Solution Found!
Package sorting time. AirExpress, an overnight mail
Chapter 13, Problem 84SE(choose chapter or problem)
Package sorting time. AirExpress, an overnight mail service, is concerned about the operating efficiency of the package-sorting departments at its Toledo, Ohio, terminal. The company would like to monitor the time it takes for packages to be put in outgoing delivery bins from the time they are received. The sorting department operates 6 hours per day, from 6:00 p.m. to midnight. The company randomly sampled four packages during each hour of operation during 4 consecutive days. The time for each package to move through the system, in minutes, is given
in the table on the next page.
a. Construct an \(\bar{x} \text {-chart }\) from these data. For this chart to be meaningful, what assumption must be made about the variation of the process? Why?
b. What does the chart suggest about the stability of the package-sorting process? Explain.
c. Should the control limits be used to monitor future process output? Explain.
Questions & Answers
QUESTION:
Package sorting time. AirExpress, an overnight mail service, is concerned about the operating efficiency of the package-sorting departments at its Toledo, Ohio, terminal. The company would like to monitor the time it takes for packages to be put in outgoing delivery bins from the time they are received. The sorting department operates 6 hours per day, from 6:00 p.m. to midnight. The company randomly sampled four packages during each hour of operation during 4 consecutive days. The time for each package to move through the system, in minutes, is given
in the table on the next page.
a. Construct an \(\bar{x} \text {-chart }\) from these data. For this chart to be meaningful, what assumption must be made about the variation of the process? Why?
b. What does the chart suggest about the stability of the package-sorting process? Explain.
c. Should the control limits be used to monitor future process output? Explain.
ANSWER:Step 1 of 17
(a)
Construct a 
Assume that the variation in the process is stable, since the 
The table below shows the calculation of 
Sample |
1 |
2 |
3 |
4 |
Minimum |
Maximum |
Range |
|
1 |
31.9 |
33.4 |
37.8 |
26.2 |
32.325 |
26.2 |
37.8 |
11.6 |
2 |
29.1 |
24.3 |
33.2 |
36.7 |
30.825 |
24.3 |
36.7 |
12.4 |
3 |
30.3 |
31.1 |
26.3 |
34.1 |
30.450 |
26.3 |
34.1 |
7.8 |
4 |
39.6 |
29.4 |
31.4 |
37.7 |
34.525 |
29.4 |
39.6 |
10.2 |
5 |
27.4 |
29.7 |
36.5 |
33.3 |
31.725 |
27.4 |
36.5 |
9.1 |
6 |
32.7 |
32.9 |
40.1 |
29.7 |
33.850 |
29.7 |
40.1 |
10.4 |
7 |
30.7 |
36.9 |
26.8 |
34 |
32.100 |
26.8 |
36.9 |
10.1 |
8 |
28.4 |
24.1 |
29.6 |
30.9 |
28.250 |
24.1 |
30.9 |
6.8 |
9 |
30.5 |
35.5 |
36.1 |
27.4 |
32.375 |
27.4 |
36.1 |
8.7 |
10 |
27.8 |
29.6 |
29 |
34.1 |
30.125 |
27.8 |
34.1 |
6.3 |
11 |
34 |
30.1 |
35.9 |
28.8 |
32.200 |
28.8 |
35.9 |
7.1 |
12 |
25.5 |
26.3 |
34.8 |
30 |
29.150 |
25.5 |
34.8 |
9.3 |
13 |
24.6 |
29.9 |
31.8 |
37.9 |
31.050 |
24.6 |
37.9 |
13.3 |
14 |
30.6 |
36 |
40.2 |
30.8 |
34.400 |
30.6 |
40.2 |
9.6 |
15 |
29.7 |
33.2 |
34.9 |
27.6 |
31.350 |
27.6 |
34.9 |
7.3 |
16 |
24.1 |
26.8 |
32.7 |
29 |
28.150 |
24.1 |
32.7 |
8.6 |
17 |
29.4 |
31.6 |
35.2 |
27.6 |
30.950 |
27.6 |
35.2 |
7.6 |
18 |
31.1 |
33 |
29.6 |
35.2 |
32.225 |
29.6 |
35.2 |
5.6 |
19 |
27 |
29 |
35.1 |
25.1 |
29.050 |
25.1 |
35.1 |
10 |
20 |
36.6 |
32.4 |
28.7 |
27.9 |
31.4 |
27.9 |
36.6 |
8.7 |
21 |
33 |
27.1 |
26.2 |
35.1 |
30.35 |
26.2 |
35.1 |
8.9 |
22 |
33.2 |
41.2 |
30.7 |
31.6 |
34.175 |
30.7 |
41.2 |
10.5 |
23 |
26.7 |
35.2 |
39.7 |
31.5 |
33.275 |
26.7 |
39.7 |
13 |
24 |
30.5 |
36.8 |
27.9 |
28.6 |
30.95 |
27.9 |
36.8 |
8.9 |
Table (1)