ou have been hired as the new hospital administrator for a rural hospital locate

Question

ou have been hired as the new hospital administrator for a rural hospital located in Wheatland, Wyoming (population about 3,725 [2015]). This town sits on Interstate 25, approximately equidistant between Casper and Cheyenne. The community is the site of a 30-bed hospital and small emergency room/trauma center that services all of Platte County, Wyoming (population approximately 8,900 with a median income of about $28,000 [2015]). This small hospital also serves as a backup for medical services for the five surrounding counties, as needed (which on several occasions in the past three years, caused the hospital to exceed capacity due to restricted operations in the other counties). One of the first projects you have been asked to tackle by the hospital’s governing board will be to study emergency room and trauma center operations in terms of waiting times of patients, as this is where the majority of operations takes place, 24 hours a day. To do this, you have decided to conduct a proper statistical sampling and analysis of patient wait times using X-Bar and R-charts to help get a grasp of what is taking place. Why these two charts? What is different about these two charts and what might they yield from an informational perspective, as they relate to waiting times? Which might serve as a better measure or does it matter? Finally, once you began to study the information being yielded by the charts, it becomes apparent that the X-Bar chart data looks to be out control, even though the R-Chart is showing different output indictors. Why is this? What do you now do as you wish to use this information as the basis to develop a new executable model that will need to be presented to the governing board and if approved, implemented in hospital operations? Please be specific with all of this.

Explanation / Answer

As we need to study the waiting time of patients, we need the mean waiting time and the range of waiting times. Hence, R and X bar chart should be used in this case. Hence from these two charts they can know the average waiting time, the waiting times in the best as well as the worst scenarios and plan accordingly.

For X bar chart to be out of control, the deviations must be very large between the sample observations. Hence this points towards high standard deviation of variations in the waiting times. In this case if the ranges do not have much variations, then the R chart is in control.

So, to use this information to develop a new model it is suggested to have more emergency rooms and trauma operations so that the waiting time is reduced and within limits.

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