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 Sample Taken 1 1 2 4 5 R Taken 1 2 3 4 5 R 60 61 60 59 67 61.4 8. 14 62 69 51 62 56 60.0 18 2 55 57 70 56 46 56.8 24 15 67 53 63 69 70 64.4 17 3 60 45 81 58 49 57 53.8 15 16 72 58 51 44 64 57.8 28 4 66 61 51 60 63.8 30 17 49 49 58 68 59 56.6 19 5 58 47 87 47 58 59.4 40 18 75 59 51 67 61 62.6 24 63 57 51 6 69 72 60 64 74 67.8 14 19 68 64 61 62.6 11 7 46 44 59 59 65 54.6 21 20 70 59 50 60 58.0 20 8 60 77 62 52 49 60.0 28 21 63 57 58 69 50 59.4 19 9 54 62 57 57 53 56.6 9 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 5 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
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 Sample Taken 1 1 2 4 5 R Taken 1 2 3 4 5 R 60 61 60 59 67 61.4 8. 14 62 69 51 62 56 60.0 18 2 55 57 70 56 46 56.8 24 15 67 53 63 69 70 64.4 17 3 60 45 81 58 49 57 53.8 15 16 72 58 51 44 64 57.8 28 4 66 61 51 60 63.8 30 17 49 49 58 68 59 56.6 19 5 58 47 87 47 58 59.4 40 18 75 59 51 67 61 62.6 24 63 57 51 6 69 72 60 64 74 67.8 14 19 68 64 61 62.6 11 7 46 44 59 59 65 54.6 21 20 70 59 50 60 58.0 20 8 60 77 62 52 49 60.0 28 21 63 57 58 69 50 59.4 19 9 54 62 57 57 53 56.6 9 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 5 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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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![This exercise contains only parts a and b.
a) For the given data, the \(\bar{x} = \Box\) hours (round your response to three decimal places).
For the given data, mean range \(=\Box\) hours (round your response to two decimal places).
With \(z=3\), the control limits for the mean chart are:
\[
UCL_{\bar{x}} = \Box \text{ hours (round your response to three decimal places).}
\]
\[
LCL_{\bar{x}} = \Box \text{ hours (round your response to three decimal places).}
\]
The control limits for the range chart are:
\[
UCL_{R} = \Box \text{ hours (round your response to two decimal places).}
\]
\[
LCL_{R} = \Box \text{ hours (round your response to two decimal places).}
\]
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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab2cc191-2fdd-4696-b5f6-58c0f2050b23%2Fe82f8e84-468f-4656-bae6-223ab631515d%2Fuca09c6_processed.png&w=3840&q=75)
Transcribed Image Text:This exercise contains only parts a and b.
a) For the given data, the \(\bar{x} = \Box\) hours (round your response to three decimal places).
For the given data, mean range \(=\Box\) hours (round your response to two decimal places).
With \(z=3\), the control limits for the mean chart are:
\[
UCL_{\bar{x}} = \Box \text{ hours (round your response to three decimal places).}
\]
\[
LCL_{\bar{x}} = \Box \text{ hours (round your response to three decimal places).}
\]
The control limits for the range chart are:
\[
UCL_{R} = \Box \text{ hours (round your response to two decimal places).}
\]
\[
LCL_{R} = \Box \text{ hours (round your response to two decimal places).}
\]
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.)
Transcribed Image Text:**West Battery Corp.: Quality Assurance Testing for 9-Volt Batteries**
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 Total Quality Management (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 tests to establish the standards for control chart limits. Those 25 tests are shown in the following table:
| Hour Sample Taken | 1 | 2 | 3 | 4 | 5 | x̄ | R |
|-------------------|----|----|----|----|----|-----|----|
| 1 | 60 | 61 | 60 | 59 | 67 | 61.4| 8 |
| 2 | 55 | 57 | 70 | 46 | 56 | 56.8| 24 |
| 3 | 60 | 45 | 58 | 49 | 57 | 53.8| 15 |
| 4 | 66 | 81 | 61 | 51 | 60 | 63.8| 30 |
| 5 | 58 | 47 | 87 | 47 | 60 | 59.4| 40 |
| 6 | 69 | 72 | 60 | 64 | 74 | 67.8| 14 |
| 7 | 46 | 44 | 52 | 59 | 59 | 52.0| 15 |
| 8 | 60 | 77 | 62 | 52 | 49 | 60.0| 28 |
| 9 | 54 | 62 | 57 | 57 | 53 | 56.6| 9 |
| 10 | 81 | 54 | 59 | 57 | 52 | 60.6|
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