Problem 1
The King Tire Company in Birmingham wants to monitor the quality of the tires it manufactures. Each day the company quality-control manager takes a sample of 100 tires, tests them, and determines the number of defective tires. The results of 20 samples have been recorded as follows:
|
Sample
|
Number of Defectives
|
Sample
|
Number of Defectives
|
|
1
|
14
|
11
|
18
|
|
2
|
12
|
12
|
10
|
|
3
|
9
|
13
|
19
|
|
4
|
10
|
14
|
20
|
|
5
|
11
|
15
|
17
|
|
6
|
7
|
16
|
18
|
|
7
|
8
|
17
|
18
|
|
8
|
14
|
18
|
22
|
|
9
|
16
|
19
|
24
|
|
10
|
17
|
20
|
23
|
|
Construct a Ρ-chart for this process using 2σlimits and describe the variation in the process.
Problem 2
One of the stages in the process of making denim cloth at the Northern Mills Company is to spin cotton yarn onto spindles for subsequent use in the weaving process. Occasionally the yarn breaks during the spinning process, and an operator ties it back together. Some number of breaks is considered normal; however, too many breaks might mean that the yarn is of poor quality. In order to monitor this process, the quality-control manager randomly selects a spinning machine each hour and checks the number of breaks during a 15-minute period. Following is a summary of the observations for the past 20 hours:
|
Sample
|
Number of Breaks
|
Sample
|
Number of Breaks
|
|
1
|
3
|
11
|
3
|
|
2
|
2
|
12
|
4
|
|
3
|
4
|
13
|
6
|
|
4
|
1
|
14
|
7
|
|
5
|
5
|
15
|
8
|
|
6
|
3
|
16
|
6
|
|
7
|
2
|
17
|
5
|
|
8
|
4
|
18
|
7
|
|
9
|
0
|
19
|
8
|
|
10
|
2
|
20
|
6
|
|
Construct a C-chart using 3σlimits for this process and indicate if the process was out of control at any time.