Enter Inspection Inputs
| Timestamp | Lot | AQL (%) | Level | Code | n | Normal Ac/Re | Tightened Ac/Re | Method |
|---|---|---|---|---|---|---|---|---|
| No saved rows yet. Run a calculation to populate history. | ||||||||
History is stored in your browser session. Clearing cookies or closing the session may remove it.
Example Data Table
These sample rows show typical inputs and outputs for quick reference.
| Lot Size | AQL (%) | Level | Code Letter | Sample Size | Tightened Ac/Re |
|---|---|---|---|---|---|
| 500 | 1.00 | II | H | 50 | Ac 1 / Re 2 |
| 12000 | 0.65 | II | M | 315 | Ac 3 / Re 4 |
| 200 | 2.50 | I | E | 13 | Ac 0 / Re 1 |
Example outputs may differ from standards tables because this tool uses probability targets to derive acceptance numbers.
Formula Used
This calculator builds a tightened single-sampling plan using three steps:
- Code letter: The lot size and inspection level map to a code letter.
- Sample size: The code letter maps to a fixed sample size n.
- Acceptance number: Defect allowance is computed using probability.
When should I use tightened inspection?
Tightened inspection is commonly applied after repeated lot rejections under normal inspection, or when risk increases due to supplier changes, process instability, or safety impact. Align switching rules with your quality system, contracts, and customer requirements.
Tips for consistent results
Keep AQL and inspection level consistent across comparable lots. Use the same method setting to avoid small rounding differences. If your plan specifies producer/consumer risk targets, enter those targets and document the chosen settings for traceability.
Convert the selected AQL to a defect probability: p = AQL / 100. Let X be the number of defects found in the sample.
- Binomial model: X ~ Binomial(n, p).
- Poisson approximation: X ~ Poisson(λ), where λ = n·p.
The acceptance number c is selected so that:
P(X ≤ c) ≥ Target
Tightened inspection uses a lower target acceptance at AQL than normal inspection, resulting in a smaller c and stricter acceptance. Rejection is Re = c + 1.
How to Use This Calculator
- Enter the lot size for the batch you received.
- Set the AQL that matches your quality requirement.
- Pick an inspection level based on effort and risk.
- Click Calculate Tightened Plan to see results above.
- Inspect n units, then accept or reject using Ac/Re.
Tightened inspection as a risk control
Tightened inspection is used when normal sampling no longer provides enough confidence for lots. This calculator estimates a stricter acceptance number by holding the sample size constant while reducing allowed defects. For example, a lot of 500 at 1.00% AQL may require n=50 with tightened Ac 1 and Re 2. That means one defect passes, but two defects trigger rejection. Apply tightened plans to protect customers fully.
Lot size and inspection level decisions
Sampling effort starts with the code letter, driven by lot size and the selected inspection level. Larger lots move to later code letters and larger sample sizes, increasing detection power. Level II is a balanced default, while Level I reduces effort and Level III increases scrutiny. In this calculator, a 12,000-unit lot at Level II maps to a higher code letter and larger n than a 200-unit lot, improving sensitivity.
AQL as a measurable defect expectation
AQL converts to a defect probability p = AQL/100, creating a basis for comparison across lots. Expected defects in the sample are n×p, which helps you sanity-check results. If n=315 and AQL=0.65%, expected defects are about 2.05, so tightened acceptance numbers near 2 or 3 are plausible. The tool can use exact binomial probabilities or a Poisson approximation when p is small or n is large.
Turning probabilities into Ac and Re
Acceptance and rejection numbers come from the cumulative probability that observed defects stay at or below a threshold. The calculator finds the smallest c such that P(X≤c) meets your target at the AQL point, then sets Re=c+1. Normal and tightened targets can be tuned; tightened should never be higher than normal. Use the shown Ac/Re during inspection: count defects in n units and decide immediately, without debating edge cases.
Traceability, downloads, and governance
Inspection results should be auditable, repeatable, and easy to share. This calculator stores up to 50 runs in session history, so teams can compare lots, AQLs, and levels across a shift. CSV export supports analysis in spreadsheets, while the PDF report is suitable for attaching to receiving records or supplier communications. For governance, standardize your default targets and document exceptions. Consistent settings make supplier performance reviews and corrective actions faster and defensible.
FAQs
What is a tightened inspection plan?
It is a stricter sampling approach used after repeated issues or higher risk. You inspect the same sample size, but accept fewer defects, reducing the chance that marginal lots pass.
Does this calculator replace official sampling standards?
No. It provides a probability-based estimate that is useful for planning and training. If your contract requires a specific standard table, follow that table and use this tool for cross-checking.
How does AQL change the tightened decision?
A lower AQL means a smaller defect probability p, which usually lowers the allowed defects in the sample. A higher AQL increases p and can raise acceptance numbers, depending on sample size.
When should I use binomial instead of Poisson?
Use binomial for smaller samples or when you want exact probabilities. Poisson is a fast approximation when AQL is small or the sample size is large, because λ=n×p summarizes the expectation.
Why must the tightened target be less than or equal to normal?
Tightened inspection should be stricter. A lower target acceptance at the AQL point produces a smaller acceptance number c, ensuring the tightened plan never allows more defects than the normal plan.
What do the CSV and PDF downloads contain?
They export your session history: timestamp, lot size, AQL, level, code letter, sample size, and normal versus tightened Ac/Re values. Use CSV for analysis and PDF for attaching to inspection records.