Change-point analysis

Change-point analysis looks back over a CRM’s results and answers three questions: did the laboratory’s results shift, where, and how sure can you be?

Overview

Change-point analysis looks back over a CRM’s results and answers three questions: did the laboratory’s results shift, where, and how sure can you be? It needs no target, no standard deviation and no control lines, and it does not assume the results are normally distributed.

Tick “Show change points” on the Shewhart or CUSUM chart. A dashed purple line marks each change found at 95% confidence or more, with the confidence on the line; on the Shewhart chart the mean of each stretch between changes is drawn across it. Every change, with its despatch (or date) and the shift in standard deviations, is listed under the chart, together with any possible change at 90 to 95%.

When to use

  • Reviewing a CRM’s history: when did the laboratory start reading high or low, and when did it stop?
  • Choosing which batches to look at again after the CUSUM signals.
  • Checking whether a change of method, laboratory or batch of the standard shows in the results.

How it is worked out

For the results on the chart, in the chart’s order (Taylor, 2000):

  1. Take the mean of the results, x̄, and the running total of each result’s difference from it:

Si = Si−1 + (xi − x̄), S0 = 0

  1. The change is after the result where Si is furthest from zero.
  2. Its strength is the range of the running total, Sdiff = max(S) − min(S), counting the 0 it starts from.
  3. The results are shuffled 1,000 times. A shuffle keeps the same results but mixes away any change. The confidence is the share of shuffles whose Sdiff is smaller than the real one.
  4. At 95% or more it is a change: the results are split there and each side is looked at again. At 90 to 95% it is a possible change, listed but not split.

A stretch of fewer than 8 results is not looked at. The shuffles always start from the same seed, so the same results always give the same changes.

Symbol Description
xi The i-th result, in the chart’s order
x̄ The mean of the results in the stretch
Si The running total of differences from the mean
Sdiff The range of the running total

Limits

  • It finds shifts in the mean, not changes in scatter.
  • It assumes each result is independent of the one before.
  • With few results the confidence is modest even for a real shift, so treat a possible change as a reason to look, not a finding. Of 100 runs with no change at all, about 10 will show a possible change.
  • The order matters: on a Check ID, Lab Job No or Despatch No axis the results are in that order; on a Date axis, in date order.

Reference

  • Taylor, W. A. (2000). Change-point analysis: a powerful new tool for detecting changes. Taylor Enterprises.
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