Research Article
Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information
Table 5
The ARL1 profile of the one-sided EDC and EDCC charts when δ ∈ [1, 5] 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 = 1, k2 = 2] |
| | δ | h1 | 2.0908 | 2.0412 | 7.300 | 7.275 | 7.300 | 7.275 | 7.300 | 7.275 | 5.480 | 5.499 | 5.480 | 5.499 | 5.480 | 5.499 | 3.600 | 3.611 | 3.600 | 3.611 | 3.600 | 3.611 | k = δ/2 | | h2 | 1.0454 | 1.0206 | 3.650 | 3.640 | 3.650 | 3.640 | 3.650 | 3.640 | 2.740 | 2.750 | 2.740 | 2.750 | 2.740 | 2.750 | 1.800 | 1.810 | 1.800 | 1.810 | 1.800 | 1.810 | | | 1.00 | ARL | 10.56 | 10.30 | 8.97 | 8.96 | 7.78 | 7.75 | 5.92 | 5.91 | 8.06 | 8.08 | 6.82 | 6.81 | 5.08 | 5.09 | 7.78 | 7.77 | 6.27 | 6.29 | 4.37 | 4.37 | 8.18 | | MRL | 8.00 | 8.00 | 8.00 | 8.00 | 7.00 | 7.00 | 6.00 | 6.00 | 7.00 | 7.00 | 6.00 | 6.00 | 5.00 | 5.00 | 7.00 | 7.00 | 5.00 | 5.00 | 4.00 | 4.00 | 7.00 | | SDRL | 8.68 | 8.48 | 3.34 | 3.34 | 2.70 | 2.69 | 1.86 | 1.85 | 3.66 | 3.65 | 2.76 | 2.74 | 1.71 | 1.71 | 4.65 | 4.64 | 3.36 | 3.35 | 1.87 | 1.86 | 4.60 | | 1.40 | ARL | 5.27 | 5.15 | 6.41 | 6.40 | 5.53 | 5.53 | 4.16 | 4.15 | 5.50 | 5.51 | 4.74 | 4.75 | 3.58 | 3.59 | 4.82 | 4.82 | 4.02 | 4.04 | 2.96 | 2.97 | 4.88 | | MRL | 4.00 | 4.00 | 6.00 | 6.00 | 5.00 | 5.00 | 4.00 | 4.00 | 5.00 | 5.00 | 5.00 | 5.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 3.00 | 3.00 | 4.00 | | SDRL | 3.58 | 3.51 | 2.05 | 2.05 | 1.70 | 1.70 | 1.21 | 1.21 | 1.94 | 1.94 | 1.54 | 1.55 | 1.08 | 1.09 | 2.18 | 2.19 | 1.63 | 1.64 | 1.02 | 1.03 | 2.64 | | 1.80 | ARL | 3.34 | 3.28 | 4.95 | 4.94 | 4.24 | 4.24 | 3.17 | 3.16 | 4.25 | 4.24 | 3.66 | 3.67 | 2.74 | 2.75 | 3.55 | 3.55 | 3.02 | 3.03 | 2.25 | 2.25 | 3.31 | | MRL | 3.00 | 3.00 | 5.00 | 5.00 | 4.00 | 4.00 | 3.00 | 3.00 | 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 | 1.87 | 1.85 | 1.49 | 1.49 | 1.24 | 1.24 | 0.86 | 0.85 | 1.33 | 1.32 | 1.10 | 1.10 | 0.80 | 0.80 | 1.33 | 1.32 | 1.05 | 1.05 | 0.76 | 0.76 | 1.73 | | 2.20 | ARL | 2.45 | 2.41 | 3.99 | 3.99 | 3.41 | 3.41 | 2.56 | 2.55 | 3.44 | 3.45 | 2.95 | 2.96 | 2.21 | 2.22 | 2.83 | 2.84 | 2.42 | 2.43 | 1.79 | 1.79 | 2.42 | | MRL | 2.00 | 2.00 | 4.00 | 4.00 | 3.00 | 3.00 | 2.00 | 2.00 | 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 | 1.20 | 1.17 | 1.15 | 1.15 | 0.94 | 0.95 | 0.65 | 0.64 | 1.03 | 1.03 | 0.87 | 0.87 | 0.61 | 0.61 | 0.98 | 0.98 | 0.82 | 0.81 | 0.62 | 0.62 | 1.25 | | 2.60 | ARL | 1.93 | 1.91 | 3.33 | 3.32 | 2.85 | 2.84 | 2.17 | 2.16 | 2.88 | 2.88 | 2.47 | 2.47 | 1.87 | 1.87 | 2.36 | 2.37 | 2.01 | 2.02 | 1.46 | 1.47 | 1.88 | | MRL | 2.00 | 2.00 | 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 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 2.00 | | SDRL | 0.85 | 0.84 | 0.91 | 0.91 | 0.74 | 0.75 | 0.49 | 0.49 | 0.84 | 0.84 | 0.70 | 0.70 | 0.52 | 0.52 | 0.80 | 0.79 | 0.68 | 0.69 | 0.53 | 0.53 | 0.94 | | 3.00 | ARL | 1.61 | 1.59 | 2.85 | 2.85 | 2.45 | 2.45 | 1.92 | 1.92 | 2.47 | 2.47 | 2.12 | 2.13 | 1.59 | 1.59 | 2.02 | 2.02 | 1.71 | 1.71 | 1.23 | 1.24 | 1.52 | | MRL | 2.00 | 2.00 | 3.00 | 3.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 1.00 | | SDRL | 0.66 | 0.66 | 0.75 | 0.75 | 0.60 | 0.61 | 0.42 | 0.42 | 0.70 | 0.70 | 0.58 | 0.58 | 0.51 | 0.51 | 0.69 | 0.68 | 0.60 | 0.60 | 0.43 | 0.43 | 0.73 | | 3.40 | ARL | 1.39 | 1.38 | 2.50 | 2.50 | 2.18 | 2.17 | 1.70 | 1.70 | 2.16 | 2.17 | 1.87 | 1.87 | 1.35 | 1.35 | 1.74 | 1.75 | 1.47 | 1.47 | 1.09 | 1.09 | 1.30 | | MRL | 1.00 | 1.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 2.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 0.54 | 0.54 | 0.62 | 0.62 | 0.49 | 0.49 | 0.47 | 0.47 | 0.59 | 0.59 | 0.52 | 0.52 | 0.48 | 0.48 | 0.61 | 0.61 | 0.53 | 0.53 | 0.29 | 0.29 | 0.55 | | 3.80 | ARL | 1.23 | 1.22 | 2.24 | 2.24 | 1.97 | 1.97 | 1.46 | 1.46 | 1.93 | 1.94 | 1.66 | 1.66 | 1.16 | 1.16 | 1.53 | 1.53 | 1.28 | 1.28 | 1.03 | 1.03 | 1.15 | | MRL | 1.00 | 1.00 | 2.00 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 2.00 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 2.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 0.44 | 0.43 | 0.52 | 0.52 | 0.42 | 0.43 | 0.50 | 0.50 | 0.53 | 0.53 | 0.51 | 0.51 | 0.36 | 0.37 | 0.55 | 0.55 | 0.46 | 0.46 | 0.16 | 0.16 | 0.39 | | 4.20 | ARL | 1.13 | 1.12 | 2.04 | 2.04 | 1.81 | 1.81 | 1.24 | 1.24 | 1.74 | 1.74 | 1.46 | 1.46 | 1.05 | 1.05 | 1.35 | 1.35 | 1.15 | 1.15 | 1.01 | 1.01 | 1.07 | | MRL | 1.00 | 1.00 | 2.00 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 2.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 0.34 | 0.33 | 0.44 | 0.44 | 0.44 | 0.44 | 0.43 | 0.43 | 0.51 | 0.51 | 0.51 | 0.51 | 0.22 | 0.23 | 0.49 | 0.49 | 0.35 | 0.36 | 0.07 | 0.07 | 0.27 | | 4.60 | ARL | 1.06 | 1.06 | 1.90 | 1.89 | 1.64 | 1.63 | 1.09 | 1.09 | 1.56 | 1.57 | 1.28 | 1.29 | 1.01 | 1.01 | 1.21 | 1.22 | 1.06 | 1.07 | 1.00 | 1.00 | 1.03 | | MRL | 1.00 | 1.00 | 2.00 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 2.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 0.24 | 0.23 | 0.42 | 0.42 | 0.49 | 0.49 | 0.29 | 0.29 | 0.51 | 0.51 | 0.45 | 0.45 | 0.11 | 0.11 | 0.41 | 0.41 | 0.24 | 0.25 | 0.03 | 0.03 | 0.18 | | 5.00 | ARL | 1.02 | 1.02 | 1.76 | 1.75 | 1.45 | 1.45 | 1.03 | 1.03 | 1.40 | 1.40 | 1.15 | 1.15 | 1.00 | 1.00 | 1.12 | 1.12 | 1.02 | 1.02 | 1.00 | 1.00 | 1.01 | | MRL | 1.00 | 1.00 | 2.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 0.15 | 0.15 | 0.46 | 0.46 | 0.50 | 0.50 | 0.17 | 0.16 | 0.49 | 0.49 | 0.36 | 0.36 | 0.05 | 0.05 | 0.32 | 0.32 | 0.16 | 0.16 | 0.01 | 0.01 | 0.11 | | EQL | 15.71 | 15.56 | 26.04 | 25.99 | 22.43 | 22.39 | 16.37 | 16.36 | 22.05 | 22.09 | 18.65 | 18.69 | 14.17 | 14.18 | 17.84 | 17.87 | 15.30 | 15.34 | 12.59 | 12.61 | 14.93 | | IRARL | 1.06 | 1.05 | 1.69 | 1.68 | 1.45 | 1.45 | 1.07 | 1.07 | 1.44 | 1.44 | 1.22 | 1.23 | 0.92 | 0.92 | 1.18 | 1.18 | 1.00 | 1.01 | 0.80 | 0.80 | 1.00 |
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