Research Article
Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information
Table 6
The ARL1 profile of the one-sided FIR based EDC and EDCC charts when δ ∈[0.25, 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 = 0.72, k2 = 1.91] |
| | δ | h1 | 3.0085 | 2.9037 | 13.801 | 13.870 | 13.801 | 13.870 | 13.801 | 13.870 | 8.680 | 8.675 | 8.680 | 8.675 | 8.680 | 8.675 | 5.468 | 5.460 | 5.468 | 5.460 | 5.468 | 5.460 | k = δ/2 | | h2 | 1.1341 | 1.0946 | 5.2025 | 5.2285 | 5.2025 | 5.2285 | 5.2025 | 5.2285 | 3.272 | 3.2702 | 3.272 | 3.2702 | 3.272 | 3.2702 | 2.0612 | 2.0582 | 2.0612 | 2.0582 | 2.0612 | 2.0582 | | 0.25 | ARL | 87.00 | 84.55 | 44.30 | 44.30 | 37.59 | 37.70 | 27.74 | 27.70 | 49.83 | 50.02 | 40.91 | 41.08 | 27.55 | 27.51 | 57.83 | 57.94 | 47.07 | 47.16 | 30.77 | 30.86 | 52.31 | | MRL | 58.00 | 56.00 | 35.00 | 35.00 | 31.00 | 31.00 | 24.00 | 24.00 | 36.00 | 36.00 | 30.00 | 30.00 | 21.00 | 21.00 | 40.00 | 40.00 | 32.00 | 33.00 | 21.00 | 22.00 | 43.00 | | SDRL | 92.15 | 89.87 | 31.93 | 31.89 | 25.51 | 25.51 | 16.52 | 16.43 | 44.99 | 45.18 | 35.93 | 36.26 | 22.36 | 22.45 | 57.62 | 57.81 | 46.53 | 46.57 | 29.55 | 29.44 | 35.36 | | 0.73 | ARL | 12.79 | 12.37 | 13.72 | 13.76 | 11.84 | 11.88 | 8.96 | 9.00 | 10.77 | 10.74 | 8.97 | 8.94 | 6.50 | 6.52 | 9.89 | 9.88 | 7.84 | 7.78 | 5.22 | 5.20 | 13.03 | | MRL | 8.00 | 8.00 | 13.00 | 13.00 | 11.00 | 11.00 | 9.00 | 9.00 | 9.00 | 9.00 | 8.00 | 8.00 | 6.00 | 6.00 | 8.00 | 8.00 | 6.00 | 6.00 | 4.00 | 4.00 | 11.00 | | SDRL | 13.17 | 12.78 | 5.66 | 5.70 | 4.59 | 4.59 | 3.18 | 3.21 | 6.24 | 6.21 | 4.68 | 4.67 | 2.82 | 2.81 | 7.65 | 7.64 | 5.57 | 5.51 | 3.07 | 3.04 | 7.66 | | 1.20 | ARL | 4.37 | 4.25 | 8.22 | 8.23 | 7.00 | 7.03 | 5.07 | 5.08 | 5.94 | 5.93 | 5.07 | 5.06 | 3.76 | 3.75 | 4.65 | 4.65 | 3.86 | 3.86 | 2.80 | 2.80 | 6.21 | | MRL | 3.00 | 3.00 | 8.00 | 8.00 | 7.00 | 7.00 | 5.00 | 5.00 | 6.00 | 6.00 | 5.00 | 5.00 | 4.00 | 4.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 5.00 | | SDRL | 3.58 | 3.52 | 2.90 | 2.89 | 2.46 | 2.48 | 1.78 | 1.78 | 2.45 | 2.45 | 1.96 | 1.95 | 1.41 | 1.41 | 2.57 | 2.58 | 1.93 | 1.92 | 1.22 | 1.22 | 3.41 | | 1.68 | ARL | 2.45 | 2.40 | 5.58 | 5.60 | 4.65 | 4.67 | 3.30 | 3.31 | 4.10 | 4.10 | 3.48 | 3.48 | 2.48 | 2.48 | 3.06 | 3.06 | 2.59 | 2.59 | 1.89 | 1.90 | 3.68 | | 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 | 3.00 | 3.00 | 2.00 | 2.00 | 3.00 | | SDRL | 1.53 | 1.51 | 1.98 | 1.98 | 1.62 | 1.63 | 1.10 | 1.10 | 1.53 | 1.53 | 1.32 | 1.32 | 1.00 | 0.99 | 1.37 | 1.37 | 1.11 | 1.11 | 0.80 | 0.79 | 1.94 | | 2.15 | ARL | 1.76 | 1.72 | 4.09 | 4.10 | 3.40 | 3.41 | 2.40 | 2.40 | 3.08 | 3.07 | 2.55 | 2.56 | 1.77 | 1.77 | 2.31 | 2.30 | 1.94 | 1.94 | 1.41 | 1.42 | 2.51 | | MRL | 2.00 | 2.00 | 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 | 2.00 | 2.00 | 2.00 | 1.00 | 1.00 | 2.00 | | SDRL | 0.90 | 0.89 | 1.41 | 1.40 | 1.13 | 1.14 | 0.79 | 0.79 | 1.19 | 1.19 | 1.02 | 1.02 | 0.72 | 0.72 | 0.97 | 0.97 | 0.81 | 0.81 | 0.57 | 0.56 | 1.30 | | 2.63 | ARL | 1.40 | 1.38 | 3.16 | 3.16 | 2.62 | 2.63 | 1.83 | 1.83 | 2.37 | 2.36 | 1.95 | 1.94 | 1.35 | 1.35 | 1.81 | 1.82 | 1.53 | 1.53 | 1.15 | 1.15 | 1.88 | | MRL | 1.00 | 1.00 | 3.00 | 3.00 | 3.00 | 3.00 | 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 | 2.00 | | SDRL | 0.60 | 0.59 | 1.05 | 1.04 | 0.86 | 0.87 | 0.63 | 0.63 | 0.95 | 0.95 | 0.79 | 0.79 | 0.52 | 0.52 | 0.76 | 0.76 | 0.63 | 0.63 | 0.37 | 0.37 | 0.93 | | 3.10 | ARL | 1.20 | 1.19 | 2.55 | 2.55 | 2.11 | 2.11 | 1.45 | 1.45 | 1.89 | 1.89 | 1.55 | 1.55 | 1.13 | 1.13 | 1.50 | 1.50 | 1.28 | 1.27 | 1.04 | 1.04 | 1.46 | | 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 | 0.43 | 0.42 | 0.84 | 0.84 | 0.71 | 0.71 | 0.53 | 0.53 | 0.77 | 0.77 | 0.62 | 0.62 | 0.34 | 0.34 | 0.61 | 0.61 | 0.47 | 0.47 | 0.20 | 0.20 | 0.67 | | 3.58 | ARL | 1.09 | 1.08 | 2.10 | 2.11 | 1.73 | 1.73 | 1.19 | 1.19 | 1.55 | 1.55 | 1.29 | 1.29 | 1.03 | 1.03 | 1.27 | 1.27 | 1.12 | 1.12 | 1.01 | 1.01 | 1.22 | | MRL | 1.00 | 1.00 | 2.00 | 2.00 | 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 | | SDRL | 0.29 | 0.28 | 0.71 | 0.71 | 0.61 | 0.61 | 0.39 | 0.39 | 0.62 | 0.62 | 0.48 | 0.48 | 0.17 | 0.17 | 0.47 | 0.47 | 0.33 | 0.33 | 0.08 | 0.08 | 0.47 | | 4.05 | ARL | 1.04 | 1.03 | 1.78 | 1.79 | 1.45 | 1.46 | 1.05 | 1.05 | 1.32 | 1.32 | 1.13 | 1.13 | 1.00 | 1.00 | 1.14 | 1.14 | 1.04 | 1.04 | 1.00 | 1.00 | 1.10 | | 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 | 0.18 | 0.18 | 0.62 | 0.62 | 0.53 | 0.53 | 0.23 | 0.23 | 0.50 | 0.50 | 0.34 | 0.34 | 0.07 | 0.07 | 0.35 | 0.35 | 0.20 | 0.20 | 0.03 | 0.03 | 0.31 | | 4.53 | ARL | 1.01 | 1.01 | 1.52 | 1.53 | 1.24 | 1.24 | 1.01 | 1.01 | 1.17 | 1.16 | 1.05 | 1.05 | 1.00 | 1.00 | 1.06 | 1.06 | 1.01 | 1.01 | 1.00 | 1.00 | 1.04 | | MRL | 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 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 0.10 | 0.10 | 0.55 | 0.55 | 0.43 | 0.43 | 0.10 | 0.10 | 0.38 | 0.38 | 0.21 | 0.21 | 0.02 | 0.02 | 0.23 | 0.23 | 0.10 | 0.10 | 0.01 | 0.01 | 0.19 | | 5.00 | ARL | 1.00 | 1.00 | 1.32 | 1.32 | 1.10 | 1.11 | 1.00 | 1.00 | 1.08 | 1.07 | 1.01 | 1.01 | 1.00 | 1.00 | 1.02 | 1.02 | 1.00 | 1.00 | 1.00 | 1.00 | 1.01 | | MRL | 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 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 0.05 | 0.05 | 0.48 | 0.48 | 0.30 | 0.31 | 0.03 | 0.04 | 0.27 | 0.26 | 0.11 | 0.11 | 0.00 | 0.00 | 0.14 | 0.14 | 0.05 | 0.05 | 0.00 | 0.00 | 0.11 | | EQL | 11.96 | 11.83 | 20.29 | 20.35 | 16.81 | 16.87 | 12.64 | 12.64 | 15.48 | 15.43 | 13.32 | 13.31 | 11.01 | 11.01 | 13.10 | 13.10 | 11.73 | 11.71 | 10.31 | 10.32 | 13.49 | | IRARL | 0.92 | 0.90 | 1.45 | 1.45 | 1.20 | 1.21 | 0.89 | 0.89 | 1.12 | 1.12 | 0.95 | 0.95 | 0.75 | 0.75 | 0.95 | 0.95 | 0.83 | 0.83 | 0.68 | 0.69 | 1.00 |
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