he manager of a $1500-$bed healthcare organization is concerned about the rate of healthcare$-$associated infections $($HAIs$)$ recorded in the facilities under her responsibility. She collects monthly data for HAIs rates across all the facilities for $24$ months. Plot one Run Chart $($Line Graph$)$ of the provided $2-$year data set using Microsoft Excel. $($Hint: There should be just one continuous line chart for both years, starting with year $1.)$

How many $$Runs$$ are present in the Run Chart? Did you detect any special cause variation? If so$,$ briefly explain how these were detected.

The national average rate for HAI is about $1$ in $31$ hospital patients. How do the provided data compare with the national average? Give some possible explanations for the observed data and provide recommendations for addressing the problem.

What are $$Type I$$ and $$Type II$$ errors in Control Chart analysis? Provide an example of each.

Year $1$: Monthly Rates of HAIs per $1500$ patients

J F M A M J J A S O N D

$506540455510511610050454060$

Year $2$: Monthly Rates of HAIs per $1500$ patients

J F M A M J J A S O N D

$55604447599511011560473755$