Statistical Methods
Find anomalous transitions with a lag-pair display
Preserve both ends of a transition
A lag-one display places each observation on the horizontal axis and its successor on the vertical axis. Save both occasion identifiers with every plotted point. Sorting by the measured value before creating pairs destroys the time ordering. Splitting by instrument or run prevents artificial transitions across unrelated series.
Classify the pattern
Examine whether points follow a diagonal, form clusters, alternate between two levels or contain isolated transitions. Use fixed units and comparable axis scales. Follow up an isolated pair in the original sequence, where a single unusual reading can create two unusual pairs.
Hypothetical example
Values 8, 9, 20, 9, 8 generate four transitions. The upward transition (9,20) and downward transition (20,9) surround the same third reading. Treating those two points as independent outliers would suggest two events where one measurement could explain both. Inspect calibration and capture conditions at occasion three before changing a record.
A lag diagram makes nonlinear patterns visible even when a single correlation is small. It does not establish an autoregressive model or identify the direction of causation. Keep the original sequence, plot and annotated transition list together so another analyst can reproduce the investigation.
Method checked 9 November 2026. NIST/SEMATECH Engineering Statistics Handbook, 1.3.3.15. Lag Plot.