Research Article
Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information
Table 2
The ARL1 profile of the one-sided EDC and EDCC charts when δ ∈[0.25, 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 = 0.47, k2 = 1.16] |
| | δ | h1 | 4.7347 | 4.5605 | 23.018 | 23.150 | 23.0180 | 23.150 | 23.018 | 23.150 | 20.200 | 20.233 | 20.200 | 20.2330 | 20.200 | 20.233 | 11.599 | 11.60 | 11.5990 | 11.60 | 11.599 | 11.60 | k = δ/2 | | h2 | 1.9184 | 1.8478 | 9.3263 | 9.3797 | 9.3263 | 9.3797 | 9.3263 | 9.3797 | 8.1845 | 8.1979 | 8.1845 | 8.1979 | 8.1845 | 8.1979 | 4.6996 | 4.70 | 4.6996 | 4.70 | 4.6996 | 4.70 | | 0.25 | ARL | 80.04 | 78.80 | 46.77 | 46.90 | 40.16 | 40.46 | 30.37 | 30.42 | 75.78 | 75.82 | 61.40 | 61.30 | 41.46 | 41.67 | 89.27 | 88.80 | 70.52 | 70.69 | 45.09 | 45.22 | 52.31 | | MRL | 57.00 | 56.00 | 39.00 | 39.00 | 35.00 | 35.00 | 27.00 | 27.00 | 60.00 | 60.00 | 50.00 | 50.00 | 35.00 | 36.00 | 67.00 | 66.00 | 54.00 | 54.00 | 36.00 | 36.00 | 43.00 | | SDRL | 75.48 | 74.59 | 30.03 | 30.10 | 24.13 | 24.34 | 16.22 | 16.29 | 57.52 | 57.08 | 44.08 | 43.66 | 26.05 | 26.13 | 76.07 | 76.03 | 57.50 | 58.01 | 33.25 | 33.17 | 35.36 | | 0.53 | ARL | 25.27 | 24.52 | 21.15 | 21.25 | 18.15 | 18.17 | 13.60 | 13.64 | 25.79 | 25.82 | 21.16 | 21.18 | 14.72 | 14.69 | 26.06 | 26.10 | 20.88 | 20.94 | 13.97 | 13.97 | 20.48 | | MRL | 20.00 | 19.00 | 19.00 | 19.00 | 17.00 | 17.00 | 13.00 | 13.00 | 23.00 | 23.00 | 20.00 | 20.00 | 13.00 | 13.00 | 22.00 | 22.00 | 18.00 | 19.00 | 13.00 | 13.00 | 17.00 | | SDRL | 20.34 | 19.87 | 9.81 | 9.88 | 7.99 | 8.00 | 5.23 | 5.24 | 13.91 | 13.91 | 10.71 | 10.72 | 6.78 | 6.72 | 16.17 | 16.13 | 12.10 | 12.05 | 7.19 | 7.23 | 12.50 | | 0.80 | ARL | 12.40 | 12.06 | 13.63 | 13.67 | 11.74 | 11.77 | 8.97 | 9.01 | 14.73 | 14.74 | 12.15 | 12.18 | 8.69 | 8.68 | 14.02 | 14.02 | 11.37 | 11.37 | 7.70 | 7.68 | 11.40 | | MRL | 11.00 | 10.00 | 13.00 | 13.00 | 11.00 | 11.00 | 9.00 | 9.00 | 13.00 | 13.00 | 11.00 | 11.00 | 8.00 | 8.00 | 13.00 | 13.00 | 11.00 | 11.00 | 7.00 | 7.00 | 10.00 | | SDRL | 8.22 | 8.09 | 5.28 | 5.26 | 4.16 | 4.17 | 2.67 | 2.68 | 6.74 | 6.79 | 5.21 | 5.25 | 3.06 | 3.05 | 7.23 | 7.24 | 5.60 | 5.57 | 3.50 | 3.49 | 6.63 | | 1.08 | ARL | 7.66 | 7.40 | 10.02 | 10.04 | 8.70 | 8.72 | 6.77 | 6.78 | 9.97 | 9.94 | 8.38 | 8.39 | 6.26 | 6.27 | 9.05 | 9.07 | 7.36 | 7.38 | 5.08 | 5.09 | 7.29 | | MRL | 7.00 | 7.00 | 9.00 | 9.00 | 8.00 | 8.00 | 7.00 | 7.00 | 9.00 | 9.00 | 8.00 | 8.00 | 6.00 | 6.00 | 8.00 | 8.00 | 7.00 | 7.00 | 5.00 | 5.00 | 6.00 | | SDRL | 4.41 | 4.33 | 3.22 | 3.22 | 2.54 | 2.53 | 1.67 | 1.66 | 3.85 | 3.82 | 2.88 | 2.87 | 1.69 | 1.70 | 4.27 | 4.28 | 3.29 | 3.32 | 1.92 | 1.91 | 4.06 | | 1.35 | ARL | 5.42 | 5.23 | 8.08 | 8.11 | 7.06 | 7.08 | 5.55 | 5.56 | 7.66 | 7.65 | 6.57 | 6.57 | 5.05 | 5.06 | 6.59 | 6.58 | 5.40 | 5.41 | 3.89 | 3.89 | 5.17 | | MRL | 5.00 | 5.00 | 8.00 | 8.00 | 7.00 | 7.00 | 5.00 | 5.00 | 7.00 | 7.00 | 6.00 | 6.00 | 5.00 | 5.00 | 6.00 | 6.00 | 5.00 | 5.00 | 4.00 | 4.00 | 5.00 | | SDRL | 2.94 | 2.87 | 2.24 | 2.23 | 1.78 | 1.78 | 1.19 | 1.19 | 2.46 | 2.44 | 1.84 | 1.84 | 1.15 | 1.15 | 2.85 | 2.84 | 2.11 | 2.11 | 1.21 | 1.21 | 2.81 | | 1.63 | ARL | 4.05 | 3.91 | 6.77 | 6.80 | 5.96 | 5.96 | 4.71 | 4.72 | 6.28 | 6.28 | 5.47 | 5.46 | 4.26 | 4.27 | 5.11 | 5.09 | 4.27 | 4.25 | 3.18 | 3.19 | 3.86 | | MRL | 4.00 | 4.00 | 7.00 | 7.00 | 6.00 | 6.00 | 5.00 | 5.00 | 6.00 | 6.00 | 5.00 | 5.00 | 4.00 | 4.00 | 5.00 | 5.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | | SDRL | 2.12 | 2.08 | 1.66 | 1.67 | 1.34 | 1.34 | 0.91 | 0.91 | 1.70 | 1.70 | 1.32 | 1.32 | 0.87 | 0.87 | 1.93 | 1.91 | 1.42 | 1.41 | 0.86 | 0.86 | 2.04 | | 1.90 | ARL | 3.20 | 3.10 | 5.90 | 5.92 | 5.20 | 5.22 | 4.13 | 4.14 | 5.40 | 5.41 | 4.73 | 4.73 | 3.73 | 3.74 | 4.22 | 4.22 | 3.60 | 3.60 | 2.73 | 2.73 | 3.05 | | MRL | 3.00 | 3.00 | 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 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | | SDRL | 1.64 | 1.60 | 1.32 | 1.32 | 1.07 | 1.07 | 0.74 | 0.75 | 1.30 | 1.30 | 1.03 | 1.03 | 0.70 | 0.71 | 1.39 | 1.39 | 1.05 | 1.05 | 0.68 | 0.68 | 1.60 | | 2.18 | ARL | 2.59 | 2.51 | 5.23 | 5.25 | 4.63 | 4.64 | 3.69 | 3.70 | 4.76 | 4.77 | 4.19 | 4.19 | 3.33 | 3.33 | 3.61 | 3.62 | 3.11 | 3.12 | 2.41 | 2.40 | 2.46 | | MRL | 2.00 | 2.00 | 5.00 | 5.00 | 5.00 | 5.00 | 4.00 | 4.00 | 5.00 | 5.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 2.00 | 2.00 | 2.00 | | SDRL | 1.28 | 1.25 | 1.08 | 1.08 | 0.88 | 0.88 | 0.64 | 0.64 | 1.04 | 1.04 | 0.85 | 0.84 | 0.58 | 0.58 | 1.06 | 1.06 | 0.83 | 0.83 | 0.55 | 0.55 | 1.27 | | 2.45 | ARL | 2.17 | 2.12 | 4.73 | 4.74 | 4.00 | 4.20 | 3.34 | 3.35 | 4.29 | 4.29 | 3.78 | 3.79 | 3.05 | 3.05 | 3.20 | 3.20 | 2.78 | 2.77 | 2.18 | 2.19 | 2.06 | | MRL | 2.00 | 2.00 | 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 | 2.00 | | SDRL | 1.02 | 1.01 | 0.91 | 0.92 | 0.76 | 0.75 | 0.54 | 0.54 | 0.87 | 0.88 | 0.72 | 0.72 | 0.49 | 0.49 | 0.86 | 0.87 | 0.70 | 0.70 | 0.44 | 0.43 | 1.05 | | 2.73 | ARL | 1.87 | 1.82 | 4.32 | 4.33 | 3.82 | 3.84 | 3.08 | 3.09 | 3.90 | 3.91 | 3.46 | 3.46 | 2.81 | 2.81 | 2.88 | 2.87 | 2.50 | 2.51 | 2.03 | 2.03 | 1.75 | | MRL | 2.00 | 2.00 | 4.00 | 4.00 | 4.00 | 4.00 | 3.00 | 3.00 | 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 | | SDRL | 0.83 | 0.82 | 0.79 | 0.79 | 0.67 | 0.67 | 0.44 | 0.44 | 0.75 | 0.75 | 0.62 | 0.62 | 0.48 | 0.48 | 0.73 | 0.73 | 0.60 | 0.60 | 0.34 | 0.34 | 0.87 | | 3.00 | ARL | 1.64 | 1.60 | 3.99 | 4.00 | 3.53 | 3.54 | 2.89 | 2.90 | 3.60 | 3.60 | 3.21 | 3.21 | 2.58 | 2.58 | 2.62 | 2.62 | 2.30 | 2.30 | 1.93 | 1.93 | 1.52 | | MRL | 2.00 | 2.00 | 4.00 | 4.00 | 3.00 | 4.00 | 3.00 | 3.00 | 4.00 | 4.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 2.00 | 2.00 | 2.00 | 2.00 | 1.00 | | SDRL | 0.70 | 0.69 | 0.71 | 0.71 | 0.60 | 0.60 | 0.43 | 0.42 | 0.66 | 0.66 | 0.54 | 0.53 | 0.51 | 0.51 | 0.64 | 0.64 | 0.51 | 0.5 | 0.33 | 0.33 | 0.73 | | EQL | 10.47 | 10.17 | 18.60 | 18.66 | 16.27 | 16.42 | 13.04 | 13.08 | 14.09 | 14.12 | 12.28 | 12.28 | 9.70 | 9.57 | 12.65 | 11.69 | 9.99 | 10.01 | 7.61 | 7.63 | 9.67 | | IRARL | 1.12 | 1.09 | 1.75 | 1.76 | 1.53 | 1.54 | 1.22 | 1.22 | 1.36 | 1.36 | 1.18 | 1.18 | 0.92 | 0.91 | 1.26 | 1.17 | 0.99 | 0.99 | 0.74 | 0.74 | 1.00 |
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