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work only parts b) through d); the mean and the standard deviation for the data in Table 3.7 are 162.7

grams and 2.83 grams respectively.  The data in Table 3.7 represents the results from the initial capability study

Beaver Brothers, Inc. is conducting a study to assess the capability of its 150-gram bar soap production line. A critical quality measure is the weight of the soap bars after stamping. The lower and upper specification limits are 162 and 170 grams respectively. As a part of an initial capability study, 25 samples of size 5 were collected by the quality assurance group and the observations in Table 3.7 were recorded.

After analyzing the data by using statistical control charts, the quality assurance group calculated the process capability ratio, Cpx and the process capability index, Cpk. It then decided to improve the stamping process, especially the feeder mechanism. After making al lthe changes that were deemed necessary, 18 additional samples were collected. The summary data for these samples are

X-bar =162.7  grams

R-bar = 2.326 grams

standard deviation= 2.83 grams

b. What were the values obtained by the group for Cp and Cpk for the initial capability study? Comment on your findings and explain why further improvements were necessary.

c. What are the Cp and Cpk after the improvements? Comment on your findings, indicating why the group decided to change the centering of the process.

d. What are the Cp and Cpk if the process were centered at 166? Comment on your findings.

TABLE 1. SAMPLE DATA FOR BEAVER BROTHERS, INC.
Sample
OBS. 1
OBS. 2
OBS. 3
OBS. 4
1
167.0
OBS. 5
159.6
161.6
164.0
2
156.2
165.3
159.5
161.7
167.0
164.0
165.3
162.9
162.9
164.0
167.0
165.4
159.6
163.7
164.1
156.3
165.4
160.0
162.9
164.0
164.1
164.2
165.5
163.0
164.2
161.3
163.9
163.0
164.2
157.0
8
163.1
160.6
164.2
156.9
9
164.3
160.1
157.0
163.1
161.2
10
163.2
156.9
164.4
161.0
163.2
11
164.3
161.0
157.3
163.3
12
164.4
163.3
157.6
160.6
164.5
158.4
13
160.1
158.2
163.3
161.3
163.5
14
164.6
161.5
158.7
163.5
164.7
15
158.6
163.6
164.8
162.5
158.0
16
162.4
164.5
163.6
158.5
160.3
17
163.4
164.9
164.6
157.9
162.3
18
163.7
155.0
165.1
162.2
163.7
19
164.8
162.1
159.6
163.9
165.1
20
159.3
165.2
162.0
159.1
161.6
21
163.9
164.9
165.1
165.2
22
159.9
162.0
167.6
163.7
165.6
165.6
23
156.7
167.7
165.7
165.8
165.9
24
156.9
166.0
165.9
166.0
165.6
25
165.6
163.7
165.5
163.7
165.6
165.6
166.2

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