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G Chart¶
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QXL Stat Tools Tab > Control Charts > Rare Event Charts > G Chart (Count Between Events)
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How-To works through a finished chart step by step, from sample data you copy off the page straight into Excel. The data has a point that is out of control, so the result has something to read rather than twenty points in a row.
How-To with GroupBy does the same thing with a GroupBy column, so one run produces a separate chart per group.
A G chart plots the count of opportunities between one rare event and the next: patients discharged between two infections, parts made between two rejects, days between two outages. One point is one event, and the value plotted is the gap that preceded it.
| Panel title on the worksheet | G Chart, one panel only |
| What it plots | the count between consecutive events |
| Y axis | Count Between Events, or Days Between Events when the input is dates |
| X axis | Subgroup |
| Distribution behind the lines | geometric |
The ribbon button reads G Chart (Count Between Events). The dialog that opens is titled G Chart, and the worksheet it writes is named G Chart too.
When to use it¶
- The event is rare enough that a count-based chart runs out of resolution. A c or u chart plots how many events occurred per sample; when most samples contain none, that chart has almost nothing to plot and its limits stop being usable. A G chart turns the question round and plots the gap instead.
- You can count opportunities between events, in whole numbers: units produced, patients admitted, days elapsed.
- If the gap is a measurement rather than a count, use the T Chart. The two charts answer the same question about the same events and differ only in whether the spacing is counted or measured.
How it works¶
Each row is one event. The value is either the count since the previous event, or the date the event happened, in which case Quantum XL converts the dates into between-event counts for you.
One number drives the whole chart. From the gaps you supply, Quantum XL estimates the probability that any single opportunity is an event, written \(\hat{p}\) and reported as pHat in the summary table. Everything drawn on the chart is then a quantile of the geometric distribution with that probability: the center line is its median, and the limits are its far tails.
Three consequences follow, and all three surprise people who arrive from a Shewhart chart:
- The band is not symmetric. The center line sits much closer to the lower limit than to the upper one, because a gap can be 0 but has no ceiling.
- The center line is a median, not an average. It is the gap that half of the gaps should fall below. It will not equal the mean of your data.
- The lower limit is 0 at any realistic event rate, so a point can only be marked for being above the upper limit. On this chart that is a gap longer than the model expects, which means events became rarer. The signal you are most likely to get is an improvement.
The sigma multiplier still applies: it does not become a distance, it selects which quantiles the lines are drawn at. At the default 3 the limits sit at the 0.135th and 99.865th percentiles, the same probabilities a 3-sigma normal band would cover.
Two settings change what the lines are estimated from rather than how. Baseline Estimation estimates \(\hat{p}\) from the first few events only and extends the result across the whole chart. Split Control Limits divides the chart into phases and re-estimates inside each one. There is also a Historical pHat box for supplying a known rate outright.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet named G Chart. Under GroupBy there is one worksheet per group, each named G Chart - {GroupName}.
Worksheets are divided by GroupBy group, not by chart. Every chart belonging to a group is stacked down that one worksheet, one below the other, so selecting three measurement columns without GroupBy produces three charts on a single sheet rather than three sheets. The User Input block is written once at the top of each worksheet; everything after it repeats for each chart on the sheet.
On the sheet, from the top:
- A User Input block in the first two columns, holding the analysis title, the data column, the X-axis label column and any GroupBy columns, and whether the calculation type was Excel or GroupBy. Modify Existing Analysis reads it back.
- The G Chart panel, plotting each between-event count with its center line and limits, the zone lines if you asked for them, any reference lines, and phase dividers when the chart is split. Points that broke an enabled out-of-control test are drawn in a different color.
- A summary table to the right, listing pHat, CenterLine, UCL, LCL, Total subgroups, OOC points and Outliers marked. A split chart adds a Per-Phase Breakdown block below it.
There is no capability block and no histogram on a G chart worksheet: this dialog has no Capability tab, and the capability output is switched off in the engine as well.
When the analysis finishes, the Control Chart task pane opens on the right. See Task Pane for what it can and cannot change.