A manufacturer of plastic bottles has a quality control system in place to monitor the production process. The diameter of the bottles is a critical quality characteristic that needs to be within a specification range of 20 0.05 mm. The manufacturer takes samples of 5 bottles every hour and measures their diameters using a digital micrometer. The standard deviation of the process is 0.015. The data for the last samples are provided in the table below: Sample Bottle 1 Bottle 2 Bottle 3 Bottle 4 Bottle 5

1 20.03 20.02 20.01 20.04 20.01

2 20.01 20.03 20.02 20.02 20.03

3 20.05 20.01 20.03 20.02 20.01

4 20.04 20.02 20.04 20.05 20.01

5 20.02 20.01 20.03 20.02 20.04

6 20.02 20.03 20.02 20.04 20.05

7 20.01 20.02 20.05 20.03 20.04

8 20.05 20.04 20.02 20.02 20.01

9 20.03 20.01 20.03 20.01 20.04

10 20.02 20.05 20.03 20.02 20.04

11 20.01 20.02 20.01 20.02 20.03

12 20.03 20.04 20.02 20.03 20.04

13 20.01 20.02 20.05 20.03 20.02

14 20.05 20.04 20.01 20.02 20.01

15 20.02 20.03 20.04 20.05 20.01

16 20.01 20.02 20.03 20.04 20.03

17 20.05 20.04 20.02 20.03 20.02

18 20.03 20.05 20.02 20.01 20.04

19 20.02 20.02 20.03 20.02 20.05

20 20.01 20.02 20.04 20.03 20.02

21 20.05 19.97 19.98 19.99 20.01

22 19.99 20.04 20 20.02 19.99

23 20.01 20.02 20.03 20.01 20.01

24 20.02 20 20.01 20 19.99

25 20.03 20.01 20.02 20.03 20.01

26 19.98 20.01 20.03 20.01 20.02

27 20 20 20.02 20.01 20

28 20.01 19.99 20 19.99 20.02

29 20.04 20.03 20.01 20.02 20.03

30 20.02 20.01 20 20.01 20.02

31 19.99 20.03 20.04 20.02 20.03

32 20.01 20.01 20.03 20.02 20.01

33 20.02 20.01 20 20.02 20

34 19.98 19.99 19.98 20.01 19.99

35 20.03 20.02 20.02 20.01 20.02

36 20 20.03 20.01 20.02 20.03

37 20.02 20 20.01 20 20.01

38 20.03 20.01 20.02 20.03 20.01

39 20.01 20 20 20.01 20.01

40 19.99 20.03 20.04 20.02 20.03

1. Calculate sample averages and ranges and plot them on the X-bar and R charts for the data set and determine if the process is in control.

2. Calculate the process capability indices (Cp, Cpk) and interpret the results.

3. Judging by the charts, their patterns, and capability indexes, provide the evaluation of the entire process.