Home / Statistical Tools / Control Charts / T² and Generalized Variance / Options

Options¶

Every control on the dialog, which has four tabs: Data, Estimation, Historical Parameters and Display. The footer buttons are Back, Help, Cancel and Finish.

There is no panel control. Which panels are drawn is decided by the ribbon command you started from, so a dialog opened from Hotelling T² draws the T² panel and there is nothing here to change that.

There is no out-of-control test control either. This chart runs exactly one test, beyond the control limit, on both panels, and it cannot be turned off. The other eight tests the Shewhart charts offer are not run and are not offered here.

The Data tab¶

The same Excel and GroupBy data source the other variable charts use, with the item lists and the >, >>, < and << buttons for moving columns between them.

Control	What it does
Available Items	every column the data source offers, with its Data Types beside it
Variable Columns (select 2 or more):	the measurements watched jointly. Two is the minimum and the dialog will not finish with fewer
Subgroups	the group box holding the size box, with Subgroup size: inside it, annotated 1 = individuals; n groups consecutive rows
Stage Column (Optional)	splits the run into stages, each with its own estimated parameters
X-Axis Labels (Optional)	a column whose values label the points instead of their position
GroupBy Order	when the source is GroupBy, the columns that split the data into separate charts

The row count must divide by the subgroup size. A trailing partial subgroup is refused rather than plotted short.

Stage Column is disabled once any historical parameter is filled in, with the reason on the dialog: Stages are ignored when historical parameters are supplied. A supplied mean and covariance replace what a stage would have estimated, so the two cannot both apply.

The Estimation tab¶

Estimate Limits From¶

Control	What it does
All subgroups	the default. Every included subgroup contributes to the estimated mean and covariance
First N subgroups:	estimate from the first N included subgroups only, and plot all of them

Every subgroup is plotted either way. First N changes what the centre and the limits are computed from, not what is drawn, which is how a chart shows later data against a baseline period.

First N cannot be combined with a historical covariance, and the dialog says so: First-N estimation cannot be combined with a historical covariance. A supplied covariance is the baseline, so there is no estimation period left to choose.

Control Limit Alpha¶

Control	What it does
Alpha (false-alarm rate):	the T² limit's false-alarm rate. Annotated Greater than 0 and less than 1; default 0.0027

The default is not exactly 0.0027, and the page says 0.0027 because that is what the dialog says. The value the engine uses when none is given is 0.0026997960632601918, which is the exact two-sided three-sigma rate, 2 x Phi(-3). Type 0.0027 and you get 0.0027; leave it alone and you get the three-sigma rate the other charts use.

Alpha is disabled on a Generalized Variance chart, with the reason: Alpha applies only to the T² limit. The Generalized Variance limits are three-sigma moment limits with no alpha in them at all, which is on Math Details.

Transformation¶

Control	What it does
None	the default
Use Box-Cox Transformation	annotated Fits an optimal lambda per variable

Box-Cox fits its own lambda for each variable, not one shared lambda. Both panels, the parameter table and the limits are then in transformed units, and the parameter table says so with Values are in Box-Cox transformed units.

Box-Cox cannot be combined with historical parameters, and the dialog says Historical parameters cannot be combined with Box-Cox. A mean and a covariance you typed are in your measurement's units, and the transformed data is not.

The Historical Parameters tab¶

Leave this tab empty for Phase I, where the chart estimates its own parameters. Fill it in for Phase II, where the chart is judged against parameters you supply.

Control	What it does
Historical Mean (Mu)	a grid with a Variable column and a Mean column, one row per variable column you selected
Historical Covariance (Sigma)	a p by p grid, one row and one column per variable
Sample count behind the historical covariance:	how many observations the supplied covariance was computed from

What must be filled in together¶

Either leave a grid completely empty or fill it completely. A partly filled grid is not a valid dialog, and Finish stays unavailable.

If you supply	You must also supply
the covariance	the mean, every cell of it
the covariance	the sample count
the mean alone	nothing else. A mean with no covariance is allowed, and the covariance is still estimated from the data

On an individuals chart the sample count must exceed the number of variables. With two variables a sample count of 2 is refused; 3 is the smallest that works. The limit's degrees of freedom are m - p, and at or below zero there is no limit to compute.

Pasting the covariance in¶

The grid accepts a paste from Excel: tab-separated cells, newline-separated rows, a trailing newline tolerated. What it accepts is strict:

exactly p by p. A block of the wrong size is refused and the message says the size it wanted
every cell numeric. A refusal names the cell
symmetric, within a relative tolerance of 1e-8. A refusal names where the asymmetry is

A block that passes is mirrored, upper triangle winning, so the two halves agree exactly afterwards. Nothing else about your numbers is altered.

The clipboard being empty is its own message: The clipboard is empty.

The Display tab¶

Reference lines, the same control the other variable charts carry: extra horizontal lines at values you choose, drawn on the panels without taking part in any calculation.

What is disabled when, in one table¶

Every one of them carries the dialog's own wording, so a greyed control always explains itself:

Control	Disabled when	The dialog says
First N subgroups:	a historical covariance is filled in	First-N estimation cannot be combined with a historical covariance.
Historical Covariance (Sigma)	First N is selected, or historical parameters are unavailable
The whole Historical Parameters tab	Box-Cox is on	Historical parameters cannot be combined with Box-Cox.
The whole Historical Parameters tab	a stage column is chosen	Historical parameters cannot be combined with stages.
Stage Column (Optional)	any historical parameter is filled in	Stages are ignored when historical parameters are supplied.
Alpha (false-alarm rate):	the chart is Generalized Variance only	Alpha applies only to the T² limit.

Box-Cox, stages and historical parameters are mutually exclusive three ways, and the reason is the same each time: each of the three decides what the centre and the covariance are, and only one of them can.