Parts manufactured by an injection molding process are subjected to a compressive strength test. Twenty samples of five parts each are collected and the compressive strengths (inpsi) are shown in the table that follows.
|
x1
|
x2
|
x3
|
x4
|
x5
|
2
|
S
|
|
83.0
|
81.2
|
78.7
|
75.7
|
77.0
|
79.1
|
2.99
|
|
88.6
|
78.3
|
78.8
|
71.0
|
84.2
|
80.2
|
6.65
|
|
85.7
|
75.8
|
84.3
|
75.2
|
81.0
|
80.4
|
4.79
|
|
80.8
|
74.4
|
82.5
|
74.1
|
75.7
|
77.5
|
3.88
|
|
83.4
|
78.4
|
82.6
|
78.2
|
78.9
|
80.3
|
2.49
|
|
75.3
|
79.9
|
87.3
|
89.7
|
81.8
|
82.8
|
5.78
|
|
74.5
|
78.0
|
80.8
|
73.4
|
79.7
|
77.3
|
3.22
|
|
79.2
|
84.4
|
81.5
|
86.0
|
74.5
|
81.1
|
4.53
|
|
80.5
|
86.2
|
76.2
|
84.1
|
80.2
|
81.4
|
3.86
|
|
75.7
|
75.2
|
71.1
|
82.1
|
74.3
|
75.7
|
4.01
|
|
80.0
|
81.5
|
78.4
|
73.8
|
78.1
|
78.4
|
2.89
|
|
80.6
|
81.8
|
79.3
|
73.8
|
81.7
|
79.4
|
3.31
|
|
82.7
|
81.3
|
79.1
|
82.0
|
79.5
|
80.9
|
1.57
|
|
79.2
|
74.9
|
78.6
|
77.7
|
75.3
|
77.1
|
1.94
|
|
85.5
|
82.1
|
82.8
|
73.4
|
71.7
|
79.1
|
6.14
|
|
78.8
|
79.6
|
80.2
|
79.1
|
80.8
|
79.7
|
0.81
|
|
82.1
|
78.2
|
75.5
|
78.2
|
82.1
|
79.2
|
2.85
|
|
84.5
|
76.9
|
83.5
|
81.2
|
79.2
|
81.1
|
3.11
|
|
79.0
|
77.8
|
81.2
|
84.4
|
81.6
|
80.8
|
2.55
|
|
84.5
|
73.1
|
78.6
|
78.7
|
80.6
|
79.1
|
4.12
|
(a) Is there evidence to support the claim that compressive strength is normally distributed?
[If your statistical package does not have a subprogram that allows you to answer this, you can briefly explain how normality can be verified or tested.]
(b) Construct X and s charts to show that the process in statistical control. (If you are constructing the charts manually, you only need to use the last two columns)
(c) After establishing that the process is in control, the charts were used for future monitoring. The readings for the next 13 samples are shown on the next page. Plot the X and s values against the control limits from part (b). What do the charts indicate re the process mean and variability?
|
|
X2
|
X3
|
X4
|
X5
|
2
|
S
|
|
79.2
|
84.4
|
81.5
|
86.0
|
74.5
|
81.1
|
4.53
|
|
80.2
|
86.2
|
76.5
|
84.1
|
80.2
|
81.4
|
3.78
|
|
75.7
|
75.2
|
71.1
|
82.1
|
73.4
|
75.5
|
4.11
|
|
80.0
|
84.0
|
78.4
|
73.8
|
78.1
|
78.9
|
3.68
|
|
80.6
|
81.8
|
79.3
|
73.5
|
79.0
|
78.8
|
3.19
|
|
87.3
|
76.9
|
87.0
|
80.2
|
77.4
|
81.8
|
5.08
|
|
79.2
|
88.2
|
96.1
|
92.1
|
81.5
|
87.4
|
7.08
|
|
79.1
|
86.1
|
86.0
|
78.2
|
81.4
|
82.2
|
3.74
|
|
80.1
|
75.5
|
80.1
|
81.6
|
85.5
|
80.6
|
3.59
|
|
90.4
|
82.2
|
97.5
|
81.5
|
80.3
|
86.4
|
7.38
|
|
70.0
|
73.0
|
76.1
|
82.3
|
86.5
|
77.6
|
6.75
|
|
84.2
|
84.3
|
90.4
|
80.2
|
80.8
|
84.0
|
4.05
|
|
93.0
|
84.5
|
88.3
|
86.6
|
93.4
|
89.2
|
3.93
|