Two observable quality characteristic and 2 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 =- 1 2 3 4 5 6 55 30 7 8 and S = (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 1. The data are sample means of each quality characteristic. Determine the T2 for these 15 samples. Based on the UCL from part (a), do you see any out of control samples? Sample Number T T2 | 58 | 32 | 60 | 33 50 27 54 31 63 38 53 30 42 20 55 31 200 130 130 120 Table 1: Data for Exercise 4(b) Sample Number 9 10 11 12 13 14 15 I1 I2 46 25 50 29 49 27 57 30 58 33 75 45 55 27