Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma)

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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

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:

	Sample Data								Sample Data
Hour Sample Taken	1	2	3	4	5	x	R	Hour Sample Taken	1	2	3	4	5	x	R
1	60	61	60	59	67	61.4	8	14	61	67	51	63	55	59.4	16
2	55	57	70	56	46	56.8	24	15	67	51	63	68	70	63.8	19
3	61	55	53	55	56	56.0	8	16	71	59	51	43	66	58.0	28
4	65	80	60	40	61	61.2	40	17	50	48	60	68	59	57.0	20
5	58	47	87	47	58	59.4	40	18	75	61	53	66	59	62.8	22
6	68	73	46	63	77	65.4	31	19	67	62	63	59	60	62.2	8
7	46	42	60	57	66	54.2	24	20	69	60	52	50	61	58.4	19
8	61	77	62	52	50	60.4	27	21	63	56	57	68	51	59.0	17
9	53	62	56	58	53	56.4	9	22	65	49	65	60	55	58.8	16
10	80	54	60	57	52	60.6	28	23	56	57	61	60	57	58.2	5
11	67	65	72	54	47	61.0	25	24	59	61	59	61	62	60.4	3
12	65	63	56	53	73	62.0	20	25	62	60	60	62	71	63.0	11
13	51	81	69	55	53	61.8	30

With z=3, the control limits for the mean chart are:

UCLx = hours (round your response to three decimal places).

LCLx = 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	1	2	3	4	5	x	R
26	59	62	50	68	72	enter your response here	enter your response here
27	56	63	58	55	77	enter your response here	enter your response here
28	72	58	59	54	62	enter your response here	enter your response here
29	66	81	56	63	71	enter your response here	enter your response here
30	55	49	57	65	62	enter your response here	enter your response here

Part 9

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 In control or out of control

Based on the R-chart, the process has been In control or out of control