CUSUM Chart calculator

Build a tabular CUSUM control chart online to detect a sustained shift in a process mean. Set the target, sigma, slack k and decision interval h, and see where the chart signals.

What it does

Accumulates how far each observation sits from a target, so a small persistent shift builds into a visible climb. Where a run chart asks 'is this point unusual?', a CUSUM asks 'has the process moved, and when did that become clear?'

When to use it

You are monitoring a measurement over a sequence — cases in order, months, batches — and want to catch a modest but sustained change in its average. It is much better than eyeballing a line chart for shifts smaller than about 1.5σ.

Alternatives

• Change points — you want to know WHERE the mean moved and to what, rather than be alerted that it did
• CUSUM for a pass/fail outcome — each observation is an event or a non-event rather than a measurement
• Funnel — you are comparing units to each other at one point in time, not one unit over time
• Line — you want to show the data itself — a CUSUM plots accumulated deviation, not the values

How to read the output

The two arms

Upper accumulates evidence that the process has drifted UP, lower that it has drifted DOWN. Each stays at zero while things are on target and climbs away once they are not. An arm sitting flat at zero is information — it says there is no drift in that direction, not that the chart is broken.

The decision interval (h)

The dashed lines. Crossing one is the signal: the accumulated evidence has passed the threshold you set. Crossing h is not a p-value and there is no significance test here. h trades how fast a real shift is caught against how often the chart cries wolf.

The slope after a shift

Once the process moves, the arm climbs at a roughly steady rate. The steeper it climbs, the larger the shift relative to the noise. The chart signals AFTER the shift, never at it — accumulating evidence takes observations. Read the crossing point as 'by here it was clear', not 'this is when it started'.

Target and σ

Everything is measured in standard deviations from target. Both can be supplied, or estimated from the series. If they were estimated from the same data being monitored, the chart says so — a shift present throughout drags the target towards itself and the drift is understated.

How this calculator is validated · Which statistical test should I use?