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Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in...

Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped. Management is concerned about whether the filling process for tubes of caulking is in statistical control. The process should be centered on 8 ounces per tube. Several samples of eight tubes were taken, each tube was weighed, and the weights in Table 3.3 were obtained.

  1. Assume that only six samples are sufficient and develop the control charts for the mean and the range.

  2. Plot the observations on the control chart and comment on your findings.

TUBE NUMBER
Sample 1 2 3 4 5 6 7 8
1 7.98 8.34 8.02 7.94 8.44 7.68 7.81 8.11
2 8.33 8.22 8.08 8.51 8.41 8.28 8.09 8.16
3 7.89 7.77 7.91 8.04 8.00 7.89 7.93 8.09
4 8.24 8.18 7.83 8.05 7.90 8.16 7.97 8.07
5 7.87 8.13 7.92 7.99 8.10 7.81 8.14 7.88
6 8.13 8.14 8.11 8.13 8.14 8.12 8.13 8.14

Solutions

Expert Solution

# SAMPLE

1

2

3

4

5

6

7

8

AVERAGE

RANGE

1

7.98

8.34

8.02

7.94

8.44

7.68

7.81

8.11

8.04

0.76

2

8.33

8.22

8.08

8.51

8.41

8.28

8.09

8.16

8.26

0.43

3

7.89

7.77

7.91

8.04

8

7.89

7.93

8.09

7.94

0.32

4

8.24

8.18

7.83

8.05

7.9

8.16

7.97

8.07

8.05

0.41

5

7.87

8.13

7.92

7.99

8.1

7.81

8.14

7.88

7.98

0.33

6

8.13

8.14

8.11

8.13

8.14

8.12

8.13

8.14

8.13

0.03

AVERAGE

8.067

0.38


XBAR = 8.067

RBAR = 0.38

A2 FOR N = 8 = 0.373

D3 & D4 FOR N = 0.136, 1.864

CONTROL LIMITS FOR X CHART

UCL X = XBAR + (A2 * RBAR) = 8.067 + (0.373 * 0.38) = 8.209

LCL X = XBAR - (A2 * RBAR) = 8.067 - (0.373 * 0.38) = 7.925

CONTROL LIMITS FOR CHART

UCL R = RBAR * D4 = 0.38 * 1.864 = 0.708

LCL R = RBAR * D3 = 0.38 * 0.136 = 0.052

2. Both the processes are not in control since one or more points are outside the limit, creating an understanding of the variations not be due to natural causes.

keosha answered 2 hours ago
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