Problem 1. (50 p.) ABC Ltd. has recently been receiving complaints from retailers that their batteries are not lasting as long as other name brands. A quality manager decided, therefore, to take 26 samples (in randomly selected time intervals) of the batteries (each sample consisting of five batteries) to establish the standards for relevant control chart limits. The results are shown in the table below (the numbers represent how many hours a battery lasted):

Sample no. Battery 1 Battery 2 Battery 3 Battery 4 Battery 5 1 49 50 51 48 46 2 36 48 39 47 50 3 50 62 46 64 49 4 44 45 42 38 55 5 38 36 36 57 58 6 55 64 51 53 42 7 64 62 55 48 44 8 47 54 62 42 37 9 36 55 48 35 55 10 51 39 64 37 45 11 45 40 38 37 43 12 43 42 45 48 37 13 64 54 55 56 56 14 45 46 66 55 61 15 38 54 36 64 49 16 45 39 41 63 59 17 48 45 58 45 44 18 55 64 48 65 54 19 51 39 56 65 45 20 47 63 48 53 39 21 43 55 54 47 45 22 38 52 47 39 55 23 43 48 39 56 56 24 55 37 62 55 45 25 51 45 45 48 51 26 42 51 64 49 48

With these limits established, the manager now takes 6 more samples, which are shown in the following table:

Sample no. Battery 1 Battery 2 Battery 3 Battery 4 Battery 5 27 45 53 54 49 47 28 48 47 38 48 53 29 51 61 44 61 46 30 39 44 49 39 52 31 37 39 38 55 53 32 54 60 55 55 49

Q1. (30 p.) Determine the upper and lower control limits for all relevant charts. Show all your calculations.

Q2. (20 p.) Is the manufacturing process in control in Time Periods 27-32?