Q.In a control chart, a sample mean is found to plot above the Upper Control Limit (UCL). What does this indicate, and what action should be taken?

A point outside the control limits is the chart doing exactly what it is designed to do — flagging that ordinary chance-cause variation alone is no longer a believable explanation for what was observed. …

The control limits (UCL and LCL) are set so that, if a process is affected by chance causes only, virtually all sample means are expected to fall between them. A sample mean plotting above the UCL is therefore statistically very unlikely to be explained by chance causes alone — the far more likely explanation is that some assignable cause (a tool going out of adjustment, a bad batch of material, an operator error, and so on) has entered the process and shifted it away from its normal target. …

Assuming a single out-of-limit point should simply be ignored or explained away as 'probably nothing' — the entire statistical justification of the control chart is that such a point is unlikel …