Question

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 TOM 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 time 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 property, 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 2 3 4 5 X R Taken 1 2 3 4 5 1 60 61 0 59 07 614 8 14 61 68 62 50 304 18 56 56 81 57 45 50.0 36 15 06 52 62 70 63.4 18 50 46 59 48 68 56.0 22 10 73 50 52 44 65 58.6 4 64 66 62 60 6 17 51 48 60 68 57 558 20 5 58 47 87 47 58 59.4 40 18 74 59 51 68 60 62.4 23 6 70 71 62 65 65 19 61 58 60 61.6 8 7 45 42 58 59 67 542 25 20 69 60 52 52 61 17 2 588 Enter your answer in each of the answer boxes

Answer 1

RANGE 8 36 22 6 40 9 25 28 7 29 26 SUBGROUP NUMBER AVERAGE (X-BAR) 1 61.4 2 59 3 56 4 62.8 5 59.4 6 66.6 7 54.2 8 60.8 9 56.4 10 60.4 11 60.6 12 61.8 13 61.8 14 59.4 15 63.4 16 58.6 17 56.8 18 62.4 19 61.6 20 58.8 21 22 59 23 58.2 24 60.2 25 63.4 AVERAGE 60.064 19 29 18 18 29 20 23 58.6 8 17 19 17 2 3 12 18.8

(A) X-DOUBLE BAR - AVERAGE OF X-BAR X-DOUBLE BAR = 60.064 RANGE BAR = AVERAGE OF RANGE RANGE BAR = 18.8 (A) FOR RANGE CHART (A) FOR MEAN CHART USE MEAN FACTOR TABLE TO FIND VALUE OF D3 AND D4 AT N=5 SAMPLE SIZE (N) = 5 USE MEAN FACTOR TABLE TO FIND VALUE OF A2 AT N=5 VALUE OF D3 = 0 VALUE OF D4 = 2.115 VALUE OF A2 = 0.577 UCL = X-DOUBLE BAR + (RANGE BAR X A2) UCL = 60.064 + (0.577 x 18.8) UCL = 70.912 UCL = D4 x (RANGE BAR) UCL = 2.115 x 18.8 UCL = 39.76 LCL = X-DOUBLE BAR - (RANGE BAR x A2) LCL = 60.064 - (0.577 x 18.8) LCL = 49.216 LCL = D3 X (RANGE BAR) LCL = 0 X 18.8 LCL = 0

X2 SAMPLE 26 X1 57 X3 50 57 62 MAXIMUM 72 MINIMUM 50 54 27 28 29 62 58 X4 67 55 54 63 64 X5 72 75 63 72 54 74 68 56 AVERAGE (X-BAR) 61.6 60.6 61.8 67.8 57.2 60 RANGE 22 21 20 26 54 75 74 81 81 55 55 30 47 56 63 47 64 17 SINCE ALL THE VALUES OF X-BAR ARE WITHIN THE CONTROL LIMITS, THEREFORE THE PROCESS IS IN CONTROL. SINCE ALL THE VALUES OF RANGE ARE WITHIN THE CONTROL LIMITS, THEREFORE THE PROCESS IS IN CONTROL.

All the parts have been done as shown. In case of any doubt, please mention it in the comments. Thank you.