The CUSUM Chart, Explained

A CUSUM chart — cumulative sum — plots the running total of deviations between each measurement and a target value. The idea is disarmingly simple: a small persistent shift, invisible point by point, piles up when the deviations are summed, turning into an unmistakable slope. Along with the EWMA chart, it is one of the two classic answers to the Shewhart chart’s known weakness — slowness against small sustained shifts.

How it works

The standard tabular form keeps two running sums: one accumulating deviations above target, one accumulating deviations below. Before adding each deviation, a slack value — usually set at half the shift size you care about detecting — is subtracted, so that on-target performance keeps both sums hovering near zero. When the process genuinely shifts, one sum starts climbing steadily and eventually crosses a decision interval, and the chart signals.

The CUSUM carries a bonus no Shewhart chart offers: a built-in estimate of when the shift began. The point where the winning sum left zero and began its climb dates the change, which converts an open-ended investigation into a review of what happened on or around a particular day.

A worked example

A filling line targets a declared weight, and a valve begins to wear, adding a small but persistent overfill — far too small for any single reading to look wrong, and the individuals chart stays silent for weeks. The upper CUSUM, meanwhile, begins a steady climb and crosses its decision interval. Tracing the slope back to where it left zero points to a specific Tuesday; the maintenance log for that day shows a valve service performed with a substitute part. The team refits the correct part, resets the sums, and quantifies what the quiet weeks of overfill had been costing in free product.

• Decide what shift size matters before building the chart — the slack value and decision interval both follow from that choice.
• Reset the sums after a signal has been investigated and resolved, or the old accumulation contaminates the next detection.
• Use the change-point feature deliberately: date the start of the climb and go read the logs for that period.
• Keep a plain time plot of the raw data alongside — the CUSUM shows accumulation, not the measurements themselves.
• If your audience finds cumulative sums opaque, an EWMA chart attacks the same problem with an easier-to-explain picture.

Point by point, a small shift hides in the noise. Summed, it draws a straight line back to the day something changed.

Like the EWMA, the CUSUM chart is advanced SPC and lives in our Black Belt curriculum ($499, about 60 hours, 150-question proctored exam). Green Belts meet the Shewhart family first; Black Belts learn what to reach for when the shifts worth money are the small ones.