What is trend analysis?
Every measure moves up and down from period to period. Trend analysis separates that noise from a real, sustained change. It answers three questions: is there a trend? (a significance test), how big is it? (the change per period with its confidence interval) and where is it going? (a forecast, and when the target will be reached at the current rate).
Methods used
| Method | What it tells you |
|---|---|
| Linear regression | Change per period, its 95% confidence interval, p-value and R² (share of variation explained) |
| Mann–Kendall test | Whether there is a consistent upward or downward trend, without assuming normal data |
| Sen's slope | A robust estimate of the change per period |
| Moving average | A smoothed line that makes the direction easier to see |
| Forecast | The trend line extended, with a 95% prediction interval for single future values |
Trend analysis example
A manufacturer tracks customer complaints per 10,000 units shipped for 24 months. The values bounce between 3.4 and 7.6, but the trend is clear: complaints fall by 0.11 per month (95% CI 0.08 to 0.14), about 39% over the two years. Both the regression (p < 0.001, R² 0.71) and the Mann–Kendall test (p < 0.001) confirm it, and Sen's slope agrees at −0.11 per month. At this rate the target of 3.5 is reached in about five months; the forecast band shows that individual months will still vary by about ±1.2.
Tips
- Use at least 8 to 10 points; with fewer, a trend is hard to separate from noise.
- Watch for step changes. A sudden shift after a process change is not a gradual trend; check with a run chart or before-and-after analysis.
- Seasonality can look like a trend over short periods. Compare the same months year on year.
- Normalise counts by volume (per million units, per 100 batches) so growth does not look like a quality trend.
How to use this Trend Analysis tool
- Describe the measure. Name the measure, its unit and whether lower or higher is better; add a target if there is one.
- Enter the data. Enter or paste the values in time order, oldest first, with their period labels.
- Choose the settings. Pick the moving average window and how many periods to forecast.
- Read the result. The conclusion states whether the trend is significant, its rate per period and when the target is reached.
- Check the chart. Look at the moving average and the forecast band to judge the trend beyond the numbers.
- Export. Export the chart, statistics and forecast to PDF, PNG or Excel.
Frequently asked questions
What is trend analysis?
Trend analysis looks at a measure over time to decide whether it is consistently rising or falling, how fast, and where it is heading. In quality, it is used for complaints, defect rates, deviations, cycle times and costs, to confirm that improvement is real and to warn early when a measure starts drifting.
How do I know if a trend is significant?
This tool uses two tests. Linear regression tests whether the slope differs from zero (p-value) and gives a 95% confidence interval for the change per period. The Mann–Kendall test checks for a consistent upward or downward pattern without assuming normal data or a straight line. When both p-values are below 0.05, the trend is very unlikely to be chance.
What is the Mann–Kendall test?
A non-parametric test for a monotonic trend. It compares every pair of values and counts how often the later one is higher or lower. Kendall's tau summarises the strength (−1 to +1). It is robust to outliers and skewed data, which makes it popular for environmental and quality data.
What is Sen's slope?
Sen's slope (Theil–Sen estimator) is the median of the slopes between all pairs of points. It estimates the rate of change and, unlike the regression slope, is not pulled by a few extreme values.
How far can I forecast?
A trend forecast assumes the past trend continues, which is rarely true for long. The 95% prediction interval widens as the forecast goes further out; treat anything beyond a few periods as a scenario, not a prediction.
How is this different from a run chart?
A run chart uses simple run rules (shifts, trends, runs) to detect non-random patterns around the median, especially after a change. Trend analysis quantifies a gradual trend, its rate and its projection. Use a run chart to see whether a change made a difference, and trend analysis to measure a drift.