This exercise contains only parts a and b.a) For the given data, the x=___ hours (round your response to three decimal places).For the given data, mean range =____hours (round your response to two decimal places).With z=3, the control limits for the mean chart are:UCLx = ____ hours (round your response to three decimal places).LCLx = _____ hours (round your response to three decimal places). West Battery Corp. has recently been receiving complaints from retailers that its 9-volt batteries are not lasting as long as other name brands. James West, head of the TQM program atWest's Austin plant, believes there is no problem because his batteries have had an average life of 60 hours, about 10% longer than competitors' models. To raise the lifetime above thislevel would require a new level of technology not available to West. Nevertheless, he is concerned enough to set up hourly assembly line checks. Previously, after ensuring that theprocess was running properly, West took samples of 5 9-volt batteries for 25 test to establish the standards for control chart limits. Those 25 tests are shown in the following table:Sample DataSample DataHourHourSampleTaken1SampleTaken1245R234R1606160596761.4814626951625660.018555770564656.82415675363697064.417604558495753.81516725851446457.828668161516063.83017494958685956.619584787475859.44018755951676162.624697260647467.81419686463576162.611464459596554.62120705950516058.020607762524960.02821635758695059.419546257575356.622664966595458.81710815459575260.62923565961605858.811676573544661.02724606160626160.8212666456517261.82125615961627363.21413518167545361.2302 34 5 6 7 8 9 With these limits established, West now takes 5 more hours of data, which are shown in the following table. Calculate the mean and range for each hour that the sample data is taken.(Enter your responses for the mean to one decimal place and enter your responses for the range as whole numbers.)Sample DataHourSampleTaken1234R265961486872275664595577287258605664296781556370305548576362b) Do the samples for hours 26 through 30 indicate that the process is in control?Based on the X-chart, the process has beenBased on the R-chart, the process has been

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Answered: West Battery Corp. has recently been…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

This exercise contains only parts a and b.

a) For the given data, the x=___ hours (round your response to three decimal places).

For the given data, mean range =____hours (round your response to two decimal places).

With z=3, the control limits for the mean chart are:

UCLx = ____ hours (round your response to three decimal places).

LCLx = _____ hours (round your response to three decimal places).

West Battery Corp. has recently been receiving complaints from retailers that its 9-volt batteries are not lasting as long as other name brands. James West, head of the TQM program at
West's Austin plant, believes there is no problem because his batteries have had an average life of 60 hours, about 10% longer than competitors' models. To raise the lifetime above this
level would require a new level of technology not available to West. Nevertheless, he is concerned enough to set up hourly assembly line checks. Previously, after ensuring that the
process was running properly, West took samples of 5 9-volt batteries for 25 test to establish the standards for control chart limits. Those 25 tests are shown in the following table:
Sample Data
Sample Data
Hour
Hour
Sample
Taken
1
Sample
Taken
1
2
4
5
R
2
3
4
R
1
60
61
60
59
67
61.4
8
14
62
69
51
62
56
60.0
18
55
57
70
56
46
56.8
24
15
67
53
63
69
70
64.4
17
60
45
58
49
57
53.8
15
16
72
58
51
44
64
57.8
28
66
81
61
51
60
63.8
30
17
49
49
58
68
59
56.6
19
58
47
87
47
58
59.4
40
18
75
59
51
67
61
62.6
24
69
72
60
64
74
67.8
14
19
68
64
63
57
61
62.6
11
46
44
59
59
65
54.6
21
20
70
59
50
51
60
58.0
20
60
77
62
52
49
60.0
28
21
63
57
58
69
50
59.4
19
54
62
57
57
53
56.6
22
66
49
66
59
54
58.8
17
10
81
54
59
57
52
60.6
29
23
56
59
61
60
58
58.8
11
67
65
73
54
46
61.0
27
24
60
61
60
62
61
60.8
2
12
66
64
56
51
72
61.8
21
25
61
59
61
62
73
63.2
14
13
51
81
67
54
53
61.2
30
2 34 5 6 7 8 9

With these limits established, West now takes 5 more hours of data, which are shown in the following table. Calculate the mean and range for each hour that the sample data is taken.
(Enter your responses for the mean to one decimal place and enter your responses for the range as whole numbers.)
Sample Data
Hour
Sample
Taken
1
2
3
4
R
26
59
61
48
68
72
27
56
64
59
55
77
28
72
58
60
56
64
29
67
81
55
63
70
30
55
48
57
63
62
b) Do the samples for hours 26 through 30 indicate that the process is in control?
Based on the X-chart, the process has been
Based on the R-chart, the process has been

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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