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 ils 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: 5 x R Sample Data Hour Sample Taken 1 2 3 1 62 59 51 61 61 2 56 56 81 57 45 3 61 55 53 55 56 4 64 66 6280 62 5 5 58 47 87 47 58 6 70 71 62 65 65 7 7 45 42 59 57 65 8 8 61 77 63 54 49 9 9 53 62 55 56 53 10 80 54 59 5750 11 68 64 71 56 46 12 67 64 57 51 73 13 51 79 69 54 54 x 58.8 59.0 56.0 62.8 594 66.6 53.6 60.8 55.8 60.0 61.0 62.4 61.4 R R 11 36 8 6 40 9 23 Sample Data Hour Sample Taken 1 2 3 4 5 14 62 67 49 61 55 15 67 52 61 69 70 16 716053 42 64 17 51 50 60 69 59 18 74 61 52 67 61 19 67 64 62 59 60 20 71 61 50 51 61 21 6156 58 69 22 64 49 66 60 54 23 58 57 60 59 58 24 61 59 59 61 60 25 62 60 61 62 72 58.8 63.8 58.0 57.8 83.0 62.4 58.8 58.6 58.6 58.4 60.0 63.4 18 18 29 19 22 8 21 20 17 3 2 12 28 30 25 22 28 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: UCL; = hours (round your response to three decimal places). - ( LCL: -hours (round your response to three decimal places). For the given data, mean range = hours (round your response to two decimal pleces). () 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 fround 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 3 4 R 1 58 2 62 5 5 71 28 50 67 27 54 62 57 56 75 28 74 60 61 55 64 29 66 79 55 70 30 55 49 57 63 61 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