Question

The Title 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= _________

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

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

UCL= _________

LCL= __________

Answer 1

Sample	Tread Wear			Range	Mean
1	31	42	28	14	33.67
2	26	18	35	17	26.33
3	25	30	34	9	29.67
4	17	25	21	8	21.00
5	38	29	35	9	34.00
6	41	42	36	6	39.67
7	21	17	29	12	22.33
8	32	26	28	6	28.67
9	41	34	33	8	36.00
10	29	17	30	13	25.33
11	26	31	40	14	32.33
12	23	19	25	6	22.33
13	17	24	32	15	24.33
14	43	35	17	26	31.67
15	18	25	29	11	24.00
16	30	42	31	12	34.33
17	28	36	32	8	32.00
18	40	29	31	11	33.33
19	18	29	28	11	25.00
20	22	34	26	12	27.33

1.)

= 228/20 = 11.4

Here Subgroup size = 3

So, D3 = 0

D4 = 2.574

So, LCL = D3 * = 0

UCL = D4 * = 2.574 * 11.4 = 29.344

2.)

= 583.33/20 = 29.17

Here

A2 = 1.023

LCL = - A2 *

LCL = 29.17 - 1.023 * 11.4

LCL = 17.501

UCL = + A2 *

UCL = 29.17 + 1.023 * 11.4

UCL = 40.8322