West Battery Corp. has recently been receiving complaints from retailers that its​ 9-volt batteries are not lasting as l

[answerhappygod]

West Battery Corp. has recently been receiving complaints fromretailers that its​ 9-volt batteries are not lasting as longas other name brands. James​ West, head of the TQM programat​ West's Austin​ plant, believes there is no problembecause his batteries have had an average life of 40 hours,about​ 10% longer than​ competitors' models. To raise thelifetime above this level would require a new level of technologynot available to West. ​ Nevertheless, he is concerned enoughto set up hourly assembly line checks.​ Previously, afterensuring that the process was running​ properly, West tooksamples of 5 ​9-volt batteries for 25 test to establish thestandards for control chart limits. Those 25 tests are shown in thefollowing​ table:
Sample Data
Sample Data
Hour Sample Taken
1
2
3
4
5
x
R
Hour Sample Taken
1
2
3
4
5
x
R
1
41
40
39
40
40
40.0
2
14
41
47
29
43
37
39.4
18
2
36
36
61
37
25
39.0
36
15
46
32
42
47
49
43.2
17
3
40
25
38
29
37
33.8
15
16
53
38
33
22
45
38.2
31
4
45
60
40
20
41
41.2
40
17
31
30
40
48
37
37.2
18
5
39
29
43
42
36
37.8
14
18
53
39
32
48
41
42.6
21
6
49
52
40
44
54
47.8
14
19
46
44
41
38
39
41.6
8
7
25
22
40
37
46
34.0
24
20
50
41
30
31
40
38.4
20
8
40
56
43
33
29
40.2
27
21
41
37
38
49
29
38.8
20
9
34
42
37
37
33
36.6
9
22
44
30
46
39
34
38.6
16
10
59
35
41
36
31
40.4
28
23
36
37
40
41
39
38.6
5
11
46
43
53
34
27
40.6
26
24
40
39
38
40
40
39.4
2
12
47
45
38
32
51
42.6
19
25
40
40
40
41
52
42.6
12
13
31
61
48
35
33
41.6
30
a) For the given​ data, the x bar ​= ​(roundyour response to three decimal​ places).
For the given​ data, mean range​ = ​(round yourresponse to two decimal​ places).
With ​z=3​, the control limits for the mean chart​ are:
UCL= ​ (round your response to threedecimal​ places)
LCL= ​ (round your response to threedecimal​ places)
The control limits for the range chart​ are:
UCL= (round your response to two decimal​ places)
LCL= (round your response to two decimal​ places)
With these limits​ established, West now takes 5 more hoursof​ data, which are shown in the following table. Calculatethe mean and range for each hour that the sample data is taken.​(Enter your responses for the mean to one decimal place and enteryour responses for the range as whole​ numbers.)
Sample Data
Hour Sample Taken
1
2
3
4
5
x bar
R
26
49
51
40
56
61
enter your response here
enter your response here
27
45
53
47
46
65
enter your response here
enter your response here
28
63
49
51
45
53
enter your response here
enter your response here
29
56
69
44
51
61
enter your response here
enter your response here
30
45
39
46
54
53
enter your response here
enter your response here
b) Do the samples for hours 26 through 30 indicate that theprocess is in​ control?
Based on the x​-chart, the process has been (incontrol/out of control)
Based on the R-chart, the process has been (in control/out ofcontrol)