Question

Hospital administrators wanted to understand and better control the waiting time of patients in the emergency room (ER) department. To do this, they constructed x-bar and R-charts by sampling the waiting times of the first five patients admitted to the ER at the beginning of each shift (7 a.m., 3 p.m., and 11 p.m.).

1. What do you think of this approach?

2. Will it provide the information the hospital administrators seek?

3. How might the sampling process be improved, and what would you recommend?

Answer 1

This was an actual experience encountered by one of the authors. The purpose of control charts is to understand the state of the process over time. Clearly 3 samples per day is insufficient for such a dynamic activity as an emergency room, as the patient demand will most likely fluctuate significantly over the course of a 24 hour day (rush hour accidents, sports injuries on the weekends, etc.). Also, shift changes usually have different characteristics as nurses transfer information to new shifts, which might increase the wait at those points in time. A better sampling process would be to sample patients on an hourly basis, for example. If sampling costs are high then every other hour. Another reasonable sampling plan suggested by students is to sample each shift at the beginning, middle, and end of their shift resulting in a total of 9 samples per day.