interpretation
Operating Characteristic (OC) Curve
The OC curve shows the probability of accepting a lot based on its actual quality level.
Plan Performance
| Quality Level | Probability of Acceptance | Interpretation |
|---|
Evaluate a Sampling Plan
Evaluate an existing single sampling plan to understand its performance characteristics.
Sampling Plan Evaluation
AQL (α=5%)
LTPD (β=10%)
AOQL (%)
Plan Interpretation
Operating Characteristic (OC) Curve
The OC curve shows the probability of accepting a lot based on its actual quality level.
Quality Levels
| Quality Level (% defective) | Probability of Acceptance | Interpretation |
|---|
Practical Examples
Example 1: Standard AQL Plan
AQL = 1.0%, LTPD = 5.0%, α = 5%, β = 10%
Recommended plan: n = 89, c = 2
This means that we need to sample 89 items and accept the lot if 2 or fewer are nonconforming/defective.
Example 2: Tightened Inspection
AQL = 0.65%, LTPD = 4.0%, α = 5%, β = 10%
Recommended plan: n = 139, c = 2
Tighter quality requirements require larger sample sizes.
Example 3: Reduced Inspection
AQL = 2.5%, LTPD = 10.0%, α = 5%, β = 10%
Recommended plan: n = 44, c = 2
More lenient quality requirements allow smaller sample sizes.
Understanding Acceptance Sampling
Acceptance sampling is an SQC method adopted by Quality Assurance teams to determine whether to accept or reject a lot/batch of goods/products based on inspected sample. It allows a balance between unwanted inspection costs while providing risk protection.
Key concepts in acceptance sampling:
- AQL (Acceptable Quality Level): The worst quality level that is considered acceptable
- LTPD (Lot Tolerance Percent Defective): The lowest/worst quality level/threshold that the consumer is willing to accept
- Producer's Risk (α): The probability of rejecting a good batch/lot
- Consumer's Risk (β): The probability of accepting a bad lot
- OC Curve: Shows the probability of accepting a lot as a function of quality level