Drift Test (linear trend test)

Linear regression of the metric over time, followed by a two-sided t-test on the slope β₁ — detects a creeping trend in a stability study.

Also known as: trend test, linear trend test, slope test

The drift test checks whether a process or measurement metric systematically rises or falls over time — a pattern that Nelson rule 3 (6 points in a row) sometimes catches only late, since it reacts to short local runs. The test runs a simple linear regression of y_i on t_i (timestamp or point index) and tests the slope β₁ with a two-sided t-test on β₁ = 0.

β_{1} = \frac{\sum _{i} ( t _{i} - t ˉ ) ( y _{i} - y ˉ )}{\sum _{i} ( t _{i} - t ˉ ) ^{2}}, t = \frac{β _{1}}{SE ( β _{1} )}, p = 2 (1 - F_{t} (∣ t ∣, N - 2))

H₀: β₁ = 0 (no trend) — rejected when p < α
"Strong" trend: p < α/10 — stricter than the regular significance level, because a drift alarm alone is enough to push the verdict to `unstable`
Time axis: real timestamps if available, otherwise a 1..N point index

Used in

MSA Type 6 (stability)

In the Algorithm Lab

msa/msa-typ6-stability

Sources

Montgomery, D. C. — Introduction to Statistical Quality Control, 8th Edition, Chapter 5
AIAG — Measurement Systems Analysis Reference Manual, 4th Edition (MSA-4)

Drift Test (linear trend test)

See also

Used in

In the Algorithm Lab

Sources