A company is manufacturing integrated circuits. The design specifies the nominal thickness of the IC resistance layer to be 100 units. If the thickness strays too far from 100 units IC performance may be degraded. Assume the process is in control when 25 samples of IC resistance layer thickness (each of size 4) were taken off the production line. Using the methods of section 11.3.1 Control Charts for Variables, we want to achieve statistical control of the resistance layer thickness using X-bar and R charts.
The 25 sample values are provided in the following table.
|
Sample No.
|
Sample Values
|
|
1
|
90.42
|
90.92
|
98.98
|
93.26
|
|
2
|
91.91
|
86.45
|
103.18
|
103.58
|
|
3
|
110.85
|
96.96
|
98.19
|
102.65
|
|
4
|
125.56
|
106.68
|
105.53
|
97.33
|
|
5
|
111.84
|
100.27
|
93.82
|
111.41
|
|
6
|
98.12
|
97.76
|
90.02
|
112.4
|
|
7
|
107.87
|
87.01
|
106.06
|
119.58
|
|
8
|
100.17
|
100.93
|
80.77
|
88.77
|
|
9
|
94.02
|
100.77
|
107.21
|
101.69
|
|
10
|
93.49
|
112.24
|
100.73
|
95.44
|
|
11
|
89
|
91.44
|
104.04
|
98.09
|
|
12
|
94.12
|
93.56
|
95.84
|
102.98
|
|
13
|
107.21
|
86.29
|
97.46
|
122.98
|
|
14
|
95.35
|
100.9
|
106.59
|
100.73
|
|
15
|
101.66
|
109.1
|
92.83
|
86.62
|
|
16
|
103.35
|
80.3
|
117.23
|
93.92
|
|
17
|
103.31
|
94.49
|
115.74
|
103.28
|
|
18
|
103.87
|
118.35
|
111.11
|
91.97
|
|
19
|
106.45
|
105.86
|
108.14
|
97.13
|
|
20
|
89
|
98.45
|
112.17
|
111.68
|
|
21
|
115.88
|
108.87
|
104.21
|
91.71
|
|
22
|
106.19
|
96.96
|
102.49
|
103.81
|
|
23
|
99.48
|
107.25
|
92.07
|
101.53
|
|
24
|
99.35
|
90.06
|
72.8
|
94.88
|
|
25
|
96.87
|
101.96
|
101.92
|
105.49
|
a. Calculate the center line value and control limits for the R-chart.
Hint: Center line for the R chart is mean of the ranges.
b. Calculate the center line value and control limits for the X-bar chart.
c. Can the above control limits be adopted for use in on-line statistical process control? Explain.
d. 12 additional samples of IC resistance layer thickness were collected from a later production run and are provided below. Is the process in-control or out-of-control? Use the Control Charts constructed in parts a and bto determine whether the process is in-control or out-of-control. Explain your answer.
|
Sample No.
|
Sample Values
|
|
1
|
98.46
|
105.39
|
112.11
|
105.16
|
|
2
|
83.26
|
124.86
|
129.63
|
112.92
|
|
3
|
130.74
|
97.72
|
107.69
|
118.21
|
|
4
|
83.9
|
82.79
|
79.36
|
85.87
|
|
5
|
115.22
|
99.81
|
104.54
|
100.94
|
|
6
|
114.76
|
136.91
|
147.56
|
138.03
|
|
7
|
128.38
|
109.39
|
104.58
|
114.89
|
|
8
|
111.95
|
116.33
|
139.89
|
120.6
|
|
9
|
123.52
|
128.46
|
129.76
|
131.34
|
|
10
|
140.41
|
118.69
|
126.35
|
126.99
|
|
11
|
129.16
|
106.52
|
109.77
|
118.24
|
|
12
|
111.21
|
88.04
|
141.47
|
107.52
|