Attribute Sampling Calculator

Enter Sampling Inputs

Lot size

AQL (%)

RQL / LTPD (%)

Producer risk α (%)

Consumer risk β (%)

Observed defectives in lot

Inspection cost per unit ($)

Rejection handling cost ($)

Rework cost per defective ($)

Default engineering example: Lot size 5000, AQL 1.0%, RQL 5.0%, α 5%, β 10%, and observed defectives 2. This setup helps evaluate a practical single-sampling inspection plan.

Example Data Table

Scenario	Defect level	Acceptance probability	Status
AQL point	1.0%	95.000%	Target reference
RQL point	5.0%	10.000%	Target reference
Observed lot	0.04%	Pending calculation	Submit form

This table updates after calculation and gives a simple quality decision summary for engineering inspection planning.

Formula Used

Single-sampling by attributes:

Accept the lot when observed defectives in the sample are ≤ c.

Probability of acceptance:

P(accept) = Σ [from x = 0 to c] C(n, x) p^x (1 - p)^{n - x}

Plan selection rules:

P(accept at AQL) ≥ 1 - α

P(accept at RQL) ≤ β

AOQ estimate: AOQ ≈ p × P(accept) × (N - n) / N

Here, n is sample size, c is acceptance number, p is fraction defective, N is lot size, α is producer risk, and β is consumer risk.

The calculator searches for the smallest feasible plan that satisfies both risk conditions. This makes the plan efficient while still meeting engineering quality targets.

How to Use This Calculator

Enter the lot size for the batch under inspection.
Set AQL as the acceptable defect level for normal quality.
Set RQL or LTPD as the poor quality threshold.
Choose producer risk α and consumer risk β values.
Enter observed defectives, plus inspection and rejection costs.
Press the calculate button to generate the plan.
Review sample size, acceptance number, costs, AOQ, ATI, and the OC curve.
Use CSV or PDF export to save the result.

Frequently Asked Questions

1. What does attribute sampling mean?

Attribute sampling checks whether units are conforming or defective. It does not measure variable values such as diameter or voltage. It is commonly used for pass or fail inspection decisions.

2. What is AQL in this calculator?

AQL is the acceptable quality level. It represents a defect rate that is considered satisfactory for routine production, where the lot should usually have a high chance of acceptance.

3. What is RQL or LTPD?

RQL, also called LTPD, represents a poor-quality level. At this defect rate, the lot should have a low chance of acceptance so the consumer remains protected.

4. Why are α and β important?

α measures producer risk, meaning good lots rejected by the plan. β measures consumer risk, meaning poor lots accepted by the plan. Both risks define the strictness of the inspection plan.

5. What does acceptance number c mean?

The acceptance number is the largest count of defectives allowed in the sample while still accepting the lot. If the observed count exceeds c, the lot is rejected.

6. What does the OC curve show?

The operating characteristic curve shows how likely the lot is to be accepted across different defect rates. It helps visualize plan discrimination between good and poor quality lots.

7. What is AOQ?

AOQ means average outgoing quality. It estimates outgoing defect rate after inspection and assumed rectification of rejected lots. It is useful when rejected lots are screened or reworked.

8. Can I use this for manufacturing inspection?

Yes. This tool suits engineering inspection, supplier receiving checks, assembly audits, and quality gate planning where each item is classified as defective or nondefective.