Calculator Inputs
Example Data Table
| Scenario | Lot Size | n1 | Ac1 | Re1 | n2 | Ac2 | Re2 | Defect Rate |
|---|---|---|---|---|---|---|---|---|
| Incoming fasteners | 5000 | 80 | 1 | 4 | 80 | 5 | 6 | 2.5% |
| Plastic housings | 2400 | 50 | 0 | 3 | 50 | 3 | 4 | 1.2% |
| Printed labels | 12000 | 125 | 2 | 5 | 125 | 6 | 7 | 3.8% |
| Electronic connectors | 1800 | 32 | 0 | 2 | 32 | 2 | 3 | 0.9% |
Formula Used
A double sampling plan inspects a first sample, makes an immediate acceptance or rejection when counts are decisive, and otherwise inspects a second sample.
P(accept first) = Σ C(n1,x) p^x (1-p)^(n1-x), for x = 0 to Ac1 P(reject first) = 1 - Σ C(n1,x) p^x (1-p)^(n1-x), for x = 0 to Re1-1 P(accept total) = P(accept first) + Σ [P(x defects in sample 1) × P(sample 2 keeps cumulative defects ≤ Ac2)] ASN = n1 + P(continue) × n2 Producer's Risk = 1 - P(accept at AQL), Consumer's Risk = P(accept at LTPD)The calculator uses binomial probabilities. This works well when lot size is large and the defect proportion is reasonably stable.
How to Use This Calculator
- Enter the lot size and the first and second sample sizes.
- Set first-stage acceptance and rejection counts.
- Set cumulative acceptance and rejection counts after both samples.
- Enter the current defect rate you want to evaluate.
- Enter AQL and LTPD percentages for risk comparison.
- Press Calculate Plan to display the summary above the form.
- Review acceptance probabilities, ASN, and risk values.
- Use the export buttons to save the results table as CSV or PDF.
Why Use Double Sampling Plans
Double sampling reduces average inspection effort when many lots are clearly good or clearly poor. It balances inspection cost and decision confidence better than a fixed single-sample approach in many receiving inspection settings.
FAQs
1. What is a double sampling plan?
It is an acceptance sampling method with two inspection stages. The first sample may accept, reject, or trigger a second sample before the final decision.
2. Why are Ac and Re values important?
They define decision limits. Low acceptance numbers tighten quality control, while higher rejection limits delay final rejection until more evidence is collected.
3. What does ASN mean?
ASN is the average sample number. It estimates how many units are usually inspected per lot when the sampling plan is repeatedly applied.
4. What is producer's risk?
Producer's risk is the chance of rejecting a lot that actually meets the acceptable quality level. It is commonly denoted by alpha.
5. What is consumer's risk?
Consumer's risk is the chance of accepting a lot that is worse than the limiting quality level. It is commonly denoted by beta.
6. When should I use this calculator?
Use it for incoming, in-process, or supplier quality checks when you want staged inspection decisions and clearer risk visibility.
7. Does this calculator account for rectification?
No. It reports AOQ and inspection statistics from the chosen sampling structure, but it does not model rework, sorting, or replacement actions.
8. Can I export the calculated results?
Yes. The page includes CSV and PDF export buttons for the calculated summary table shown after submission.