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Out-of-Control Tests¶

An out-of-control test is a pattern Quantum XL looks for in the points already plotted on a control chart. The tests never change the chart: the center line, the control limits, and the plotted values are the same whether every test is on or every test is off. All a test does is decide which points get marked.

Which tests a chart offers, and which arrive switched on, depends on the chart. Every chart dialog carries the same group box for them, headed Out-of-Control Rules, on the Rules & Display tab.

The Tests¶

Nine numbered tests exist. Rules 1 through 8 are the Shewhart special-cause tests and Rule 9 is offered on the G chart alone. The row labels below are the labels the dialog shows.

Row label as shown in the dialog	What it looks for	Standard threshold
Rule 1 - Beyond K sigma from center	A single point outside a control limit.	none of its own, see below
Rule 2 - N consecutive points on same side of center	A run of points all above, or all below, the center line.	N = 9
Rule 3 - N consecutive increasing or decreasing	A steady climb or a steady fall.	N = 6
Rule 4 - N consecutive alternating up/down	Points that zigzag, up then down then up, without a break.	N = 14
Rule 5 - N of M beyond 2 sigma (same side)	Most of a short window sitting far out on one side.	N = 2, M = 3
Rule 6 - N of M beyond 1 sigma (same side)	Most of a short window sitting moderately out on one side.	N = 4, M = 5
Rule 7 - N consecutive within 1 sigma	A long run hugging the center line, which is closer to it than the calculated limits allow for.	N = 15
Rule 8 - N consecutive beyond 1 sigma (either side)	A long run avoiding the center line, on either side of it.	N = 8
Rule 9 - N consecutive zero counts (Benneyan)	A stretch of exact zeros. G chart only.	N = 4

Rule 1 has no threshold box, because its width is the sigma multiplier you set in the Control Limits section of the same dialog. Changing that number changes the limits and the Rule 1 test together. On a variable chart it also moves the zone lines that rules 5 through 8 read, so it changes those tests as well.

The exact condition each rule tests, written as a formula, is on Out-of-Control Rules.

Which Chart Offers Which¶

Chart	Tests offered	On by default
Xbar-R, Xbar-S, I-MR, I-MR-R/S, Z-MR, Individuals, Xbar	1 through 8	all eight
R, S, Moving Range	1 through 8 are offered, but 5 through 8 read the zone lines of a location panel and never run on a chart drawn as a dispersion panel alone	all eight
EWMA, CUSUM	1 only	1
p, np, Laney P', c, u, Laney U'	1, 2, 3, 4	1 only
T	1, 2, 3, 4	1 only
G	1, 2, 3, 4, 9	1 only
Levey-Jennings	the six Westgard tests below	all six

A test that a chart does not offer has no row in that chart's dialog and cannot be turned on there. The difference in defaults is worth knowing before comparing charts: the same data plotted as a variable chart is tested against eight rules, and plotted as an attribute chart against one.

The Westgard Set on Levey-Jennings¶

The Levey-Jennings chart replaces the numbered rules with six clinical multi-rule tests, all six ticked by default.

Row label as shown in the dialog	What it looks for	Parameters
1-2s - one point beyond 2 sigma (warning)	one point past two standard deviations	Sigma = 2
1-3s - one point beyond the control limits	one point outside the drawn limits	none
2-2s - N of M consecutive beyond 2 sigma (same side)	two in a row past two sigma on the same side	N = 2, M = 2
R-4s - consecutive pair straddling ±2 sigma	a neighbouring pair split across the center, one past each two sigma line	none
4-1s - N of M consecutive beyond 1 sigma (same side)	four in a row past one sigma on the same side	N = 4, M = 4
10x - N consecutive on one side of the mean	ten in a row on one side of the mean	N = 10

R-4s is offered on no other chart. Rules 3, 4, 7, and 8 are not part of this set and never run here, whatever their stored settings say.

Setting the Thresholds¶

Each row is a check box followed by up to two small boxes labelled N = and M =. N is how many points the test needs and M, where a test has one, is the window those points must fall inside.

Every box arrives pre-filled with the standard value rather than blank, so the row states what it will do before you touch it.
Unticking a test locks its boxes but keeps the numbers, so a value you set survives switching the test off and on.
The two dialog families handle a refused threshold differently, and neither says anything. On the variable chart dialogs a box can be left blank, and blank, zero and negative all mean use the standard value. On the attribute and rare-event dialogs a blank is not accepted, so the box keeps the last number you typed, and anything below 2 is quietly raised to 2 as you leave it.

Which Panels Are Tested¶

Every panel of a chart is tested, the dispersion panels included: a range, standard deviation, or moving range panel runs its own tests against its own center line and its own limits.

Rules 5 through 8 are the exception. They read the zone lines and assume a spread that is symmetric about the center, which a range or a standard deviation does not have, so they run on the location panel only. On a chart drawn as a dispersion panel alone, those four rows are greyed out but keep their settings. The Z-MR moving range panel goes one step further: rules 4 through 9 are forced off there whatever the dialog says, so it runs rules 1, 2 and 3 only.

What the Chart Reports¶

The chart does not tell you which test fired

Every enabled test is run, and the results are combined into one verdict per point: this point broke at least one enabled test, or it did not. A point that broke one is drawn in a different color, and that is the whole of the report. There is no per-rule label, no per-rule marker, no per-rule column, and no list of violations anywhere on the chart or the worksheet. A point that breaks four tests looks exactly like a point that breaks one.

To find out which pattern produced a particular signal, switch the other tests off and rebuild the chart.

The summary table beside the chart reports a count of out-of-control points for each panel, and a separate count of the points you marked as outliers. Those are two different things: a marked outlier is your own exclusion, not a test result.

Not every marked point is a separate event, either. The tests that count runs mark the point that completes the pattern and each later point that extends it, so one shift can show as a row of marked points. Which point of a run gets marked is set out under Which Points a Rule Marks.

When Tests Do Not Fire¶

Condition	Effect
Control limits set to None, on a variable chart	No test fires. Every result is cleared with the limits, so no point is marked even though the rows are still ticked.
Control limits set to None, on an attribute or rare-event chart	The center line is still estimated, so rules 2, 3, and 4, and Rule 9 on a G chart, still fire. Rule 1 cannot, having no limit to exceed.
Control limits set to Manual	The tests run against the band you entered, and the zone lines are derived from it.
Manual limits with the center left blank, on an attribute chart	Rule 2 cannot fire, having no center line to take a side against. Rules 3 and 4 read only the order of the plotted values, so they still fire. Rule 1 still tests whatever UCL and LCL you did enter.
A split or phase boundary	Every run and window restarts. A run in progress when the boundary arrives is abandoned and cannot join the run after it.
A blank or excluded point	Runs break at the gap instead of bridging it. For rules 5 and 6 a blank invalidates every window that overlaps it.