Is the line running on a cycle nobody scheduled?
Sixty-four production days tested for self-similarity at every lag up to twenty. The strongest echo is at eight days, which matches nothing on the maintenance calendar, and feeding that eight into a forecast cuts its error by nearly two thirds.
Operations Advanced Forecasting free
After you install, this is the model to open.
Does Our Output Repeat on a Cycle?
- 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
- The cycle
- 8 days ACF 0.832 at lag 8, the largest in the table
- The echo, twice as far back
- 0.659 at lag 16, the same cycle again
- The antiphase
- -0.681 at lag 4, half a cycle away
- White-noise band
- ±0.245 on 64 days; outside it is a real repeat
Sixty-four production days from one line, averaging 958.7 units against a best day of 1,019 and a worst of 907, which is a swing of 11.7% of the mean. Click Run at a maximum lag of 20. The report gives one correlation per lag, and the white-noise band it prints is 0.245, so anything outside plus or minus 0.245 is a real echo rather than an accident of sixty-four numbers.
Lag 8 comes back 0.832, the largest value in the table. Lag 16 comes back 0.659, the same cycle showing up twice as far back. Lag 4 comes back -0.681, the same cycle in antiphase, the point where the plant is as far from itself as it gets. Read those three together and the conclusion is not arguable: output repeats every eight days. Now look at the calendar beside the readings, which is the reason this is worth running at all.
The plant works a five-day week and deep-cleans every ten production days. Nothing on the calendar has an eight-day period, so the cycle is not something the plant scheduled, it is something the plant does, most likely a tool wearing through and being changed on a run-hours trigger rather than a date. Lag 1 also comes back high at 0.703, and that is a different phenomenon: it is the slow upward drift, not the cycle, because a series that is climbing resembles yesterday no matter what else is true.
Trend inflates the short lags and you should read past it to the first genuine peak. Then do the run that makes the finding pay. Take the eight to Holt-Winters on the same readings, with season length 8 and a horizon of 8. The fit comes back at a mean absolute percentage error of 0.74% and a residual standard deviation of 8.33 units. Run the same forecast with season length 0, no season at all, and those become 2.00% and 22.33.
Discovering the cycle cut the forecast error by nearly two thirds, and it was invisible in the raw readings. What the autocorrelation cannot tell you is the cause, only the period. To use your own line, paste one column of readings taken at even intervals and keep the maximum lag well under half the length of the series.
The model
It arrives on a tab called Template: Does Output Repeat, carrying these columns:
- Production day
- Units produced
- On the calendar this day
- Value
with the model computed beside the data:
| Mean output | 958.7 |
| Best day | 1,019 |
| Worst day | 907 |
| Swing as a share of the mean | 0.1168 |
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: Forecasting in Google Sheets.