Research Article
Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information
Table 4
The ARL1 profile of the one-sided EDC and EDCC charts when δ ∈[1, 3] with ARL0 = 300.
| | | DC | DCC | λ = 0.05 | λ = 0.25 | λ = 0.50 | OC | | EDC | EDCC | ρ = 0.50 | ρ = 0.75 | EDC | EDCC | ρ = 0.50 | ρ = 0.75 | EDC | EDCC | ρ = 0.50 | ρ = 0.75 | | AIB-EDC | AIB-EDCC | AIB-EDC | AIB-EDCC | AIB-EDC | AIB-EDCC | AIB-EDC | AIB-EDCC | AIB-EDC | AIB-EDCC | AIB-EDC | AIB-EDCC | | [k1 = 0.75, k2 = 1.25] |
| | δ | h1 | 2.9618 | 2.8758 | 13.001 | 13.020 | 13.001 | 13.020 | 13.001 | 13.020 | 8.320 | 8.296 | 8.320 | 8.296 | 8.320 | 8.296 | 5.289 | 5.290 | 5.289 | 5.290 | 5.289 | 5.290 | k = δ/2 | | h2 | 1.7771 | 1.7255 | 7.800 | 7.810 | 7.800 | 7.810 | 7.800 | 7.810 | 4.990 | 4.980 | 4.990 | 4.980 | 4.990 | 4.980 | 3.170 | 3.170 | 3.170 | 3.170 | 3.170 | 3.170 | | 1.00 | ARL | 9.20 | 8.97 | 10.26 | 10.25 | 8.87 | 8.87 | 6.79 | 6.79 | 8.55 | 8.53 | 7.21 | 7.21 | 5.39 | 5.38 | 7.83 | 7.87 | 6.45 | 6.45 | 4.59 | 4.58 | 8.18 | | MRL | 7.00 | 7.00 | 10.00 | 10.00 | 8.00 | 8.00 | 7.00 | 7.00 | 8.00 | 8.00 | 7.00 | 7.00 | 5.00 | 5.00 | 7.00 | 7.00 | 6.00 | 6.00 | 4.00 | 4.00 | 7.00 | | SDRL | 6.61 | 6.55 | 3.59 | 3.59 | 2.88 | 2.88 | 1.88 | 1.88 | 3.59 | 3.60 | 2.77 | 2.78 | 1.79 | 1.79 | 4.15 | 4.18 | 3.09 | 3.09 | 1.87 | 1.87 | 4.60 | | 1.20 | ARL | 6.57 | 6.39 | 8.53 | 8.52 | 7.38 | 7.40 | 5.71 | 5.72 | 6.92 | 6.91 | 5.91 | 5.90 | 4.45 | 4.45 | 6.14 | 6.13 | 5.10 | 5.10 | 3.68 | 3.68 | 6.21 | | MRL | 6.00 | 5.00 | 8.00 | 8.00 | 7.00 | 7.00 | 6.00 | 6.00 | 6.00 | 6.00 | 6.00 | 6.00 | 4.00 | 4.00 | 6.00 | 6.00 | 5.00 | 5.00 | 3.00 | 3.00 | 5.00 | | SDRL | 4.25 | 4.17 | 2.71 | 2.71 | 2.16 | 2.16 | 1.41 | 1.41 | 2.62 | 2.61 | 2.06 | 2.06 | 1.31 | 1.32 | 2.88 | 2.87 | 2.19 | 2.19 | 1.35 | 1.35 | 3.41 | | 1.40 | ARL | 5.00 | 4.90 | 7.32 | 7.32 | 6.36 | 6.37 | 4.96 | 4.97 | 5.85 | 5.83 | 5.02 | 5.02 | 3.82 | 3.82 | 5.02 | 5.04 | 4.21 | 4.22 | 3.10 | 3.09 | 4.88 | | MRL | 4.00 | 4.00 | 7.00 | 7.00 | 6.00 | 6.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | 4.00 | 4.00 | 5.00 | 5.00 | 4.00 | 4.00 | 3.00 | 3.00 | 4.00 | | SDRL | 2.95 | 2.93 | 2.12 | 2.12 | 1.69 | 1.68 | 1.13 | 1.12 | 2.02 | 2.02 | 1.60 | 1.60 | 1.02 | 1.02 | 2.13 | 2.14 | 1.65 | 1.65 | 1.04 | 1.04 | 2.64 | | 1.60 | ARL | 4.02 | 3.92 | 6.43 | 6.44 | 5.63 | 5.62 | 4.40 | 4.41 | 5.06 | 5.07 | 4.38 | 4.36 | 3.37 | 3.37 | 4.27 | 4.27 | 3.61 | 3.61 | 2.68 | 2.68 | 3.97 | | MRL | 4.00 | 4.00 | 6.00 | 6.00 | 5.00 | 5.00 | 4.00 | 4.00 | 5.00 | 5.00 | 4.00 | 4.00 | 3.00 | 3.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | | SDRL | 2.20 | 2.15 | 1.71 | 1.72 | 1.38 | 1.37 | 0.92 | 0.93 | 1.63 | 1.62 | 1.28 | 1.27 | 0.85 | 0.84 | 1.68 | 1.69 | 1.32 | 1.31 | 0.83 | 0.83 | 2.11 | | 1.80 | ARL | 3.35 | 3.27 | 5.76 | 5.76 | 5.05 | 5.05 | 3.97 | 3.97 | 4.49 | 4.48 | 3.90 | 3.89 | 3.02 | 3.02 | 3.72 | 3.72 | 3.16 | 3.16 | 2.38 | 2.38 | 3.31 | | MRL | 3.00 | 3.00 | 6.00 | 6.00 | 5.00 | 5.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 2.00 | 2.00 | 3.00 | | SDRL | 1.73 | 1.70 | 1.43 | 1.42 | 1.15 | 1.15 | 0.79 | 0.79 | 1.34 | 1.33 | 1.06 | 1.06 | 0.73 | 0.72 | 1.37 | 1.37 | 1.08 | 1.08 | 0.68 | 0.68 | 1.73 | | 2.00 | ARL | 2.86 | 2.79 | 5.22 | 5.22 | 4.59 | 4.59 | 3.62 | 3.62 | 4.04 | 4.04 | 3.52 | 3.51 | 2.74 | 2.74 | 3.29 | 3.29 | 2.82 | 2.81 | 2.16 | 2.16 | 2.82 | | MRL | 3.00 | 3.00 | 5.00 | 5.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 2.00 | 2.00 | 2.00 | | SDRL | 1.41 | 1.39 | 1.22 | 1.21 | 0.99 | 0.99 | 0.69 | 0.68 | 1.12 | 1.12 | 0.91 | 0.90 | 0.64 | 0.64 | 1.15 | 1.15 | 0.90 | 0.89 | 0.58 | 0.58 | 1.45 | | 2.20 | ARL | 2.48 | 2.43 | 4.80 | 4.79 | 4.22 | 4.22 | 3.34 | 3.34 | 3.69 | 3.68 | 3.23 | 3.21 | 2.52 | 2.51 | 2.97 | 2.96 | 2.55 | 2.55 | 1.99 | 1.99 | 2.42 | | MRL | 2.00 | 2.00 | 5.00 | 5.00 | 4.00 | 4.00 | 3.00 | 3.00 | 4.00 | 4.00 | 3.00 | 3.00 | 2.00 | 2.00 | 3.00 | 3.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | | SDRL | 1.19 | 1.17 | 1.06 | 1.06 | 0.87 | 0.86 | 0.60 | 0.60 | 0.98 | 0.97 | 0.79 | 0.79 | 0.58 | 0.57 | 0.97 | 0.97 | 0.76 | 0.76 | 0.52 | 0.52 | 1.25 | | 2.40 | ARL | 2.20 | 2.15 | 4.43 | 4.43 | 3.90 | 3.91 | 3.11 | 3.11 | 3.40 | 3.39 | 2.97 | 2.97 | 2.33 | 2.33 | 2.71 | 2.71 | 2.34 | 2.34 | 1.84 | 1.84 | 2.12 | | MRL | 2.00 | 2.00 | 4.00 | 4.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 2.00 | 2.00 | 3.00 | 3.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | | SDRL | 1.02 | 1.01 | 0.94 | 0.94 | 0.77 | 0.77 | 0.53 | 0.53 | 0.85 | 0.86 | 0.71 | 0.71 | 0.50 | 0.50 | 0.85 | 0.84 | 0.66 | 0.66 | 0.49 | 0.50 | 1.08 | | 2.60 | ARL | 1.97 | 1.93 | 4.13 | 4.13 | 3.64 | 3.64 | 2.92 | 2.92 | 3.15 | 3.15 | 2.76 | 2.75 | 2.18 | 2.18 | 2.49 | 2.49 | 2.17 | 2.18 | 1.71 | 1.71 | 1.88 | | MRL | 2.00 | 2.00 | 4.00 | 4.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | | SDRL | 0.89 | 0.88 | 0.84 | 0.84 | 0.69 | 0.69 | 0.50 | 0.50 | 0.77 | 0.76 | 0.65 | 0.64 | 0.42 | 0.42 | 0.73 | 0.74 | 0.58 | 0.59 | 0.50 | 0.50 | 0.94 | | 2.80 | ARL | 1.78 | 1.74 | 3.86 | 3.87 | 3.42 | 3.42 | 2.75 | 2.75 | 2.94 | 2.94 | 2.58 | 2.58 | 2.08 | 2.07 | 2.32 | 2.32 | 2.04 | 2.03 | 1.58 | 1.58 | 1.69 | | MRL | 2.00 | 2.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | | SDRL | 0.78 | 0.78 | 0.76 | 0.76 | 0.63 | 0.63 | 0.50 | 0.50 | 0.70 | 0.70 | 0.59 | 0.59 | 0.34 | 0.34 | 0.65 | 0.65 | 0.53 | 0.53 | 0.51 | 0.51 | 0.83 | | 3.00 | ARL | 1.62 | 1.59 | 3.65 | 3.65 | 3.23 | 3.23 | 2.57 | 2.57 | 2.77 | 2.76 | 2.42 | 2.42 | 2.00 | 2.00 | 2.18 | 2.18 | 1.92 | 1.91 | 1.46 | 1.46 | 1.52 | | MRL | 2.00 | 1.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 1.00 | | SDRL | 0.70 | 0.69 | 0.69 | 0.69 | 0.56 | 0.56 | 0.51 | 0.51 | 0.65 | 0.65 | 0.54 | 0.54 | 0.30 | 0.30 | 0.59 | 0.59 | 0.5 | 0.51 | 0.5 | 0.5 | 0.73 | | EQL | 11.60 | 11.34 | 21.15 | 21.15 | 18.59 | 18.60 | 14.71 | 14.72 | 16.40 | 16.37 | 14.26 | 14.24 | 11.21 | 11.20 | 13.39 | 13.39 | 11.51 | 11.50 | 8.77 | 8.77 | 11.13 | | IRARL | 1.04 | 1.02 | 1.84 | 1.84 | 1.62 | 1.62 | 1.28 | 1.28 | 1.44 | 1.43 | 1.25 | 1.24 | 0.98 | 0.98 | 1.18 | 1.18 | 1.01 | 1.01 | 0.77 | 0.77 | 1.00 |
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