Question: In a hospital's radiology department, the radiology report turnaround times have been a concern to the department. Doctors have been complaining about the long turnaround time of their ordered radiology reports for patients. The radiology department staff decided to investigate the problem and collect turnaround time data on 10 randomly selected reports every day for one month (data shown in the table below).
a. Construct an X-bar chart using the standard deviation of the observations/sample (as an estimate of the population standard deviation). Construct an Xbar chart and R-chart using the range to calculate the control limits. Is the process in control? Explain.
b. If the physicians think that any time over 24 hours is unacceptable, what are the Cp and Cpk of this process?
c. What are the next steps for the radiology department?
d. The performance improvement specialist on your team suggests several process changes that result in reducing the turnaround time by 6 hours for each report. Reconstruct the X-bar and R charts and comment on the results.
e. Based on your answers in Parts a and d, plot the control charts for the 'before' and 'after' situation on the same chart.
| Observations (Turnaround time in hours) |
| Day |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| 1 |
11 |
12 |
21 |
18 |
35 |
16 |
18 |
22 |
11 |
23 |
| 2 |
13 |
19 |
20 |
18 |
16 |
6 |
21 |
5 |
15 |
5 |
| 3 |
8 |
1 |
16 |
8 |
16 |
23 |
12 |
5 |
7 |
22 |
| 4 |
7 |
9 |
19 |
9 |
11 |
10 |
21 |
17 |
19 |
6 |
| 5 |
1 |
14 |
9 |
18 |
18 |
22 |
20 |
8 |
11 |
16 |
| 6 |
13 |
4 |
17 |
5 |
6 |
22 |
17 |
5 |
18 |
26 |
| 7 |
15 |
15 |
9 |
6 |
21 |
23 |
16 |
7 |
3 |
9 |
| 8 |
17 |
3 |
5 |
13 |
23 |
3 |
11 |
22 |
15 |
5 |
| 9 |
5 |
2 |
12 |
17 |
8 |
14 |
21 |
21 |
20 |
19 |
| 10 |
17 |
19 |
7 |
8 |
22 |
17 |
7 |
14 |
14 |
21 |
| 11 |
20 |
20 |
18 |
23 |
15 |
11 |
23 |
8 |
15 |
33 |
| 12 |
10 |
6 |
23 |
22 |
3 |
6 |
17 |
19 |
12 |
9 |
| 13 |
1 |
23 |
24 |
7 |
8 |
3 |
20 |
11 |
22 |
1 |
| 14 |
12 |
25 |
23 |
13 |
16 |
8 |
21 |
13 |
12 |
4 |
| 15 |
7 |
17 |
4 |
13 |
2 |
17 |
4 |
4 |
15 |
6 |
| 16 |
4 |
14 |
20 |
5 |
1 |
10 |
21 |
14 |
21 |
13 |
| 17 |
3 |
11 |
13 |
14 |
6 |
11 |
15 |
23 |
23 |
20 |
| 18 |
20 |
1 |
13 |
11 |
10 |
19 |
19 |
21 |
21 |
16 |
| 19 |
19 |
3 |
5 |
12 |
22 |
9 |
15 |
2 |
22 |
7 |
| 20 |
13 |
11 |
5 |
17 |
21 |
20 |
18 |
11 |
17 |
8 |
| 21 |
14 |
23 |
8 |
12 |
18 |
8 |
19 |
9 |
30 |
6 |
| 22 |
12 |
22 |
11 |
17 |
20 |
3 |
2 |
1 |
23 |
3 |
| 23 |
11 |
12 |
21 |
18 |
35 |
16 |
18 |
22 |
11 |
23 |
| 24 |
7 |
1 |
11 |
20 |
8 |
28 |
20 |
15 |
11 |
14 |
| 25 |
13 |
30 |
12 |
2 |
3 |
6 |
9 |
6 |
7 |
17 |
| 26 |
13 |
6 |
8 |
16 |
11 |
23 |
21 |
2 |
13 |
21 |
| 27 |
2 |
12 |
19 |
14 |
15 |
22 |
7 |
11 |
8 |
15 |
| 28 |
14 |
14 |
10 |
16 |
15 |
19 |
20 |
12 |
4 |
15 |
| 29 |
9 |
12 |
4 |
18 |
17 |
1 |
3 |
15 |
13 |
6 |
| 30 |
14 |
1 |
9 |
9 |
4 |
23 |
11 |
15 |
16 |
5 |