Rare-Event Chart: Keep Watch on the Problem After the Project Team Leaves

The Rare-Event Chart monitors infrequent events using time-between or g-chart methods suited to rare occurrence data. Instead of counting defects per hundred or per thousand, you record the gap between one event and the next. Days between duplicate payments. Hours between a safety incident. Units produced between one escape and the next.

You reach for it when the event you care about has become uncommon. That is usually the position you are in by the Control phase of RDMAICS. The improvement has landed. The failure that used to happen weekly now happens rarely. A standard attribute chart starts to struggle at that point, because most subgroups contain zero events and the chart flattens into a line that never speaks.

A time-between chart solves that. Every event still produces a data point, because the gap itself is the measurement. Longer gaps mean the process is behaving. A sudden short gap is the signal that something has shifted back.

That is exactly the behaviour you want once the project team has disbanded. The chart keeps watching when nobody is watching.

The tool opens with a built-in sample dataset. It is fictional, used here only to show how the chart behaves.

The scenario is a hospitality operation tracking duplicate orders. Ten observations are recorded, labelled Day 1 through Day 10. Each value is the number of days between one duplicate order and the next. The series is named Days between duplicate orders. Each observation is also tagged to a group, either Lunch shift or Dinner shift.

The values run 18, 22, 16, 24, 20, 19, 2, 21, 23 and 17. Nine of those gaps sit in the high teens and low twenties. One does not. Observation 7, a Lunch shift reading, shows a gap of 2 days.

That single short interval is the whole story of this dataset. The question the chart answers is whether 2 is noise in a variable process or a genuine break in the pattern. Looking at the raw numbers, you might guess. The chart tells you.

The input structure is deliberately plain. Four columns carry everything the chart needs.

The Observation or period column is the label. In the sample it is Day 1 through Day 10. It drives the horizontal axis and nothing else, so use whatever naming your team already recognises.

The second column is the one that matters statistically. It holds days, hours or units between one event and the next. You enter the interval, not the event count. If two duplicate orders occur eight days apart, the value is 8.

The Group or stratum column holds Lunch shift or Dinner shift in this sample. Use it to tag where the event came from. The Series or scenario column names the measure itself, which here is Days between duplicate orders. That matters when you want to run more than one event type side by side.

From the ten points, the tool returns a centre of 2.1862, an upper limit of 3.1199, a lower limit of 1.2524 and a sigma of 0.3113. Out of control count is 1.

Those numbers look unfamiliar next to a raw gap of 18 days, and there is a reason. The chart is plotted on a transformed scale. Each interval is raised to the power 1 over 3.6, the Weibull shape recommended by Nelson. Time-between data is skewed by nature, so a straight plot would produce misleading limits. The transform makes the data behave well enough for normal-theory control limits.

The tool reports the original units alongside. On the raw scale the centre is 16.7053 days and the limits run from 2.2483 to 60.1069 days. That range reads sensibly against the data. A typical gap of around 16 to 17 days, with routine variation that could stretch to 60 days or compress to just over 2.

Limits were calculated from all 10 points. The tool notes that you can set a baseline instead, so later data is judged against an earlier period rather than against itself. In a Control phase that is usually what you want.

One signal is reported. Point 7, value 1.2123 on the transformed scale, triggers rule 1, one point beyond 3 sigma. The tool describes this as a reading so far out that chance is almost never the explanation.

That is the 2 day gap. In raw terms it sits below the lower limit of 2.2483 days. Two duplicate orders occurred closer together than the improved process should produce.

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. So the absence of other signals in this dataset is informative. There is no drift, no run, no trend. One event, cleanly isolated.

That distinction drives the decision. A trend would suggest the improvement is decaying and the whole control plan needs review. A single out of limit point points you at a specific moment. You ask what happened around observation 7. The group column tells you it was a Lunch shift. That is where the investigation starts.

The tool also offers an AI review that explains the result in plain language if you want a second read before you escalate.

Control phase tools fail for a boring reason. Nobody maintains them. A chart that needs weekly data entry from a team that no longer exists goes stale within a month.

A rare-event chart avoids that trap because it is event driven. You only touch it when the thing you are trying to prevent actually happens. Between events, the chart sits still and costs nothing. In the sample, ten events produced ten rows. That is the entire maintenance burden.

It also sets a clear handover rule. The process owner does not need to interpret statistics. The rule is simple. Log the gap. If the tool flags a signal, escalate. If it does not, carry on.

Set a baseline from the post-improvement period and later data gets judged against the gain you actually achieved, not against a slowly drifting average that quietly absorbs the decay.

The most frequent error is entering counts instead of intervals. If you type the number of duplicate orders that occurred on a day, the chart is meaningless. The column asks for days, hours or units between one event and the next.

The second is forgetting to log events during quiet periods. The chart only knows what you tell it. A missed event inflates the following gap and can hide a real cluster.

The third is over-reading a single point. The sample shows one signal at point 7. That is a prompt to investigate, not a conclusion that the improvement has failed. Nine of ten gaps in this dataset sit comfortably inside the limits.

The fourth is rebuilding the limits every time new data arrives. If you recalculate from all points each month, a slow slide back toward the old performance gets absorbed into the new centre line. Fix a baseline instead.

The chart detects a change in the rate of a rare event. It does not explain the change. Point 7 is flagged. The reason behind it is not in the data. You still need to go and look.

It will not tell you whether the gap is caused by the Lunch shift. The group column tags each observation, but ten points split across two shifts is not enough to test a difference between them. Use the tag to guide a conversation, not to assign blame.

It will not cost the event. Nothing in the result speaks to money, customer impact or risk. Those judgements sit with you.

It also depends on the assumption behind the transform. Intervals are raised to the power 1 over 3.6, a Weibull shape chosen as a general-purpose default. If your event process has a strongly different shape, the limits will be approximate. For most Control phase monitoring that approximation is good enough, because you are watching for large shifts rather than measuring a small one.

And with ten points, the limits themselves are provisional. Centre 2.1862 and sigma 0.3113 come from a short series. As events accumulate, those estimates settle. Treat early signals as questions worth asking rather than verdicts.