5. (15 pts) Two observable quality characteristic z1 and r2 of a production process is recorded for m = 50 samples with a sample size of n = 25. Assume that mean values of the quality characteristics and the covariance matrix were determined as: i = 55 130 30 and S = 200 130 120 (a) Determine the UCL for a Hotelling 72 control chart. Consider a = 0.001. (b) The first 15 samples of the data is shown in Table 2. The data are sample means of each quality characteristic. Determine the 7 for these 15 samples. Based on the UCL from part (a), do you see any out of control samples? Table 2: Data for Exercise 5(b) Sample Number | $1 32 Sample Number 1 58 32 9 46 25 2 60 33 10 50 29 3 50 27 11 49 27 4 54 31 12 57 30 5 63 38 13 58 33 6 53 30 14 75 45 7 42 15 55 27 R 55 31