This is Post 3 of the six-part VHM statistical-methods series. The previous two posts (spectral analysis and residual analysis) covered methods that examine a signal’s content — what it looks like, what its frequencies are, how it deviates from a model. This one is about something different: whether and when it changed.

A fault announces itself as a change in time. Pressure that was stable starts trending up. A vibration RMS that was running at 0.8 g jumps to 1.1 g. A residual that lived around zero starts walking. The diagnostic skill is deciding, from noisy data, that a change is real (not just scatter) and doing it fast enough to act. The methods in this monograph split cleanly by which question they answer: Changing now? (online streaming detection), When and how big? (retrospective localization), What kind? (two-sample distributional tests).

This is the post where the trade-off between false-alarm rate and detection delay becomes vivid. You can detect any change you want, instantly, if you’re willing to false-alarm constantly. The art of change detection is finding the operating point on that curve that fits your application — and the methods give you the dials to do it.

What it covers

Three groups of methods, about twenty-six minutes of careful reading.

Online streaming detection (changing now?). CUSUM (the cumulative-sum test, the workhorse since the 1950s). EWMA (exponentially weighted moving average — Shewhart’s update). GLR (generalized likelihood ratio — the theoretically optimal but computationally heavier alternative). When each one is the right reach.

Retrospective changepoint localization (when and how big?). Binary segmentation. Pruned exact linear time (PELT). The information-criterion frameworks for choosing the number of changepoints when you don’t know it a priori.

Distributional change tests (what kind?). Kolmogorov-Smirnov for general distributional shift. Wasserstein distance for “how far did the distribution move.” Mann-Whitney and the rank-based alternatives for when assumptions are scarce. The discipline of choosing the right test for the question you’re asking.

Two interactive explorers. A drag-the-changepoint demo that lets you race CUSUM, EWMA, and GLR side-by-side and see which one detects fastest. A two-sample distribution explorer that shows how each test responds to different kinds of shift.

A worked case study. One synthetic fault — a small step change with noise — run through every method above. The detection delays. The false-alarm trade-offs. The decision tree that picks the right method for the operational context.

Read it

Open the field guide →

Code & data

↓ change-detection-kit.zip — the Python source for every figure and explorer.

The VHM statistical-methods series

This is Post 3 of 6:

  1. Listening to the Machine — time-series and spectral analysis
  2. Reading the Residual — model-based fault detection and isolation
  3. Catching the Change — (this post) — change and fault detection over time
  4. Reading the Couplings — dependence measures
  5. Reading the Whole Machine — multivariate monitoring
  6. Reasoning Under Uncertainty — probabilistic methods

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