Problem 1 Tires

The Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control the manufacturing process, 20 samples, each containing three radial tires, were chosen from different shifts over several days of operation, with the following results. Assuming that these data were collected when the manufacturing process was believed to be operating in control, develop the and charts.

Sample Obs 1 Obs 2 Obs 3

1 31 42 28

2 26 18 35

3 25 30 34

4 17 25 21

5 38 29 35

6 41 42 36

7 21 17 29

8 32 26 28

9 41 34 33

10 29 17 30

11 26 31 40

12 23 19 25

13 17 24 32

14 43 35 17

15 18 25 29

16 30 42 31

17 28 36 32

18 40 29 31

19 18 29 28

20 22 34 26

Problem 2

Airline Call Center An airline operates a call center to handle customer questions and complaints. The airline monitors a sample of calls to help ensure that the service being provided is of high quality. Ten random samples of 100 calls each were monitored under normal conditions. The center can be thought of as being in control when these 10 samples were taken. The number of calls in each sample not resulting in a satisfactory resolution for the customer is as follows: 4 5 3 2 3 3 4 6 4 7 a. What is an estimate of the proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control? b. Construct the upper and lower limits for a p chart for the manufacturing process, assuming each sample has 100 calls. c. With the results of part (b), what conclusion should be made if a sample of 100 has 12 calls not resulting in a satisfactory resolution for the customer? d. Compute the upper and lower limits for the np chart. e. With the results of part (d), what conclusion should be made if a sample of 100 calls has 12 not resulting in a satisfactory conclusion for the customer?