Monitor several correlated variables together with a Hotelling T² chart, or track the gaps between rare events with a G chart. Paste your data, get the chart, control limits, and out-of-control signals — all client-side.
Choose a chart type, paste your data, and press Calculate to plot the control chart with limits and signals.
Several correlated measurements each look fine on their own, yet their combination is off. Enter the lab to see how a Hotelling T² chart catches it.
Pick Hotelling T² if you're tracking two or three linked variables (like temperature and pressure together), or the G chart if you're counting days/units between rare events.
For T², paste one row per observation with variables in columns — the calculator finds the typical centre and how variables move together. For the G chart, paste the count between events.
The T² chart shows how far each point sits from the typical centre (accounting for how variables move together). The G chart plots gaps between events. Any point outside the control limit is flagged.
When quality characteristics move together, or when defects are so rare that a traditional chart breaks down, the standard Shewhart toolkit struggles. The Hotelling T² chart watches several correlated variables with a single statistic, and the G chart monitors the gaps between rare events — together they extend SPC to situations ordinary charts cannot handle.
Multivariate SPC tracks several correlated quality characteristics with a single statistic, the Hotelling T², so a shift in any of them — or in the relationship between them — produces one signal on one chart. Rare-event SPC, such as the G chart, monitors processes where defects are so infrequent that counting them per subgroup gives mostly zeros; instead it charts the number of opportunities between events using the geometric distribution.
A Hotelling T² chart watches several correlated measurements at once. It learns how the variables normally sit together (their averages and how they move with each other), then condenses each new observation into a single number, T², that measures how unusual that whole combination is. A point above the control limit signals that the variables have drifted out of their normal relationship — even if each one looks fine on its own chart. The G chart instead handles rare events, tracking the gap between occurrences and flagging when failures start arriving unusually close together.
A chemical process tracks temperature, pH, and viscosity. Each individual chart looks fine — all within limits. But batch 23 has an unusual combination: temperature slightly high, pH slightly low, and viscosity slightly high all at once.
A multivariate T² chart flags batch 23 as out of control. No single variable triggered an alarm, but together the pattern is statistically unusual.
What to do with this: Hold batch 23 for extra testing. Multivariate charts catch problems that hide between the gaps of individual charts, especially when variables are correlated.
Modern processes are instrumented with many sensors whose readings are correlated. Watching them on one chart catches subtle shifts — a variable drifting against its partners — that individual charts miss, while keeping the false-alarm rate under control. Rare-event charts let you keep improving even when defects are already very low.
Reach for Hotelling T² when two or more characteristics are measured together and are correlated. Reach for a G chart when events are rare — a few defects per thousand, infections per month, or incidents per quarter — so a p or c chart would have limits squashed against zero and almost never signal.
These charts belong in the Control phase of DMAIC for processes that have moved beyond basic SPC. T² is the natural monitoring tool after a multiple-regression or DOE study identifies several interacting factors, and the G chart sustains gains on near-zero-defect processes where ordinary attribute charts go flat.
When T² signals, decompose the statistic or inspect the individual variables to find which characteristic — or which relationship between characteristics — moved, then investigate the special cause as you would on any control chart. When a G chart signals an unusually long gap, confirm whether a genuine improvement has taken hold and, if so, recalculate limits on the new, better baseline. A short gap (clustering) warns that events are speeding up; act quickly. Document findings in your control plan and keep monitoring.
Combine multivariate and rare-event charts with run charts, attribute control charts, and a DMAIC project structure to sustain improvements on complex or near-zero-defect processes.
Use multivariate SPC when you monitor two or more quality characteristics that are correlated — for example temperature and pressure on a moulding press, or fill weight and fill height on a filler. Charting each variable separately ignores the correlation and inflates the chance of a false alarm. A Hotelling T² chart combines all the variables into a single statistic that respects how they move together, so it signals when the joint behaviour of the process changes, even when no single variable is individually out of control.
A Hotelling T² chart is the multivariate generalisation of a Shewhart chart. For each observation it computes T² = (x − x̄)ᵀ S⁻¹ (x − x̄), the squared statistical distance of the point from the mean vector, scaled by the inverse covariance matrix S⁻¹. Because it uses the covariance matrix it accounts for the correlation between variables. A single upper control limit (derived from the beta or F distribution) is plotted; any point above it is a signal that the process has shifted in at least one direction.
A G chart (a geometric control chart) monitors the number of opportunities — units produced, patients treated, or days elapsed — between successive rare events such as defects, infections, or accidents. When events are very rare, a traditional p or c chart has limits crammed near zero and is almost useless. The G chart instead plots the count between events, models it with the geometric distribution, and sets probability-based limits. A point above the upper limit (an unusually long gap) often signals genuine improvement, while clustering near zero signals deterioration.
Running an individual chart per variable has two problems. First, with several charts the overall false-alarm rate climbs quickly — ten charts at 0.27% each give roughly a 2.7% combined false-alarm rate. Second, separate charts cannot see correlation: two variables can each sit inside their own limits while their combination is highly unusual. A Hotelling T² chart fixes both issues by testing all variables jointly with one statistic and one control limit, then you drill back to the individual charts to diagnose which variable drove a signal.
A significant paired t-test confirms your improvement worked. Structured training shows you how to sustain it and replicate it elsewhere.
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Want to monitor several correlated characteristics together inside a full DMAIC project? The Black Belt covers Hotelling T², multivariate SPC, and the advanced Control phase toolkit.
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