The four Shewhart rules help determine whether a process is in control or if there are signs of non-random variation that warrant investigation. They guide how to interpret control charts and identify potential issues.

1. One point beyond control limits - If a single data point falls outside the upper or lower control limits, it indicates an out-of-control process and suggests an assignable cause needs to be investigated.
2. Two out of three consecutive points near a control limit - If two of the last three points land in the outer third of the chart (near the control limits), it signals a possible trend toward instability.
3. Four out of five consecutive points in the outer two-thirds - If four of the last five points are in the outer two-thirds of the control chart, this suggests a systematic shift or trend that requires attention.
4. A run of eight points on one side of the centerline - If eight consecutive data points fall on the same side of the centerline, it implies a non-random trend or shift in the process, which could indicate an assignable cause.