Question

The Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control the manufacturing process, 20 samples, each containing three radial tires, were chosen from different shifts over several days of operation, with the following results. Tread wear measurements are in hundredths of an inch.

Sample	Tread Wear
1	31	42	28
2	26	18	35
3	25	30	34
4	17	25	21
5	38	29	35
6	41	42	36
7	21	17	29
8	32	26	28
9	41	34	33
10	29	17	30
11	26	31	40
12	23	19	25
13	17	24	32
14	43	35	17
15	18	25	29
16	30	42	31
17	28	36	32
18	40	29	31
19	18	29	28
20	22	34	26

Assuming that these data were collected when the manufacturing process was believed to be operating in control, develop the R chart.

Compute the upper and lower control limits for the R chart. (Round your answers to two decimal places.)

UCL=

LCL=

Construct the R chart.

• Assuming that these data were collected when the manufacturing process was believed to be operating in control, develop the x bar chart.

Compute the upper and lower control limits for the x bar chart. (Round your answers to two decimal places.)

UCL=

LCL=

Construct the x bar chart.

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Answer 1

1)for R chart:

average range R̅ =			11.4
sample size n   =			3
sample size n=3, criitcal value of D3=			0
sample size n=3, criitcal value D4=			2.575
control line (CL) = R̅=			11.40
upper control limit (UCL)=D4R̅ =			29.36
lower control limit(LCL) =D3R̅ =			0.00

35 30 25 20 15 water 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -CL-UCLLCL

2)for xbar chart:

sample mean x̅ =			29.167
average range R̅ =			11.4000
sample size n   =			3
sample size n=3, criitcal value of A2=			1.023
control line (CL) = x̅=			29.16667
upper control limit =x̅+3*A2R̅ =			40.83
lower control limit =x̅-3*A2R̅ =			17.50

for X bar Chart:

45 40 35 30 25 20 war 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -CL-UCLLCL