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$6.26 West Battery Corp. has recently been receiving com- plaints 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 50 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 size n = 5 samples 5 of 9-volt batteries for each of 25 hours to establish the standards for control chart limits. Those samples are shown in the follow- ing table: are ation ners) West Battery Data--Battery Lifetimes (in hours) HOUR SAMPLE SAMPLE TAKEN 2 3 4 5 R 1 50 49 50 50 50.0 2 2 45 47 70 46 36 48.8 34 35 48 39 47 43.8 15 55 70 50 30 51 51.2 40 38 64 36 47 46.8 28 59 62 40 54 64 55.8 24 36 33 49 48 56 44.4 23 50 67 53 43 40 50.6 27 ties. hone 44 52 46 47 44 46.6 8 10 70 45 50 47 41 50.6 29 57 54 62 45 36 50.8 26 Ving Ts to plain that ed to 12 56 54 47 42 62 52.2 20 13 48 3 8 8 9 9 9 8 8 8 8 0 - 40 70 58 45 44 51.4 30 CNN NN o W = . w 14 52 58 40 52 46 s, 10 18 15 57 42 52 58 59 49.6 53.6 48.2 the the bills 17 16 62 49 42 33 55 29 17 39 49 59 48 20 47.0 52.6 18 64 50 42 57 50 22 19 58 53 52 48 50 52.2 10 T 20 50 41 41 50 48.4 19 52 47 48 58 40 18 49.0 49.0 22 55 40 56 49 45 16 23 48 50 50 48 48.6 3 3 24 50 50 49 51 51 50.2 NU 25 50 51 51 62 53.0 12 tive. ng a this With these limits established, West now takes 5 more hours of data, which are shown in the following table: With these limits established, West now takes 5 more hours of data, which are shown in the following table: SAMPLE HOUR 1 3 4 5 26 48 52 39 57 61 27 45 53 48 46 66 28 63 49 50 45 53 29 57 70 45 52 61 30 45 38 46 54 52 a) Determine means and the upper and lower control limits for and R (using the first 25 hours only). b) Has the manufacturing process been in control? c) Comment on the lifetimes observed. P