Statistics
A CUSUM chart adds up small departures from target so a slow creep shows itself long before a standard chart reacts. This guide walks through the built-in delivery-time sample, fifteen days of data and fourteen signals, and shows how the chart keeps a Control phase honest.
The CUSUM Chart detects small persistent shifts in the process mean using cumulative sum control charts. It is sensitive to subtle drifts. That single sentence explains both why it exists and why it sits in the Control phase of RDMAICS rather than earlier.
A standard individuals chart judges each point on its own. One point, one verdict. That works well when something breaks suddenly. It works poorly when a process slides a fraction at a time, because no single reading looks strange enough to act on. The CUSUM chart takes a different view. It accumulates the difference between each reading and the target. Small departures in the same direction add up. The running total walks away from zero and crosses a limit.
Reach for it when the improvement has already landed and the project team is about to hand the process back. That is the moment the gain is most fragile. Nobody is watching closely. Habits reassert themselves. A supplier changes grade. A shift pattern shifts. CUSUM is the instrument that notices before the old performance returns in full.
The worked example here is the sample data built into the tool. It is fictional. Treat it as a teaching case, not as evidence about any real operation.
The scenario is labelled Delivery-time drift. Fifteen daily observations run from Day 1 to Day 15. Each day is also tagged by stratum, alternating between Lunch shift and Dinner shift. The series starts at 29 on Day 1 and ends at 31 on Day 15.
Read the raw numbers in order and the problem is easy to miss. Day 1 is 29. Day 5 is 29. Day 9 is 29.8. Day 12 is 30.4. No day looks alarming next to the day before it. The largest step between consecutive readings is small. Yet the process has moved two units across fifteen days, and it has moved in one direction only.
That is exactly the pattern CUSUM was built for. A one-day jump gets attention on its own. A fifteen-day creep gets explained away, one day at a time, until it becomes the new normal.
The input structure is deliberately plain. There are four columns and only one of them is compulsory.
Observation or period is the label for each row. In the sample it is Day 1 through Day 15. Observations in time order is the measured value, and the asterisk in the column heading is a reminder that order matters. CUSUM is a running total. Shuffle the rows and the chart becomes meaningless.
Group or stratum lets you tag each reading. The sample alternates Lunch shift and Dinner shift. Series or scenario lets you keep more than one storyline in the same table. Every row in the sample carries the label Delivery-time drift.
The tool reports fifteen points. The centre is 0. The upper limit is 0.7092 and the lower limit is -0.7092. Sigma is 0.1773. Fourteen points are out of control.
The centre of 0 is the first thing to understand. A CUSUM chart does not plot the delivery times themselves. It plots the accumulated departure from target. When the process sits on target, the running sum hovers around zero. When the process sits above target, the upper cumulative sum climbs and keeps climbing.
The tool draws two charts. The upper cumulative sum runs from 0 up past 4 and crosses the UCL. The lower cumulative sum runs the other way, down past -4 and across the LCL. Together they tell you the direction of the shift as well as its existence.
The signals table lists fourteen entries, from Point 2 at 29.2 through to Point 15 at 31. Every one is flagged under rule 1, one point beyond 3 sigma, with the note that a single reading this far out is almost never chance. All eight Nelson rules are applied to the main chart. A moving range or dispersion chart is tested only for points outside its limits, because its values are related to each other by construction.
Fourteen signals out of fifteen points is not subtlety. It is the cumulative sum shouting about a pattern that the raw column of numbers barely whispers. The tool also offers an AI review that explains the result in words if you want a second reading.
A Control phase needs a trigger, not just a report. CUSUM gives you one. The limit of 0.7092 is a line somebody can watch without a statistics background. Cross it and you act.
In the sample case the action is obvious in kind, if not in detail. Something changed around the middle of the series. Day 1 through Day 6 sit between 28.9 and 29.3. From Day 7 onward every reading is higher than the one before. That shape points an investigation at a date rather than at the whole process.
The stratum column supports a second decision. The sample alternates Lunch shift and Dinner shift, and the drift appears across both. That narrows the search. A cause that affects both shifts equally is unlikely to be a shift-specific habit.
Set a baseline to make the handover concrete. Judge later data against the improved period rather than against the full history. Then the chart answers the only question that matters after the project closes: is the process still where the team left it.
The first mistake is treating CUSUM as a replacement for an individuals chart. It is not. It is a complement. CUSUM is slow to react to a single large spike and fast to react to a small sustained shift. Run both if you can.
The second is reading the vertical axis as if it showed the measurement. The upper chart in the sample runs from 0 to above 4. No delivery time in the data is anywhere near 4. The axis shows accumulated departure.
The third is calculating limits from data that already contains the drift. The tool says plainly that limits were calculated from all fifteen points, and it invites you to set a baseline instead. If you build limits from a drifting period, you bake the drift into the standard you are measuring against.
CUSUM detects. It does not diagnose. The fourteen signals in the sample tell you the mean has moved. They say nothing about why. No chart knows about the new supplier, the rostering change or the car park being resurfaced.
It will not tell you whether the shift matters. A move from 29 to 31 may be trivial or may breach a customer promise. That judgement comes from the specification and the customer, not from the limit of 0.7092.
It will not fix a measurement problem. If the way you record delivery time changed partway through the fifteen days, the chart will show a drift that exists only in the measurement system. Check the measurement before you check the process.
It will not watch itself. A CUSUM chart only holds the gain if somebody looks at it on a known rhythm and somebody else is named to respond when a point crosses the limit. Write both names into the control plan. The chart is the instrument. The routine around it is the control.
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