Question: Engineers at a manufacturing plant have just been to a course to learn the basics of SPC. They have decided to set up their first charting application on a CNC turning center where a motor shaft is being machined. The quality characteristic that they wish to monitor is the outside diameter, which has a nominal value of 2.125 in. and a tolerance of +0.003 in. Recently, however, they have been feeling pressure from the company to which they are supplying the parts to improve the consistency of the part dimension in question, and the engineers feel that methods of SPC may be able to assist them in reducing variability.
Initially, they collect data on the outside diameter in subgroups/samples of five consecutive parts, at intervals of approximately one-half hour, with the results as shown in the table below. The measurements were made in inches to the nearest ten-thousandth of an inch, e.g. 2.1248", 2.1259, etc. The data is coded using the last two digits. First, find and R for each sample. Next, use all thirty-five samples to compute the center lines and control limits for and R charts. Construct the charts, plotting all of the and R values and including all appropriate information on the charts. Apply all the appropriate rules to interpret the charts, indicating every incident of an out of control condition, and identifying the rule that is violated in each case. What can be said about the stability of the process? The data table is on the opposite face.
| Sample |
X1 |
X2 |
X3 |
X4 |
X5 |
| 1 |
48 |
59 |
42 |
40
|
32 |
| 2 |
48 |
52 |
51 |
50 |
52 |
| 3 |
50 |
49 |
60 |
44 |
48 |
| 4 |
50 |
41 |
48 |
43 |
41 |
| 5 |
51 |
49 |
60 |
60 |
47 |
| 6 |
44 |
47 |
54 |
45 |
50 |
| 7 |
51 |
57 |
53 |
48 |
45 |
| 8 |
46 |
63 |
63 |
41 |
41 |
| 9 |
54 |
53 |
53 |
46 |
55 |
| 10 |
54 |
46 |
55 |
58 |
62 |
| 11 |
57 |
56 |
53 |
37 |
42 |
| 12 |
51 |
49 |
67 |
50 |
48 |
| 13 |
42 |
47 |
48 |
39 |
61 |
| 14 |
43 |
50 |
44 |
38 |
40 |
| 15 |
41 |
54 |
59 |
53 |
37 |
| 16 |
60 |
45 |
52 |
46 |
55 |
| 17 |
48 |
50 |
45 |
40 |
63 |
| 18 |
46 |
39 |
43 |
61 |
41 |
| 19 |
52 |
32 |
54 |
45 |
50 |
| 20 |
62 |
50 |
47 |
57 |
47 |
| 21 |
58 |
52 |
57 |
54 |
63 |
| 22 |
50 |
56 |
44 |
44 |
38 |
| 23 |
47 |
53 |
42 |
40 |
46 |
| 24 |
56 |
55 |
44 |
58 |
49 |
| 25 |
39 |
54 |
54 |
44 |
63 |
| 26 |
40 |
43 |
59 |
36 |
46 |
| 27 |
48 |
48 |
34 |
43 |
62 |
| 28 |
36 |
45 |
43 |
32 |
38 |
| 29 |
51 |
48 |
24 |
55 |
54 |
| 30 |
43 |
50 |
40 |
53 |
41 |
| 31 |
43 |
43 |
49 |
31 |
47 |
| 32 |
29 |
42 |
43 |
42 |
43 |
| 33 |
36 |
43 |
43 |
49 |
48 |
| 34 |
48 |
42 |
43 |
39 |
46 |
| 35 |
45 |
51 |
43 |
39 |
29 |