256Table 13.3 Minimal out-of-control ARL of the multivariate MEWMA,
MEWMAas, MC1, MCUSUM,T^2 charts for different values of parameters
kandr
a 1 \a 2 −0.9 −0.6 −0.3 0.0 0.3 0.6 0.9
−0.9 1.30(0.1) 1.43(0.1) 1.55(0.1) 1.61(0.1) 1.54(0.1) 1.39(0.1) 1.20(0.1)
1.42 (0.8) 1.64 (0.6) 1.86 (0.6) 1.97 (0.4) 1.92 (0.4) 1.69 (0.6) 1.39 (0.7)
1.48 (2.3) 1.70 (2.3) 1.90 (2.3) 2.01 (2.3) 1.95 (2.3) 1.76 (2.3) 1.49 (2.3)
1.54 (2.3) 1.78 (2.3) 2.00 (2.3) 2.12 (2.3) 2.07 (2.3) 1.87 (2.3) 1.57 (2.3)
1.43 1.67 1.95 2.10 2.04 1.76 1.41
−0.6 1.18(0.1) 1.23(0.1) 1.23(0.1) 1.13(0.1) 1.03(0.1) 1.00(0.1) 1.00(0.1)
1.25 (0.9) 1.35 (0.7) 1.38 (0.7) 1.24 (0.8) 1.06 (0.9) 1.00(0.9) 1.00(0.1)
1.30 (2.3) 1.42 (2.3) 1.45 (2.3) 1.33 (2.3) 1.11 (2.3) 1.00(2.3) 1.00(1.5)
1.33 (2.3) 1.47 (2.3) 1.52 (2.3) 1.39 (2.3) 1.14 (2.3) 1.01 (2.3) 1.00(1.4)
1.25 1.36 1.39 1.25 1.06 1.00 1.00
−0.3 1.08(0.1) 1.02(0.1) 1.00(0.2) 1.00(0.1) 1.02(0.1) 1.17(0.1) 1.30(0.1)
1.10 (0.9) 1.03 (0.8) 1.00(0.3) 1.00(0.1) 1.04 (0.9) 1.34 (0.7) 1.56 (0.6)
1.12 (2.3) 1.05 (2.3) 1.00(1.8) 1.00(1.4) 1.08 (2.3) 1.44 (2.3) 1.65 (2.3)
1.13 (2.3) 1.06 (2.3) 1.00(3.1) 1.00(1.5) 1.11 (2.3) 1.51 (2.3) 1.74 (2.3)
1.10 1.03 1.00 1.00 1.04 1.35 1.60
0.0 1.20(0.1) 2.61(0.1) 9.85(0.1) MEWMA 80.11 (0.1) 21.92 (0.1) 8.03(0.1)
1.23 (0.9) 2.95 (0.4) 11.08 (0.2) MEWMAas 76.02 (0.1) 22.75 (0.1) 9.74 (0.1)
1.26 (2.3) 2.97 (2.3) 10.21 (2.2) MC1 65.94 (1.4) 19.22(1.7) 8.20 (2.1)
1.27 (2.3) 3.08 (2.3) 10.49 (2.3) MCUSUM 65.38(1.4) 19.91 (1.8) 8.55 (2.3)
1.23 3.06 13.10 T^2 92.38 53.37 23.18
0.3 1.48(0.1) 1.12(0.1) 2.27(0.1) 14.10 (0.1) 186.57 (0.9) 76.42 (0.1) 11.14 (0.1)
1.57 (0.7) 1.14 (0.8) 2.65 (0.4) 15.89 (0.1) 188.19 (0.9) 70.17 (0.2) 12.67 (0.1)
1.64 (2.3) 1.16 (2.3) 2.64 (2.3) 13.99(1.9) 300.51 (2.3) 44.28 (1.4) 10.64(1.9)
1.67 (2.3) 1.17 (2.3) 2.77 (2.3) 14.63 (2.0) 299.16 (2.3) 44.05(1.4) 11.12 (2.2)
1.58 1.15 2.79 22.76 183.68 142.91 39.71
0.6 1.00(0.1) 3.26(0.1) 1.21(0.1) 8.22(0.1) 248.34 (0.9) 14.75 (0.1) 4.33(0.1)
1.00(0.7) 3.80 (0.4) 1.25 (0.9) 9.72 (0.2) 247.14 (0.9) 15.97 (0.1) 5.59 (0.2)
1.00(2.3) 3.81 (2.3) 1.28 (2.2) 8.59 (2.2) 422.18 (2.3) 13.19(1.9) 4.88 (2.3)
1.00(2.3) 3.88 (2.3) 1.31 (2.3) 8.86 (2.3) 181.66(2.3) 13.61 (2.0) 5.15 (2.3)
1.00 3.93 1.25 14.03 242.34 58.32 12.62
0.9 1.00(0.1) 1.00(0.3) 1.00(0.1) 6.44(0.1) 3.83(0.1) 1.51(0.1) 1.17(0.1)
1.01 (0.9) 1.00(0.5) 1.00(0.1) 7.71 (0.2) 4.99 (0.2) 1.95 (0.4) 1.37 (0.6)
1.03 (2.3) 1.00(2.3) 1.00(1.4) 6.90 (2.2) 4.41 (2.3) 1.98 (2.3) 1.47 (2.3)
1.04 (2.3) 1.00(2.3) 1.00(1.4) 7.21 (2.3) 4.66 (2.3) 2.12 (2.3) 1.56 (2.3)
1.01 1.00 1.00 11.00 10.73 2.20 1.39