Sigma Test

Sigma Tests:

These tests point out the possible presence of an assignable cause.

The three sigma test can be applied to both, X and R charts.

The One and Two sigma tests are Zone Tests and thus they should not be applied to R the chart due to its lack of symmetry around the mean.

There are three sigma test used in six-sigma i.e.

1. Three Sigma Test (Extreme Points Test)

2. Two Sigma Test

3. One Sigma Test

Three Sigma Test (Extreme Points Test):

The existence of a single point beyond a control limit signals the presence of an out-of -control condition, i.e. the presence of an assignable cause.

Two Sigma Test:

This test watches for two out of three points in a row in Zone A or beyond. The existence of two of any three successive points that fall on the same side of, and more than two sigma units away from, the central line, signals the presence of an out-of -control condition. This test provides an "early warning" of a process shift.

One Sigma Test:

This test watches for four out of five subgroups in a row in Zone B or beyond. The existence of four of any five successive points that fall on the same side of, and more than one sigma unit away from, the central line, signals the presence of an out-of-control condition. Like the previous test, this test may be considered to be an "early warning indicator" of a potential shift in process performance.
The three sigma test is the most (and often the “only” one) used test in software engineering literature.

Limit Tests:

All the tests included in this class use chart Zones and thus they are applicable to the X charts only.
Run above or below the Centerline Test: This test watches for 7, 8 or 9 consecutive observations above or below the centerline. The presence of such a run indicates that the evidence is strong and that the process mean or variability has shifted from the centerline.
Mixing/Overcontrol Test: Also called the Avoidance of Zone C Test. This test watches for eight subgroups in a row on both sides of the centerline avoiding Zone C. The rule is: Eight successive points on either side of the centerline avoiding Zone C, signals an out-of-control condition.
Stratification Test: Also known as the Reduced Variability Test. This test watches for fifteen subgroups in a row in Zone C, above and below the centerline. When 15 successive points on the X chart fall in Zone C, to either side of the centerline, an out-of control condition is signaled.

Trend Tests:

This class of tests point out a trend resulting in a process performance shift. Neither the chart centerline nor the zones come into play for these tests and thus they may be applied to both X and R charts.
Oscillatory Trend Test: it watches for fourteen alternating up or down observations in a row. When 14 successive points oscillate up and down, a systematic trend in the process is signaled.
Linear Trend Test: it watches for six observations in a row steadily increasing or decreasing. It fails when there is a systematic increasing or decreasing trend in the process.

Causes Investigation

SPC is only able to detect whether the process performance is “out of control” and if an anomaly exists.
It doesn’t support the manager during the cause’s investigation and the selection of the appropriate corrective actions. This solution extends the SPC-theory by providing a specific interpretation of the anomaly for each run test failure from the software process point of view, and suggesting possible causes that make the process “Out of Control” (Baldassarre, 2004). More precisely, the authors have arranged and interpreted the selected SPC indicators in logical classes:

A. Sigma (RT1, RT2, RT3),

B. Limit (RT4, RT5, RT6) and

C. trend (RT7, RT8)