Calculator
Example data table
| Scenario | Inputs | Estimated n |
|---|---|---|
| Incoming inspection defect rate | Confidence 95%, p=0.02, E=0.01, N not set | ≈ 753 |
| Conservative attribute sampling | Confidence 95%, p=0.50, E=0.05, N not set | ≈ 385 |
| Measurement precision planning | Confidence 95%, σ=1.5, E=0.5, N not set | ≈ 35 |
| Detect a mean shift | Confidence 95%, Power 80%, σ=1.5, Δ=1.0, N not set | ≈ 18 |
| Finite lot inspection | Confidence 95%, p=0.02, E=0.01, N=2000, FPC on | ≈ 548 |
Formula used
1) Defect rate (proportion) sample size
This estimates a sample size for a proportion using a normal approximation:
Where p is expected defect rate, E is margin of error, and Z is the Z-score from the confidence level.
2) Mean (measurement) sample size for precision
This targets a confidence interval half-width around the mean:
Where σ is estimated standard deviation and E is the desired margin of error in measurement units.
3) Mean shift detection planning
For detecting a shift Δ with power, an approximate Z method is used:
Zα/2 comes from confidence, and Zβ from the selected power.
Finite population correction (optional)
When the sample is a meaningful fraction of a finite population, adjust:
How to use this calculator
- Choose defect rate for pass/fail inspection, or mean for measurements.
- Set confidence level, then provide a margin of error or shift target.
- Add population size for lot-based inspection, if applicable.
- Press “Estimate Sample Size” to view results above the form.
- Download CSV or PDF to document assumptions and outcomes.
Confidence and inspection risk
Confidence level controls how often repeated samples bracket the true parameter. Using 95% corresponds to Z≈1.96, while 99% raises Z and increases n. In quality control, higher confidence reduces estimation risk but costs time and labor. Use higher confidence for safety‑critical parts, supplier disputes, or regulatory evidence. Use moderate confidence for internal trending, pilot studies, or rapid containment decisions on the shop floor. When sample costs are acceptable.
Precision for defect estimates
For defect sampling, the margin of error E sets the half‑width of the interval around p. Smaller E demands larger samples because n grows with 1/E². If historical p is unknown, selecting worst‑case p=0.5 produces the largest n and protects against under‑sampling. When p is small, use a realistic estimate from recent lots or a pilot run to avoid oversizing inspections and slowing material release. To protect throughput.
Finite lots and correction
When a lot is finite, sampling without replacement slightly increases information per unit. The finite population correction reduces n when n0 is not negligible relative to N. This matters most in small lots, expensive destructive tests, or 100% traceability situations. If N is huge compared with n0, the correction changes little. Record N and whether correction was applied for audit transparency and repeatable planning. At staged release gates.
Measurement sampling for averages
For variable data, precision planning uses n0=(Z·σ/E)², where σ reflects process spread. Estimate σ from control charts, capability studies, or a short pilot under stable conditions. If the process is not in control, σ inflates and the computed n may be misleading. Pair sampling plans with measurement system analysis and calibration. When units are meaningful, choose E based on tolerance, customer needs, and decision thresholds. For unit decisions.
Power for shift detection
Shift detection adds power by combining Zα/2 and Zβ, increasing n for stronger detection capability. Power represents the chance of detecting a true change of size Δ. Smaller Δ or higher power increases n quickly. Use this mode when you need to catch drift before defects rise, such as tool wear or chemical concentration changes. Align Δ with practical significance, and update σ as process improvements reduce variation.
FAQs
When should I use worst-case p=0.5?
Use it when defect rate is unknown or highly variable. It yields the largest proportion sample size, preventing under-sampling. Replace it with a realistic p after you collect pilot data or reliable historical inspection results.
How do I choose a practical margin of error E?
Pick E based on the decision you must make. Smaller E tightens the estimate but increases cost. For screening and trend checks, larger E may be acceptable. For release decisions, use tighter E aligned with risk.
When does finite population correction matter?
It matters when your planned sample is a meaningful fraction of the lot. If n0 is small compared with N, the adjustment is tiny. For small lots or destructive tests, it can reduce required sampling.
Where should σ come from for measurement sampling?
Use a stable estimate from control charts, capability studies, or a short pilot run with a capable measurement system. If the process is unstable or the gauge is noisy, σ may be inflated and the plan less efficient.
What does power mean in shift detection mode?
Power is the probability of detecting a true mean shift of size Δ under the stated conditions. Higher power lowers missed-detection risk but usually requires a larger sample. Choose Δ based on what is practically important.
Does this replace acceptance sampling standards?
No. It provides general statistical estimates for planning. If you must comply with a formal acceptance plan or industry standard, follow that plan’s rules and use this tool to support internal scoping and documentation.