Table 4 The \({ARL}_{1} \text{and} {SDRL}_{1}\) values of the proposed \(R{EEWMA}_{WSR}\) under different choices of \({(\lambda }_{1}{,\lambda }_{2}\)) and \(n\) with \({ARL}_{0}\) \(\approx\) 370.
From: A modified EWMA signed rank control chart for enhanced quality monitoring in the automobile industry
\(n\) | \({(\lambda }_{1}{,\lambda }_{2}\)) | \(L\) | Metrices | \(C\) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | |||||
5 | (0.1,0.03) | 2.4300 | ARL | 133.81 | 45.81 | 23.10 | 14.52 | 10.13 | 7.57 | |
SDRL | 129.74 | 39.05 | 17.31 | 9.83 | 6.37 | 4.48 | ||||
(0.2,0.07) | 2.5900 | ARL | 172.17 | 63.58 | 30.38 | 17.69 | 12.06 | 8.95 | ||
SDRL | 169.70 | 57.51 | 24.90 | 12.94 | 8.00 | 5.41 | ||||
(0.3,0.15) | 2.6820 | ARL | 206.21 | 82.74 | 39.91 | 22.84 | 15.18 | 11.00 | ||
SDRL | 204.23 | 77.33 | 33.99 | 17.27 | 10.37 | 6.63 | ||||
(0.5,0.25) | 2.7640 | ARL | 264.96 | 134.96 | 71.74 | 41.08 | 25.51 | 17.32 | ||
SDRL | 263.18 | 131.69 | 67.30 | 37.29 | 21.50 | 13.48 | ||||
6 | (0.1,0.03) | 2.3300 | ARL | 104.55 | 33.84 | 16.95 | 10.74 | 7.57 | 5.75 | |
SDRL | 97.99 | 27.29 | 11.95 | 6.89 | 4.51 | 3.22 | ||||
(0.2,0.07) | 2.4880 | ARL | 141.01 | 46.16 | 21.77 | 12.86 | 8.81 | 6.58 | ||
SDRL | 135.83 | 40.04 | 16.58 | 8.63 | 5.38 | 3.72 | ||||
(0.3,0.15) | 2.5650 | ARL | 169.24 | 60.47 | 27.49 | 16.20 | 10.88 | 8.01 | ||
SDRL | 162.17 | 54.15 | 22.01 | 11.28 | 6.69 | 4.47 | ||||
(0.5,0.25) | 2.6250 | ARL | 241.15 | 107.36 | 50.47 | 27.22 | 16.46 | 11.16 | ||
SDRL | 241.15 | 103.62 | 46.95 | 23.31 | 12.75 | 7.85 | ||||
8 | (0.1,0.03) | 2.1820 | ARL | 67.23 | 21.01 | 10.72 | 6.84 | 4.84 | 3.71 | |
SDRL | 60.25 | 15.34 | 7.02 | 4.06 | 2.65 | 1.89 | ||||
(0.2,0.07) | 2.3280 | ARL | 93.31 | 27.04 | 12.93 | 7.96 | 5.60 | 4.26 | ||
SDRL | 88.66 | 21.56 | 8.75 | 4.67 | 3.00 | 2.12 | ||||
(0.3,0.15) | 2.3950 | ARL | 114.34 | 33.69 | 15.69 | 9.57 | 6.62 | 5.00 | ||
SDRL | 108.05 | 28.04 | 10.81 | 5.74 | 3.57 | 2.52 | ||||
(0.5,0.25) | 2.4370 | ARL | 172.01 | 58.90 | 24.77 | 13.41 | 8.51 | 6.07 | ||
SDRL | 167.04 | 55.43 | 20.94 | 10.01 | 5.55 | 3.53 | ||||
10 | (0.1,0.03) | 2.0730 | ARL | 46.62 | 14.59 | 7.53 | 4.81 | 3.49 | 2.69 | |
SDRL | 40.08 | 10.02 | 4.56 | 2.66 | 1.79 | 1.29 | ||||
(0.2,0.07) | 2.2040 | ARL | 62.37 | 17.55 | 8.72 | 5.53 | 3.93 | 3.06 | ||
SDRL | 57.10 | 12.83 | 5.38 | 2.99 | 1.97 | 1.42 | ||||
(0.3,0.15) | 2.2670 | ARL | 80.06 | 21.90 | 10.51 | 6.55 | 4.66 | 3.56 | ||
SDRL | 73.82 | 16.58 | 6.45 | 3.50 | 2.27 | 1.66 | ||||
(0.5,0.25) | 2.3050 | ARL | 129.40 | 36.23 | 14.88 | 8.32 | 5.50 | 4.03 | ||
SDRL | 125.06 | 32.40 | 11.65 | 5.34 | 3.13 | 2.10 |
\(n\) | \(C\) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
5 | 0.40 | 0.50 | 0.70 | 0.90 | 1.00 | 1.50 | 2.00 | 2.50 | 3.00 | 5.00 |
4.99 | 3.67 | 2.46 | 1.93 | 1.76 | 1.33 | 1.11 | 1.03 | 1.01 | 1.00 | |
2.66 | 1.77 | 1.02 | 0.71 | 0.63 | 0.47 | 0.32 | 0.17 | 0.09 | 0.00 | |
5.69 | 4.17 | 2.71 | 2.05 | 1.85 | 1.33 | 1.11 | 1.03 | 1.01 | 1.00 | |
3.02 | 2.05 | 1.19 | 0.83 | 0.73 | 0.48 | 0.31 | 0.17 | 0.08 | 0.00 | |
7.03 | 5.11 | 3.40 | 2.66 | 2.44 | 2.04 | 2.00 | 2.00 | 2.00 | 2.00 | |
3.64 | 2.30 | 1.26 | 0.81 | 0.66 | 0.21 | 0.04 | 0.00 | 0.00 | 0.00 | |
9.71 | 6.50 | 3.93 | 2.92 | 2.64 | 2.09 | 2.01 | 2.00 | 2.00 | 2.00 | |
6.43 | 3.66 | 1.73 | 1.03 | 0.83 | 0.29 | 0.08 | 0.02 | 0.00 | 0.00 | |
6 | 3.82 | 2.85 | 1.93 | 1.51 | 1.37 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 |
1.93 | 1.31 | 0.77 | 0.58 | 0.51 | 0.21 | 0.04 | 0.01 | 0.00 | 0.00 | |
4.29 | 3.12 | 2.02 | 1.53 | 1.38 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | |
2.20 | 1.51 | 0.88 | 0.62 | 0.53 | 0.21 | 0.05 | 0.01 | 0.00 | 0.00 | |
5.20 | 3.78 | 2.45 | 1.81 | 1.59 | 1.12 | 1.01 | 1.00 | 1.00 | 1.00 | |
2.56 | 1.73 | 1.06 | 0.75 | 0.64 | 0.32 | 0.10 | 0.03 | 0.00 | 0.00 | |
6.45 | 4.43 | 2.65 | 1.89 | 1.66 | 1.11 | 1.01 | 1.00 | 1.00 | 1.00 | |
3.81 | 2.34 | 1.26 | 0.85 | 0.72 | 0.32 | 0.10 | 0.02 | 0.00 | 0.00 | |
8 | 2.49 | 1.91 | 1.33 | 1.09 | 1.04 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
1.16 | 0.82 | 0.50 | 0.28 | 0.19 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | |
2.87 | 2.17 | 1.48 | 1.17 | 1.09 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
1.27 | 0.91 | 0.57 | 0.37 | 0.28 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | |
3.29 | 2.39 | 1.52 | 1.17 | 1.09 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
1.55 | 1.09 | 0.65 | 0.39 | 0.29 | 0.03 | 0.01 | 0.00 | 0.00 | 0.00 | |
3.75 | 2.69 | 1.72 | 1.28 | 1.17 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
1.85 | 1.23 | 0.71 | 0.47 | 0.38 | 0.07 | 0.01 | 0.00 | 0.00 | 0.00 | |
10 | 1.87 | 1.44 | 1.08 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
0.81 | 0.57 | 0.27 | 0.08 | 0.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
2.09 | 1.58 | 1.12 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
0.90 | 0.64 | 0.33 | 0.11 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
2.37 | 1.76 | 1.19 | 1.02 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
1.03 | 0.73 | 0.40 | 0.15 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
2.53 | 1.82 | 1.20 | 1.03 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
1.21 | 0.82 | 0.41 | 0.16 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |