Can you check my interpretations for the run chart, frequency histogram, and u$-$chart for the following question?

Tom Pyzdek, a noted quality consultant, presented data on patient falls at the Great Falls Hospital $($fictitious name$),$ for patients as shown in the $$HW$2\_$Data.xlsx$$ file found on Canvas. Note that the $$sample size$$ is in $100$s of Patient Care Days $($PCDs$).$ Develop a run chart, a frequency histogram, and a u$-$chart for these data, and include these $3$ charts in your answers. What insights do you get from each chart? What would you advise the administration of the hospital to do about patient falls?

The run chart of patient falls over time analysis a relatively stable pattern with occasional fluctuations. Most months show a consistent number of falls, with no significant upward or downward trends. However, there are a few month with noticeable spikes in patient falls $($e$.$g$.,$ March $2007,$ November $2007,$ June $2008,$ and August $2008),$ which could indicate periods when patient safety may have been compromised. These outlier months warrant closer attention to investigate potential factors contributing to the rise in falls, such as changes in staffing levels, patient conditions, or facility operations. Despite these outliers, the overall trend appears to be stable, suggesting that the hospital$$s patient fall prevention measures may generally be effective but need fine$-$tuning during high$-$risk periods.

The frequency histogram shows that $2$ PCDs $($Patient Care Days$)$ are more common than $1$ PCD across the entire data set, with most months falling into the $2$ PCDs category. This suggests that patient falls tend to occur more frequently during periods of higher patient care volume or longer stays, as represented by higher PCD counts. The histogram helps highlight variability in patient care, pointing to potential issues during higher$-$care$-$volume periods. Although most months report $2$ falls per $100$ PCDs$,$ the occasional higher counts indicate that, during certain months, the fall rate could be higher than expected, and further investigation is warranted in those months.

The u$-$chart, which normalizes the fall data against PCDs$,$ provides an overview of the fall rate per unit of patient care. From the u$-$chart, most of the data points fall within control limits$,$ indicating that the process is generally in control. However, the chart reveals some out$-$of$-$control points, particularly in the months of March $2007,$ November $2007,$ June $2008,$ and August $2008,$ where the falls rates exceed the upper control limits $($UCL$).$ These spikes indicate special causes or significant deviations in the process, suggesting that these months may required additional scrutiny to identify any root causes for the higher fall rates. The u$-$chart suggest that while the overall process is table, the hospital should focus on preventing such out$-$of$-$control events by reviewing operational factors during those specific months.