Question

Problem 2. (15 pts) The data shown in Table 2 are x? and R values for 24 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345). Sample Number x? R Sample Number x? R 1 34.5 3 13 35.4 8 2 34.2 4 14 34.0 6 3 31.6 4 15 37.1 5 4 31.5 4 16 34.9 7 5 35.0 5 17 33.5 4 6 34.1 6 18 31.7 3 7 32.6 4 19 34.0 8 8 33.8 3 20 35.1 4 9 34.8 7 21 33.7 2 10 33.6 8 22 32.8 1 11 31.9 3 23 33.5 3 12 38.6 9 24 34.2 2 Table 2: Bearing Diameter Data for Problem 2 (a) (8 pts) Set up x? and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. (b) (7 pts) If specifications on this diameter are 0.5030 0.0010, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.

          Problem 2. (15 pts) The data shown in Table 2 are x? and R values for 24 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345).

Sample Number x? R Sample Number x? R
1 34.5 3 13 35.4 8
2 34.2 4 14 34.0 6
3 31.6 4 15 37.1 5
4 31.5 4 16 34.9 7
5 35.0 5 17 33.5 4
6 34.1 6 18 31.7 3
7 32.6 4 19 34.0 8
8 33.8 3 20 35.1 4
9 34.8 7 21 33.7 2
10 33.6 8 22 32.8 1
11 31.9 3 23 33.5 3
12 38.6 9 24 34.2 2

Table 2: Bearing Diameter Data for Problem 2

(a) (8 pts) Set up x? and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits.
(b) (7 pts) If specifications on this diameter are 0.5030  0.0010, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.

Problem 2. (15 pts) The data shown in Table 2 are x? and R values for 24 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345).

Sample Number x? R Sample Number x? R
1 34.5 3 13 35.4 8
2 34.2 4 14 34.0 6
3 31.6 4 15 37.1 5
4 31.5 4 16 34.9 7
5 35.0 5 17 33.5 4
6 34.1 6 18 31.7 3
7 32.6 4 19 34.0 8
8 33.8 3 20 35.1 4
9 34.8 7 21 33.7 2
10 33.6 8 22 32.8 1
11 31.9 3 23 33.5 3
12 38.6 9 24 34.2 2

Table 2: Bearing Diameter Data for Problem 2

(a) (8 pts) Set up x? and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits.
(b) (7 pts) If specifications on this diameter are 0.5030 0.0010, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.

Added by Andrew R.

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