Calculator Inputs
Example Data Table
| Numeric ID | Sample Label | Lot | Line | Shift | Status |
|---|---|---|---|---|---|
| 1001 | QC-1001 | Lot A | Line 1 | Morning | Eligible |
| 1002 | QC-1002 | Lot A | Line 1 | Morning | Eligible |
| 1003 | QC-1003 | Lot A | Line 1 | Morning | Eligible |
| 1004 | QC-1004 | Lot A | Line 2 | Evening | Excluded |
| 1005 | QC-1005 | Lot A | Line 2 | Evening | Eligible |
| 1006 | QC-1006 | Lot A | Line 2 | Evening | Eligible |
This example shows how a sequential lot can be labeled, screened, and randomized before inspection or audit selection.
Formula Used
1) Eligible Units
E = N - X
Where N is total population size and X is excluded units.
2) Sampling Fraction
f = n / E
This shows the share of eligible units covered by the requested sample.
3) Inclusion Probability Without Replacement
π = n / E
Each eligible unit has the same direct chance of selection in simple random sampling without replacement.
4) Inclusion Probability With Replacement
π = 1 - (1 - 1/E)n
This gives the chance that one eligible unit is selected at least once across repeated draws.
5) Systematic Interval
k = E / n
A random start is chosen, then every k-spaced position is selected across the eligible frame.
How to Use This Calculator
- Enter the full population size for the inspection frame.
- Enter the required sample size for audit, control, or review.
- Set the starting numeric ID and optional label prefix.
- Choose padding digits to standardize label formatting.
- Select subgroup size if you want block references in output.
- Pick a sampling method that matches your quality plan.
- Add a seed when you need repeatable sampling results.
- List any numeric IDs that must be excluded first.
- Submit the form to generate randomized sample labels.
- Review the summary, detailed table, and export files.
FAQs
1) What does this tool randomize?
It randomizes sample IDs from a defined population frame. You can generate inspection picks for lots, batches, lines, or audit pools using controlled selection rules.
2) Why should I use a random seed?
A seed recreates the same result later. That helps with traceability, review meetings, supplier discussions, and audit evidence when someone asks how a sample list was produced.
3) What is systematic sampling with random start?
It chooses a random starting point, then selects units at regular intervals across the eligible frame. This often improves spread when you want better coverage across a lot.
4) How do exclusions work?
Excluded numeric IDs are removed before randomization. Use this for damaged units, retained samples, missing records, or blocked items that should never enter the draw.
5) When should I use sampling with replacement?
Use it when repeated draws of the same unit are acceptable in your model. Most physical inspection plans prefer no replacement, but simulation studies may allow replacement.
6) Why is sampling fraction important?
Sampling fraction shows how much of the eligible frame is covered. Higher fractions usually increase review effort while improving the chance of detecting problems in the lot.
7) Should I sort the output after randomization?
Sorting makes the final list easier to follow on the floor or in documents. Keeping draw order is better when you need to preserve the original random sequence.
8) Does this tool replace formal sampling standards?
No. It supports sample selection and traceability. You should still follow your approved quality procedures, customer requirements, and any formal acceptance sampling standard in use.