When evaluating a control chart, which of the following is not a warning
signal that a random variable x is out of control? 8. __________
(a) A run of nine consecutive points on one side of the center line
(the line at target value ).
(b) One point falls beyond the 3 level.
(c) Two points fall beyond the 3 level.
(d) At least two points lie beyond the 2 level on the same side of the center line.
(e) At least two of three consecutive points lie beyond the 2 level on the same side of the center line.
To evaluate a control chart, we need to understand what warning signals indicate that a random variable x is out of control. Let's consider each option and determine if it is a warning signal or not.
(a) A run of nine consecutive points on one side of the center line: This is indeed a warning signal that indicates x is out of control. It suggests that a systematic change has occurred, and the process needs to be investigated.
(b) One point falls beyond the 3σ level: This is a warning signal because it indicates a significant deviation from the normal variation. It suggests that the process may be out of control.
(c) Two points fall beyond the 3σ level: This is another warning signal that indicates a substantial deviation from the expected variation. It is stronger evidence that the process is out of control compared to (b).
(d) At least two points lie beyond the 2σ level on the same side of the center line: This is also a warning signal because it suggests a consistent deviation from the expected mean. It indicates that the process may be drifting away from the target value.
(e) At least two of three consecutive points lie beyond the 2σ level, on the same side of the center line: This is a warning signal similar to (d). It suggests a potential steady deviation from the expected mean.
Therefore, when evaluating a control chart, all the given options (a), (b), (c), (d), and (e) are warning signals that indicate x is out of control. None of these options are the correct answer to the question of what is not a warning signal.