Fujiyama Electronics, corporation has been having difficulties with circuit boards bought from an outside supplier. Unacceptable variability occurs between two drilled holes that are supposed to be 5 cm apart on the circuit boards. Twenty-five samples of four boards each were taken from shipments sent by the supplier as shown in the data listed in the part a).
a. Construct;x - and R-charts for these data.

Observations
Sample 1 2 3 4

1 4.92 4.26 4.94 4.29
2 4.65 5.54 5.00 5.42
3 5.77 5.26 4.76 4.79
4 6.25 4.88 5.66 4.44
5 5.27 5.41 6.02 4.91
6 5.22 5.38 5.08 4.65
7 5.47 4.68 4.56 4.70
8 5.71 4.54 4.17 4.87
9 5.24 5.58 4.72 5.41
10 4.42 5.18 4.79 4.73
11 5.14 4.26 4.71 5.48
12 4.92 5.78 5.50 5.05
13 5.79 3.83 4.30 4.78
14 4.92 4.80 4.75 5.59
15 5.68 5.74 4.65 5.20
16 5.43 4.81 5.27 4.96
17 4.79 6.04 4.47 5.18
18 4.43 5.08 3.69 6.43
19 6.35 5.95 6.29 5.89
20 5.03 4.66 5.25 4.46
21 6.32 6.09 5.57 5.91
22 4.30 5.47 4.27 4.34
23 6.07 4.97 5.51 5.02
24 5.11 4.90 5.91 4.66
25 4.50 5.24 4.86 4.35

b. If the supplier's plant quality manager admitted that they were experiencing quality problems for shipments 18, 19, and 21, how would that affect your control chart? Show this adjustment on revised;x - and R-charts for these data.
c. Ten more observations were taken, as shown in the second table in the worksheet. Using the revised;x - and R-charts from part (b), comment on what the chart shows after extending it with the new data.

Observations
Sample 1 2 3 4

1 4.92 5.54 5.00 5.42
2 4.65 5.14 4.26 4.71
3 5.78 5.50 5.05 4.79
4 5.95 3.83 4.30 4.44
5 4.92 4.80 4.75 5.59
6 5.68 5.74 4.65 4.65
7 4.78 5.79 5.20 4.70
8 4.43 4.81 5.27 4.87
9 6.04 4.47 5.18 5.41
10 4.96 5.18 5.48 4.73