Refer to Table 56.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. 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 55 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 x R 1 2 3 4 R 8 24 15 6 14 44 58 47 54 Hour Sample Taken 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 2 3 4 5 55 56 55 54 62 50 52 65 51 41 55 40 53 44 52 59 61 57 55 57 54 44 58 57 51 65 66 57 60 60 42 37 54 54 61 57 72 58 48 45 50 57 52 52 50 75 51 56 53 45 62 60 BA 51 42 60 59 51 47 66 45 76 64 49 49 56.4 51.8 48.8 57.8 52.8 61.6 49.6 56.0 52.2 56.0 56.6 56.6 56.6 Hour Sample Taken 14 15 16 17 18 19 20 21 22 23 24 25 56 62 66 45 70 62 66 57 59 52 54 56 62 46 53 44 54 58 54 52 45 52 9 24 27 7 30 26 19 31 48 58 47 52 61 54 54 56 56 62 39 65 63 52 47 63 53 56 56 58 5 5 51 65 60 52 56 56 55 45 49 52 56 66 53.8 58.6 53.0 52.0 58.2 57.2 53.8 53.8 53,4 53.2 55.0 57.6 18 19 27 21 22 10 19 18 16 4 2 2 12 55 54 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). 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: UCL; -hours (round your response to three decimal places). LCL; = hours (round your response to three decimal places). ) The control limits for the range chart are: UCLR-hours (round your response to two decimal places). LCLR = 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.) Sample Data Hour Sample Taken 26 1 2 3 4 5 5 R 54 58 45 62 66 27 49 57 54 52 72 28 69 53 55 51 59 29 62 74 51 56 66 30 49 43 52 59 56 U b) Do the samples for hours 26 through 30 indicate that the process is in control? UCL-hours (round your response to three decimal places). LCL;-hours (round your response to three decimal places). ( = The control limits for the range chart are: UCLR = hours (round your response to two decimal places). LCLR = 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.) Sample Data Hour Sample Taken 26 2 4 5 x R 1 54 3 45 58 62 66 27 49 57 54 52 72 69 53 55 51 59 28 29 62 74 51 56 66 30 49 43 52 59 56 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