Home / Statistical Tools / Control Charts / T Chart
T Chart¶
From Excel click...
QXL Stat Tools Tab > Control Charts > Rare Event Charts > T Chart (Time Between Events)
Want to build one first?
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 T chart plots the measured time between one rare event and the next: hours between machine failures, days between adverse drug reactions, minutes between line stoppages. One point is one event, and the value plotted is the interval that preceded it.
| Panel title on the worksheet | T Chart, one panel only |
| What it plots | the elapsed time between consecutive events |
| Y axis | Time Between Events, or Days, Hours, Minutes or Seconds Between Events when the input is date-times |
| X axis | Subgroup |
| Distribution behind the lines | Weibull, or the exponential special case |
The ribbon button reads T Chart (Time Between Events). The dialog that opens is titled T Chart. The worksheet it writes is named TChart, with no space, which does not match either of them.
When to use it¶
- The event is rare, and the spacing between events is a measurement rather than a count: elapsed time, running hours, mileage.
- If the spacing is a count of opportunities, use the G Chart. The two charts answer the same question about the same events and differ only in whether the spacing is measured or counted. A record of dates alone can go on either: the G chart truncates to whole days, the T chart keeps the fraction.
How it works¶
Each row is one event. The value is either the elapsed time since the previous event, or the date and time the event happened, in which case Quantum XL differences consecutive stamps for you and lets you choose the unit.
Two numbers drive the whole chart. Quantum XL fits a Weibull distribution to the intervals you supply, estimating a shape and a scale, reported in the summary table as Weibull β (shape) and Weibull α (scale). Everything drawn is then a quantile of that distribution: the center line is its median, and the limits are its far tails.
There are two ways to reach those two numbers, and the dialog makes it a single check box:
- Left clear, which is the default, both parameters are fitted from the data.
- Ticked, Fit exponential distribution only, the shape is fixed at 1 and the scale is simply the average of your intervals. Shape 1 is the constant-rate model: how long you have already waited tells you nothing about how much longer you will wait.
Three consequences hold either way, and each surprises people arriving from a Shewhart chart:
- The band is not symmetric. A waiting time cannot be negative but has no ceiling, so the distribution is right-skewed and the band drawn from it is lopsided.
- The center line is a median, not an average. It is the interval half of your intervals should fall below.
- The lower limit sits just above zero, so in practice a point can only be marked for being above the upper limit: a wait longer than the model expects, meaning events became rarer. On this chart the signal you are most likely to get is an improvement.
The sigma multiplier does not become a distance. It selects which quantiles the lines are drawn at: at the default 3 the limits are the 0.135th and 99.865th percentiles, the same probabilities a 3-sigma normal band would cover.
Two settings change what the fit is computed from rather than how. Baseline Estimation fits from the first few events only and extends the result. Split Control Limits divides the chart into phases and re-fits inside each one. There are also Historical Weibull α and β boxes for supplying known parameters outright.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet named TChart. Under GroupBy there is one worksheet per group, each named TChart - {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 T Chart panel, plotting each interval 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 Weibull α (scale), Weibull β (shape), 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 T 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.