Problem 1: Using the following data, prepare a run chart, scatter chart, and control chart. A late surgery is defined as any surgical operation that was started more than 30 minutes after its scheduled time
Number of Late Surgeries
|
Month
|
Number of Surgeries
|
Number of Late Surgeries
|
|
January
|
435
|
112
|
|
February
|
401
|
129
|
|
March
|
572
|
186
|
|
April
|
409
|
103
|
|
May
|
577
|
89
|
|
June
|
329
|
67
|
|
July
|
467
|
156
|
|
August
|
301
|
94
|
|
September
|
235
|
89
|
|
October
|
325
|
127
|
|
November
|
378
|
156
|
|
December
|
444
|
124
|
|
|
|
|
|
Total
|
4873
|
1432
|
Calculate the moving range by time interval (e.g., month), sum the differences, and then divide this sum by the number of range calculation. In the example, divide by 11 to determine the average moving range. For the example, the average moving range is 5.5 births.
The upper control limit for a moving range chart (of individual values) is the average moving range × 3.27-3.27 is a constant, just as 1.96 is the constant used to calculate a 95% confidence interval when we use the central limit theorem.
In our example, therefore, the upper control limit for the moving range chart is:
Average Moving Range = 5.5 × (the constant) 3.27 = 17.985
For this control chart, 17.985 is the upper threshold limit used to evaluate the variation presented in the time series analysis we have been using involving medically complicated births. It is the upper boundary or control limit. Given the nature of this chart there is no lower limit.
Problem 2: Using the following data set on hospital admissions, define the service area for Hospital A, based only on quantitative factors (Table).
Compute the target bed capacity of Cheswick Community Hospital 10 years from now, based on the following information: Assume current population of Cheswick Community Hospital's service area = 145,000Assume projected population increase of 8% in service area over the next 10 years.
Hospital Admissions, by Community
|
Community
|
Hospital A
|
Hospital B
|
Hospital C
|
Other Hospitals
|
|
North
|
45
|
64
|
76
|
123
|
|
South
|
159
|
324
|
12
|
521
|
|
East
|
65
|
24
|
137
|
311
|
|
West
|
145
|
68
|
95
|
113
|
|
Central
|
32
|
56
|
78
|
159
|
|
Upper
|
29
|
84
|
45
|
814
|
|
Lower
|
37
|
14
|
8
|
57
|
Assume a future admission rate per 1000 of 102. Assume average length of stay of 4.7 days in 10 years. Assume a target occupancy rate of 78% in 10 years.
- Newgroveton is a community of 445,000. In the most recent year, there were 750 new cases of disease A in the community. Assume the expected incidence rate for disease A is 245 per 100,000 people. Was the community's experience better or worse than expected? Explain your answer.