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
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.

The stage column moved off this tab. It used to be a Stage Column (Optional) group box here. Splitting the run is now done with the standard Split Control Limits control on the Estimation tab, the same control the other control charts use, so a TSGV chart can be split by a column's value or at manual break rows instead of by a column only.

Split Control Limits is disabled once any historical parameter is filled in, with the reason underneath it: Splits are ignored when historical parameters are supplied. A supplied mean and covariance replace what a split 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 split is chosen	Historical parameters cannot be combined with splits.
Split Control Limits	any historical parameter is filled in	Splits 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, splits 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.

When a number box refuses what you typed¶

A refused number box now tells you why. Type something this box cannot use, then leave it, and a message box opens naming the box and what it wanted:

The box name must be what it wanted.

The title is the analysis name, for example "G Chart" or "Type 1 Gage Study". A box that wants a proportion adds a second sentence, "It is a proportion, not a percent, so type 0.05 for 5 percent.", because typing 5 for five percent is the mistake it is there to catch. The box then goes back to the value it held before, so nothing is lost and nothing wrong is carried into the run.

Text that is not a number at all gets the same message. Type a word, a stray letter beside a figure, or nothing but a minus sign into any number box on this dialog, leave the box, and a message box opens reading:

The box name must be a number.

The box then shows the value it held before. Before this, a box given text simply would not take it: the entry was dropped on the way to the setting, so none of the rules below could be reached and nothing was said. The box looked as though it had accepted what was typed until the moment the focus moved.

The dialog no longer runs the analysis while a setting is unusable. Changing almost any option on this dialog redraws the chart straight away, without waiting for Finish. That redraw now reads the same rule the Finish button reads. When something on the dialog is wrong, the redraw does not happen and the dialog stays open, with the reason printed beside the Finish button.

Where the problem is two settings that contradict each other, and you have finished making both choices, a message box says so as well. Where it is a box you have not finished filling in, the dialog waits quietly instead, with the reason still beside Finish.

Nothing you typed or clicked is undone. The setting you just changed stays changed, the number you typed stays in its box, and the same sentence stays on screen beside the Finish button, which is switched off until you resolve it. Change the other half of the pair, or put the number back, and the chart redraws as usual.

A message box is shown once per reason, not once per redraw. A single click can raise a dozen redraws internally, and repeating the same message box a dozen times would be worse than saying it once, so a second attempt that hits the same reason shows no message box. That is not the dialog ignoring you: the reason is still printed beside Finish the whole time.

This matters because these two-setting rules were previously unreachable. The sentence beside Finish was written and Finish was switched off, but the redraw ran the analysis anyway without ever consulting either, so the chart was drawn from the settings the dialog had already refused.

This dialog keeps its own copies of the baseline and historical controls, so its limits differ from the other variable charts. These are its boxes:

Box	What it must be
Subgroup size:	a whole number of 1 or more. 1 means individuals.
Alpha (false-alarm rate):	a number greater than 0 and less than 1
First N subgroups: count	a whole number of 2 or more. This is the one control chart where the minimum is 2 rather than 4 or 5, because the T² limit needs only two subgroups to form an estimate.
Mean in the Historical Mean (Mu) grid	a number, or blank. The message names the variable: "The historical mean for Thickness must be a number, or blank."
An off-diagonal cell of the historical covariance grid	a number, or blank. The message names the position: "The covariance value in row 2, column 3 must be a number, or blank."
A cell on the diagonal of that grid	a number greater than 0, or blank, because a diagonal cell is a variance. The message names the variable instead of the position: "The variance for Thickness must be a number greater than 0, or blank."
Sample count behind the historical covariance:	a whole number of 1 or more

The covariance matrix is checked as a whole when you press Finish¶

Each cell is checked on its own as you type it, but a matrix whose cells are individually fine can still fail to describe a real spread. That check happens when you press Finish: the dialog stays open, a message box opens reading "The historical covariance matrix must be positive definite.", and the cursor moves to the first cell of the grid so you can start correcting it there.

A sample count that is too small for the number of variables¶

With a complete historical mean and covariance and a subgroup size of 1, the sample count behind that covariance has to exceed the number of variables, or the limits cannot be computed. Each box is fine on its own, so neither is refused. The chart stops redrawing instead, Finish switches off, and the reason appears beside it and in a message box.