Could your sample keep checking the same head?
A 480-unit batch sampled every twelfth unit gives forty units that all came off the same filling head. Changing the period to eleven fixes it, and the sheet shows you why in one column.
Operations Starter Sampling free
After you install, this is the model to open.
Pull the Units to Inspect
- 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
- Every 11th unit
- 43 pulled covering all twelve filler heads
- Every 12th unit
- 40 pulled every single one off head twelve
- Heads unexamined
- 11 of 12 and the inspection report looks normal
A batch of 480 units in production order, from a filler with twelve heads that run in strict rotation, so the Filling head column tells you which head made each unit. Click Run with the method set to Periodic and the period at 11: the tool returns 43 serials, starting 4011, 4022, 4033, 4044, and those 43 units cover all twelve heads. Now change the period to 12 and run it again.
You get 40 serials, starting 4012, 4024, 4036, 4048, and every single one of them came off head twelve. Forty units inspected, one head sampled, eleven heads unexamined, and the inspection report will look completely normal. That is aliasing, and it is the one thing that can go seriously wrong with systematic sampling: your period and the process period lined up, so the sample locked onto one position in the cycle and stayed there.
Try 10 and it is subtler and just as bad, 48 serials covering six heads, all of them even-numbered, because 10 and 12 share a factor of two. The rule is simple once you have seen it: pick a period that shares no factor with any cycle in your process. Eleven is prime and twelve is the machine, so eleven works, and so does seven. The block beside the data lists how many of the twelve heads each period can reach, and twelve, ten, eight and six all fail here in different degrees.
It matters here in particular, because heads four and twelve on this line run about a gram and a half heavy: a sample locked onto head twelve would report that as a whole-batch problem, and a sample locked onto any other head would miss it entirely. The general point is that these cycles are rarely written down. A filler has heads, a shift has a break pattern, a palletiser has a layer count, and a sampling period that quietly matches one of them produces a clean report about a fraction of your production.
Before you set a period, ask what repeats on this line and how often. If you cannot find out, use the Random method with a number of samples instead, which cannot alias, and accept that it draws with replacement, so ask for more than you need and remove the duplicates. Set a seed on any draw you will have to explain. To use your own line, put the serial or sequence number in the first column, put whatever cycles in your process beside it so you can check the sample against it, and choose a period with no common factor.
The model
It arrives on a tab called Template: Pull the Units to Inspect, carrying these columns:
- Serial
- Filling head (1-12)
- Hour of run
- Net weight (g)
- What a period can reach
- Distinct heads (out of 12)
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.
Next question
- What repeats in your numbers that nobody planned?Find the Cycle You Did Not Know Was There
- Should you buy more than you expect to sell?How Much Stock, When Demand Is a Guess
- One store takes more. Real, or a good fortnight?Are These Two Stores Really Different?
- How few units tell you the batch average?How Many Units Do We Have to Check?
- Which of your stores should share a target?Which Stores Behave the Same Way?
- Is unit cost driven by the price or by the volume?Will Unit Cost Land Where the Budget Says?
Every model like this one, and the method behind them: Statistics in Google Sheets.