How few units tell you the batch average?
Put in the precision you need and the batch size and get back how many units to check. Checking net weight to within half a gram needs 67 units out of a 5,000-unit batch. Tightening it to a quarter of a gram needs 258, and the batch size barely matters at all.
Words on this sheet
- Standard deviation: How far a typical reading sits from the average, in the same units as the readings.
Operations Starter Sample Size (General) free
After you install, this is the model to open.
How Many Units Do We Have to Check?
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
The answer
- Units to weigh
- 67 for ±0.5 g at 95% confidence on a 5,000-unit batch
- Tighten to ±0.25 g
- 258 four times the work for twice the precision
- Batch size barely matters
- 68 vs 67 an unlimited batch against 5,000 units
- Time on the scale
- 28 min per batch at 25 seconds a unit
You are checking the average net weight of a 5,000-unit batch against a 500 gram declared weight, and you want the answer to within half a gram at 95% confidence. Click Run with the goal set to estimating an average: 67 units. Clear the Population box and run it again and it is 68. That single unit is the whole story of the finite-population correction on a batch this size, and it is why the answer to how many you have to check almost never depends on how big the batch is.
Double the batch to 10,000 units and the requirement goes to 68, which is one more unit for twice the work. The setting that does matter is the spread you expect. Sample size for an average scales with the square of the standard deviation, so a line running at 2.1 grams of variation needs 68 checks and the same line tightened to 1.05 grams would need 17.
Getting the process under control is four times cheaper than checking harder, and that is a maintenance decision rather than a quality-plan decision. The margin behaves the same way in reverse: read down the table and one gram costs 17 units, half a gram costs 67, 0.35 costs 135 and 0.25 costs 258. The minutes per batch line turns the chosen line of that table into 28 minutes of checkweighing per batch, which is the number an operations manager will actually argue about.
Two limits worth stating plainly. This sizes an estimate of the average, and an average is not what a regulator asks about; if the question is what share of units falls below a legal minimum, that is a percentage rather than an average, so switch the goal to estimating a percentage and give it your expected defect rate. And the expected spread has to come from somewhere real, here 240 checkweigher readings from last month, because the whole calculation is a function of it and a guessed spread gives you a guessed sample size wearing a decimal point.
If you have no history, run a pilot of 30 units, take their standard deviation, and come back. To use your own line, change the spread, the margin and the batch size and rerun.
The model
It arrives on a tab called Template: How Many Units to Check, carrying these columns:
- What we are estimating
- The average net weight of the batch
with the model computed beside the data:
| Minutes per batch at the chosen margin | 27.92 |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
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Every model like this one, and the method behind them: Statistics in Google Sheets.