What indicates that a process is out of control?

A process is considered out of control when there are clear signals indicating that the variability within the process is not due to random causes. Each of the options presented provides different criteria for identifying a lack of control.

A single point plotting outside the control limits is a direct indicator that the process has experienced an unusual event, suggesting the presence of an assignable cause. Control limits are statistically determined boundaries that define the expected range of variation within the process. When a point falls outside these limits, it signifies a significant deviation from what is expected.

When two out of three points are on the same side of the centerline, it illustrates a tendency in the data that may suggest shifts or trends, which could also point to an issue with the process that isn't purely random. This condition indicates that the process may not be stable.

A run of eight points on the same side of the centerline indicates a sustained directional trend, which statistically indicates that there may be a persistent issue affecting the process. This signal is significant because it suggests that the process is moving in a particular direction rather than exhibiting the randomness expected of a controlled process.

Given that each of these indicators demonstrates a different form of instability or non-randomness within the process, the best response is that all of