Table 6 The \({ARL}_{1} \text{and} {SDRL}_{1}\) values of the proposed \(R{EEWMA}_{WSR}\) under different choices of \(n\) and \({(\lambda }_{1}{,\lambda }_{2})=(\text{0.1,0.03}\)) for all distributions with \({ARL}_{0}\) \(\approx\) 370.
From: A modified EWMA signed rank control chart for enhanced quality monitoring in the automobile industry
Distribution | \(L\) | \(n\) | Metrices | \(C\) | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
0.00 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | ||||
Normal | 2.4300 | 5 | ARL | 370.51 | 133.81 | 45.81 | 23.10 | 14.52 | 10.13 | 7.57 |
SDRL | 379.98 | 129.74 | 39.05 | 17.31 | 9.83 | 6.37 | 4.48 | |||
t(4) | ARL | 376.55 | 99.71 | 32.13 | 16.49 | 10.33 | 7.39 | 5.62 | ||
SDRL | 376.77 | 92.84 | 25.75 | 11.46 | 6.55 | 4.44 | 3.15 | |||
Logistic | ARL | 370.87 | 118.49 | 40.57 | 20.19 | 12.69 | 8.99 | 6.81 | ||
SDRL | 374.83 | 114.13 | 33.59 | 14.83 | 8.34 | 5.59 | 3.96 | |||
Laplace | ARL | 372.83 | 86.20 | 28.34 | 14.76 | 9.52 | 6.92 | 5.38 | ||
SDRL | 377.88 | 80.44 | 22.29 | 10.15 | 6.06 | 4.11 | 3.06 | |||
CN | ARL | 368.57 | 135.89 | 48.04 | 24.05 | 14.97 | 10.52 | 7.86 | ||
SDRL | 370.93 | 131.79 | 40.89 | 17.97 | 10.19 | 6.76 | 4.71 | |||
Normal | 2.3300 | 6 | ARL | 373.02 | 104.55 | 33.84 | 16.95 | 10.74 | 7.57 | 5.75 |
SDRL | 375.84 | 97.99 | 27.29 | 11.95 | 6.89 | 4.51 | 3.22 | |||
t(4) | ARL | 368.72 | 76.65 | 23.72 | 12.32 | 7.82 | 5.60 | 4.33 | ||
SDRL | 374.23 | 70.02 | 17.99 | 8.22 | 4.73 | 3.21 | 2.30 | |||
Logistic | ARL | 373.78 | 92.86 | 29.69 | 15.03 | 9.48 | 6.78 | 5.16 | ||
SDRL | 380.27 | 86.48 | 23.46 | 10.28 | 5.90 | 3.98 | 2.84 | |||
Laplace | ARL | 368.34 | 67.47 | 21.45 | 11.17 | 7.26 | 5.28 | 4.13 | ||
SDRL | 374.15 | 60.84 | 15.82 | 7.36 | 4.42 | 3.02 | 2.23 | |||
CN | ARL | 370.06 | 108.16 | 35.29 | 17.76 | 11.15 | 7.82 | 5.94 | ||
SDRL | 376.40 | 103.02 | 28.57 | 12.60 | 7.20 | 4.75 | 3.36 | |||
Normal | 2.1820 | 8 | ARL | 366.52 | 67.23 | 21.01 | 10.72 | 6.84 | 4.84 | 3.71 |
SDRL | 367.16 | 60.25 | 15.34 | 7.02 | 4.06 | 2.65 | 1.89 | |||
t(4) | ARL | 364.18 | 47.90 | 14.92 | 7.84 | 5.01 | 3.64 | 2.87 | ||
SDRL | 371.13 | 40.48 | 10.39 | 4.86 | 2.80 | 1.89 | 1.41 | |||
Logistic | ARL | 371.58 | 59.03 | 18.56 | 9.48 | 6.09 | 4.37 | 3.37 | ||
SDRL | 376.51 | 51.79 | 13.43 | 6.04 | 3.54 | 2.37 | 1.72 | |||
Laplace | ARL | 368.16 | 42.94 | 13.50 | 7.23 | 4.77 | 3.51 | 2.77 | ||
SDRL | 377.25 | 36.19 | 9.14 | 4.39 | 2.67 | 1.82 | 1.37 | |||
CN | ARL | 368.13 | 70.14 | 21.89 | 11.17 | 7.10 | 5.05 | 3.85 | ||
SDRL | 373.17 | 63.76 | 15.99 | 7.24 | 4.25 | 2.84 | 2.03 | |||
Normal | 2.0730 | 10 | ARL | 373.64 | 46.62 | 14.59 | 7.53 | 4.81 | 3.49 | 2.69 |
SDRL | 381.19 | 40.08 | 10.02 | 4.56 | 2.66 | 1.79 | 1.29 | |||
t(4) | ARL | 371.91 | 33.40 | 10.44 | 5.55 | 3.62 | 2.68 | 2.12 | ||
SDRL | 380.85 | 26.59 | 6.73 | 3.18 | 1.89 | 1.29 | 0.96 | |||
Logistic | ARL | 372.51 | 41.08 | 12.82 | 6.66 | 4.33 | 3.13 | 2.46 | ||
SDRL | 379.63 | 34.30 | 8.58 | 3.95 | 2.33 | 1.58 | 1.15 | |||
Laplace | ARL | 365.16 | 29.98 | 9.60 | 5.20 | 3.45 | 2.58 | 2.09 | ||
SDRL | 370.47 | 23.83 | 6.15 | 2.98 | 1.82 | 1.24 | 0.96 | |||
CN | ARL | 371.64 | 48.78 | 15.02 | 7.86 | 5.01 | 3.59 | 2.79 | ||
SDRL | 377.90 | 42.16 | 10.52 | 4.78 | 2.81 | 1.89 | 1.38 | |||
Distribution | \(C\) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
0.40 | 0.50 | 0.70 | 0.90 | 1.00 | 1.50 | 2.00 | 2.50 | 3.00 | 5.00 | |
Normal | 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 | |
t(4) | 3.85 | 2.96 | 2.10 | 1.71 | 1.59 | 1.25 | 1.12 | 1.06 | 1.03 | 1.01 |
1.98 | 1.40 | 0.88 | 0.67 | 0.63 | 0.45 | 0.33 | 0.24 | 0.18 | 0.07 | |
Logistic | 4.50 | 3.38 | 2.32 | 1.86 | 1.71 | 1.30 | 1.13 | 1.05 | 1.02 | 1.00 |
2.37 | 1.63 | 0.98 | 0.72 | 0.64 | 0.47 | 0.34 | 0.23 | 0.15 | 0.03 | |
Laplace | 3.74 | 2.91 | 2.12 | 1.75 | 1.64 | 1.30 | 1.15 | 1.07 | 1.04 | 1.00 |
1.94 | 1.44 | 0.94 | 0.71 | 0.66 | 0.48 | 0.36 | 0.26 | 0.18 | 0.05 | |
CN | 5.15 | 3.81 | 2.53 | 1.99 | 1.82 | 1.35 | 1.14 | 1.05 | 1.02 | 1.00 |
2.80 | 1.90 | 1.08 | 0.77 | 0.67 | 0.49 | 0.35 | 0.22 | 0.15 | 0.04 | |
Normal | 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 | |
t(4) | 2.95 | 2.30 | 1.65 | 1.35 | 1.26 | 1.06 | 1.02 | 1.01 | 1.00 | 1.00 |
1.44 | 1.04 | 0.69 | 0.53 | 0.46 | 0.24 | 0.13 | 0.09 | 0.06 | 0.02 | |
Logistic | 3.44 | 2.60 | 1.82 | 1.45 | 1.32 | 1.06 | 1.01 | 1.00 | 1.00 | 1.00 |
1.72 | 1.20 | 0.75 | 0.57 | 0.50 | 0.24 | 0.10 | 0.04 | 0.01 | 0.00 | |
Laplace | 2.96 | 2.32 | 1.69 | 1.39 | 1.30 | 1.07 | 1.02 | 1.00 | 1.00 | 1.00 |
1.45 | 1.08 | 0.72 | 0.56 | 0.50 | 0.26 | 0.13 | 0.06 | 0.03 | 0.01 | |
CN | 3.94 | 2.93 | 1.98 | 1.55 | 1.42 | 1.07 | 1.02 | 1.01 | 1.00 | 1.00 |
2.02 | 1.38 | 0.82 | 0.61 | 0.55 | 0.26 | 0.14 | 0.09 | 0.05 | 0.00 | |
Normal | 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 | |
t(4) | 2.02 | 1.59 | 1.22 | 1.09 | 1.06 | 1.02 | 1.01 | 1.00 | 1.00 | 1.00 |
0.91 | 0.66 | 0.43 | 0.28 | 0.23 | 0.13 | 0.08 | 0.06 | 0.04 | 0.02 | |
Logistic | 2.30 | 1.77 | 1.28 | 1.09 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
1.06 | 0.75 | 0.47 | 0.29 | 0.22 | 0.07 | 0.02 | 0.01 | 0.00 | 0.00 | |
Laplace | 2.02 | 1.62 | 1.25 | 1.10 | 1.07 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 |
0.92 | 0.68 | 0.45 | 0.31 | 0.25 | 0.10 | 0.05 | 0.03 | 0.01 | 0.00 | |
CN | 2.61 | 1.96 | 1.38 | 1.12 | 1.08 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 |
1.24 | 0.88 | 0.55 | 0.33 | 0.27 | 0.11 | 0.05 | 0.02 | 0.00 | 0.00 | |
Normal | 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 | |
t(4) | 1.53 | 1.24 | 1.04 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
0.63 | 0.45 | 0.20 | 0.07 | 0.05 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | |
Logistic | 1.73 | 1.36 | 1.07 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
0.75 | 0.53 | 0.25 | 0.08 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
Laplace | 1.54 | 1.27 | 1.05 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
0.63 | 0.47 | 0.23 | 0.10 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
CN | 1.93 | 1.50 | 1.11 | 1.03 | 1.02 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
0.86 | 0.62 | 0.32 | 0.18 | 0.15 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | |
