Refer to Table $6.1 - 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 40 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 concemed 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: 4 5 Sample Data Hour Sample Taken 1 2 2 3 1 42 39 31 41 41 2 36 36 61 37 38 25 3 3 40 25 38 29 37 4 4 46 61 41 31 40 5 38 27 67 27 38 6 6 48 53 26 43 57 7 25 23 40 39 47 8 42 58 44 3330 934 42 36 36 34 9 10 60 34 41 38 31 11 48 44 53 36 25 12 47 43 38 3153 13 31 60 47 36 34 x 38.8 39.0 33.8 43.8 39.4 45.4 34.8 41.4 36.4 40.8 412 42.4 41.8 R 11 36 15 30 40 31 24 28 8 29 28 22 29 Sample Data Hour Sample Taken 1 2 3 4 5 14 41 49 30 42 37 15 47 33 41 47 48 16 53 38 31 23 45 17 31 30 38 48 37 18 55 40 33 48 39 19 46 43 43 37 41 2051 41 31 30 39 21 41 36 39 48 31 22 45 29 47 39 36 23 37 39 39 40 39 24 40 39 38 40 40 25 41 40 40 40 53 39.8 43.2 38.0 36.8 43.0 42.0 38.4 39.0 39.2 38.8 39.4 42.8 R 19 15 30 18 22 9 21 17 18 3 2 13 8 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, miean range = hours (round your response to two decimal places). ( With zu 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 3 5 R 2 43 4 48 39 30 50 27 36 42 37 35 55 28 53 38 41 34 43 29 48 61 36 42 51 30 35 27 36 44 43 b) Do the samples for hours 28 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