Question

1. [10 points] The data shown in the table below are ( ar{x} ), R and S values for 10 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 ( ar{x} ) R S number 1 34.5 3 0.5 2 34.2 4 0.67 3 31.6 4 0.67 4 31.5 4 0.67 5 35.0 5 0.83 6 34.1 6 1.00 7 32.6 4 0.67 8 33.8 3 0.67 9 34.8 7 1.75 10 33.6 8 1.33 (a) Setup the control charts to monitor the process variability based on the 10 samples drawn. Show the center line and the control limits (you don't need to draw the chart). Does the process appear to be in control? (b) If specifications on this diameter are 0.50300 ( pm ) 0.0001, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.

          1. [10 points] The data shown in the table below are ( ar{x} ), R and S values for 10 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
( ar{x} )
R
S
number
1
34.5
3
0.5
2
34.2
4
0.67
3
31.6
4
0.67
4
31.5
4
0.67
5
35.0
5
0.83
6
34.1
6
1.00
7
32.6
4
0.67
8
33.8
3
0.67
9
34.8
7
1.75
10
33.6
8
1.33
(a) Setup the control charts to monitor the process variability based on the 10 samples drawn. Show the center line and the control limits (you don't need to draw the chart). Does the process appear to be in control?
(b) If specifications on this diameter are 0.50300 ( pm ) 0.0001, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.

1. [10 points] The data shown in the table below are ( arx ), R and S values for 10 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
( arx )
R
S
number
1
34.5
3
0.5
2
34.2
4
0.67
3
31.6
4
0.67
4
31.5
4
0.67
5
35.0
5
0.83
6
34.1
6
1.00
7
32.6
4
0.67
8
33.8
3
0.67
9
34.8
7
1.75
10
33.6
8
1.33
(a) Setup the control charts to monitor the process variability based on the 10 samples drawn. Show the center line and the control limits (you don't need to draw the chart). Does the process appear to be in control?
(b) If specifications on this diameter are 0.50300 ( pm ) 0.0001, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.

Added by Benjamin W.

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