Which of the following statements is most accurate based on Xbar and R charts developed from previous data?

In control charts, X-bar and R charts are utilized for monitoring process stability over time. An X-bar chart displays the averages of subsets of data collected, while the R chart shows the range within those subsets.

When a previously developed X-bar chart indicates that the mean is in control, it implies that the process average remains stable and consistent over time, with no trends, shifts, or out-of-control points present in the data. Conversely, if the R chart indicates that the range is not in control, this suggests variability within the data is excessively high or fluctuating. This could imply that while the average is stable, the consistency in the data points is failing -- pointing to issues in the process that might cause this variability, such as machine wear or changes in measurement methods.

Thus, stating that the mean is in control while the range is not conveys a scenario where the process is producing outputs that are consistent in average but exhibit problematic variability. Understanding this distinction is crucial for making informed decisions about process adjustments and improvements.