Share
The Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control the ma
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 =
in progress
0
Mathematics
3 years
2021-08-17T17:01:07+00:00
2021-08-17T17:01:07+00:00 1 Answers
5 views
0
Answers ( )
Answer:
LCL = 4.72
UCL = 18.08
Step-by-step explanation:
Sample size, n = 20
Sample _ tread wear, x __ Range
1 ______ 33.67 ___ 14
2______ 26.33 ___ 17
3 _____ 29.67 ____ 9
4 ______ 21 ______ 8
5 ______ 34 ______ 9
6 ______ 39.67 ___ 6
7 ______ 22.33 ___ 12
8 ______ 28.67 ___ 6
9 ______ 36 ______8
10 _____ 25.33 ___ 13
11 _____ 32.33 ____14
12 _____ 22.33 ___ 6
13 _____ 24.33 ___ 15
14 _____ 31.67 ___ 26
15 _____ 24 _____ 11
16 ____ 34.33 ____ 12
17 ____ 32 _______ 8
18 ____ 33.33 ____ 11
19 ____ 25 _______11
20 ___ 27.33 _____12
Sample mean, xbar = Σx / n = 29.167
Rbar = ΣR/ n = 11.4
The R chart control limit is given by :
Rbar(1 – 3(d3/d2))
From the R chart :
d3 = 0.729 ; d2 = 3.735
Hence,
LCL = 11.4(1 – 3(0.729/3.735))
LCL = 11.4(0.4144578) =
LCL = 4.72481892 = 4.72
UCL = 11.4(1 – 3(0.729/3.735))
UCL = 11.4(1.5855421)
UCL = 18.075180 = 18.08