Question

Quiz: QuizO2 Time Remaining: 00:35:45 Submit Qubz This Question: 9 pts 5 of 16 (13 complete) This Quiz: 31 pts possible West Battery Corp. hasrecently 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 o 55 hours about 10% onger than competitors' models. To raise he lifetime above this level would require a new level of technology not available o 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: Hour Definition Sample Taken 1 56 2 49 3 56 4 59 5 54 6 65 7 40 8 56 9 48 10 74 11 62 12 62 13 45 Sample Size, n 4 19 4 30 Mean Factor, Upper Range, Lower Range, 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 3.268 2.574 2 282 2.115 2.004 1.924 1.864 1816 0 22 0 8 2 20 2 18 8 14 0.076 0.136 0.184 0.223 0.284 0 2 4 13 10 12 1.716 This exercise contains only parts ae and b. a) For the given data, thex-hours (round your response to three For the given data, mean range-hours (round your response to two Print Done With z-3, the control limits for the mean chart are Enter your answer in each of the answer boxes.

Answer 1

1. Xbarbar =55.12

Rbar = 16.72

2. UCL_xbar = Xbarbar + A₂Rbar = 55.12 +0.577 x16.72 =64.76

LCL_xbar = Xbarbar - A₂Rbar = 55.12 - 0.577 x16.72 = 45.47

3. UCL_R = D₄ x Rbar = 2.115 x 16.72 =35.36

LCL_R =D₃ x Rbar =0

For sample 26 to 30

Hour / sample	1	2	3	4	5	Xbar	R
26	54	56	45	61	66	56.4	21
27	51	58	53	52	70	56.8	19
28	68	54	56	51	58	57.4	17
29	62	76	51	58	66	62.6	25
30	49	44	50	58	56	51.4	14

Based on the R chart the process is in control

Based on the Xbar chart, the process is under control, as all Xbar values are within range.