The thickness of a metal part is an important quality parameter. Data on thickness (in inches) are given in the following table, for 25 samples of five parts each.
Sample Number x1 x2 x3 x4 x5
1 0.0629 0.0636 0.064 0.0634 0.0641
2 0.063 0.0632 0.062 0.0624 0.0627
3 0.0628 0.0631 0.0633 0.0633 0.063
4 0.0634 0.063 0.0631 0.0632 0.0633
5 0.0619 0.0628 0.063 0.0619 0.0625
6 0.0613 0.0629 0.0634 0.0625 0.0628
7 0.063 0.0639 0.0625 0.0629 0.0627
8 0.0628 0.0627 0.0622 0.0625 0.0627
9 0.0623 0.0626 0.0633 0.063 0.0624
10 0.0631 0.0631 0.0633 0.0631 0.063
11 0.0635 0.063 0.0638 0.0635 0.0633
12 0.0623 0.063 0.063 0.0627 0.0629
13 0.0635 0.0631 0.063 0.063 0.063
14 0.0645 0.064 0.0631 0.064 0.0642
15 0.0619 0.0644 0.0632 0.0622 0.0635
16 0.0631 0.0627 0.063 0.0628 0.0629
17 0.0616 0.0623 0.0631 0.062 0.0625
18 0.063 0.063 0.0626 0.0629 0.0628
19 0.0636 0.0631 0.0629 0.0635 0.0634
20 0.064 0.0635 0.0629 0.0635 0.0634
21 0.0628 0.0625 0.0616 0.062 0.0623
22 0.0615 0.0625 0.0619 0.0619 0.0622
23 0.063 0.0632 0.063 0.0631 0.063
24 0.0635 0.0629 0.0635 0.0631 0.0633
25 0.0623 0.0629 0.063 0.0626 0.0628
(a) Using all the data find trial control limits for X¯ and R charts. Round your answers to 5 decimal places (e.g. 98.76543).
X¯ Control Limits:
UCL =
CL =
LCL =
R Control Limits:
UCL =
CL =
LCL =
(b) Construct X¯ and R control charts using the control limits from part (a) to identify out-of-control points. (Use Minitab, Excel or any other statistical software.)
Does the process appear to be in control or out-of-control?
How many of the subgroups fall outside the control limits on both charts combined. (If none are outside the limits, type "0".)
