257Table 13.4Minimal out-of-control ARL of the simultaneous 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 1.75(0.1) 1.63(0.1) 1.49(0.1) 1.33(0.1) 1.19(0.1) 1.09(0.1) 1.03(0.1)
2.70 (0.2) 2.46 (0.2) 2.16 (0.2) 1.85 (0.3) 1.56 (0.4) 1.31 (0.6) 1.13 (0.7)
2.77 (1.1) 2.51 (1.1) 2.18 (1.1) 1.86 (1.1) 1.56 (1.2) 1.31 (1.9) 1.13 (2.0)
2.82 (1.1) 2.55 (1.1) 2.21 (1.3) 1.88 (1.3) 1.57 (1.5) 1.32 (2.0) 1.13 (1.9)
3.97 3.42 2.77 2.18 1.70 1.35 1.13
−0.6 1.72(0.1) 1.46(0.1) 1.22(0.1) 1.06(0.1) 1.00(0.1) 1.00(0.1) 1.00(0.1)
2.63 (0.2) 2.15 (0.2) 1.64 (0.3) 1.24 (0.4) 1.03 (0.9) 1.00(0.7) 1.00(0.1)
2.70 (1.1) 2.16 (1.2) 1.64 (1.2) 1.24 (2.0) 1.03 (2.0) 1.00(1.5) 1.00(1.1)
2.76 (1.1) 2.20 (1.3) 1.66 (1.3) 1.25 (1.9) 1.03 (2.0) 1.00(1.7) 1.00(1.1)
3.83 2.75 1.82 1.26 1.03 1.00 1.00
−0.3 1.76(0.1) 1.10(0.1) 1.00(0.1) 1.00(0.1) 1.00(0.1) 1.02(0.1) 1.03(0.1)
2.67 (0.2) 1.34 (0.4) 1.00(0.7) 1.00(0.1) 1.02 (0.9) 1.11 (0.6) 1.15 (0.6)
2.74 (1.1) 1.34 (1.9) 1.00(1.5) 1.00(1.1) 1.02 (2.0) 1.12 (1.7) 1.15 (2.0)
2.80 (1.1) 1.34 (2.0) 1.00(1.7) 1.00(1.1) 1.02 (2.0) 1.12 (1.9) 1.15 (1.9)
3.89 1.39 1.00 1.00 1.02 1.12 1.16
0.0 1.00(0.1) 1.34(0.1) 6.21(0.1) simMEWMA 9.52(0.1) 3.21(0.1) 1.84(0.1)
1.00(0.3) 1.84 (0.3) 8.14 (0.1) simMEWMAas 11.77 (0.1) 4.67 (0.1) 2.74 (0.2)
1.00(1.1) 1.84 (1.1) 11.83 (1.1) simMC1 19.42 (1.1) 5.38 (1.1) 2.81 (1.1)
1.00(1.3) 1.87 (1.3) 11.94 (1.1) simMCUSUM 19.53 (1.1) 5.44 (1.1) 2.85 (1.1)
1.00 2.17 20.95 simT^2 29.03 9.56 4.03
0.3 1.00(0.1) 1.17(0.1) 2.58(0.1) 8.61(0.1) 9.97(0.1) 3.46(0.1) 1.84(0.1)
1.01 (0.8) 1.51 (0.4) 3.96 (0.1) 10.88 (0.1) 12.40 (0.1) 5.09 (0.1) 2.77 (0.2)
1.01 (2.0) 1.51 (1.7) 4.34 (1.1) 17.31 (1.1) 20.53 (1.1) 6.03 (1.1) 2.84 (1.1)
1.01 (2.0) 1.52 (1.8) 4.42 (1.1) 17.49 (1.1) 20.90 (1.1) 6.13 (1.1) 2.91 (1.1)
1.01 1.64 7.38 26.38 28.44 10.53 4.12
0.6 1.00(0.1) 1.00(0.1) 1.44(0.1) 5.08(0.1) 5.11(0.1) 1.95(0.1) 1.28(0.1)
1.00(0.1) 1.01 (0.9) 2.10 (0.2) 6.96 (0.1) 7.21 (0.1) 3.00 (0.2) 1.78 (0.3)
1.00(1.1) 1.02 (2.0) 2.11 (1.1) 9.37 (1.1) 10.12 (1.1) 3.13 (1.1) 1.79 (1.2)
1.00(1.1) 1.02 (2.0) 2.15 (1.1) 9.46 (1.1) 10.29 (1.1) 3.19 (1.1) 1.81 (1.2)
1.00 1.02 2.68 16.43 16.30 4.64 2.06
0.9 1.00(0.2) 1.00(0.1) 1.00(0.1) 4.07(0.1) 1.23(0.1) 1.02(0.1) 1.00(0.1)
1.00(0.7) 1.00(0.1) 1.00(0.1) 5.79 (0.1) 1.68 (0.3) 1.10 (0.6) 1.02 (0.8)
1.00(1.7) 1.00(1.1) 1.00(1.1) 7.19 (1.1) 1.68 (1.2) 1.11 (1.9) 1.02 (2.0)
1.00(1.3) 1.00(1.1) 1.00(1.1) 7.29 (1.1) 1.70 (1.4) 1.11 (1.8) 1.02 (2.0)
1.00 1.00 1.00 12.85 1.88 1.11 1.02