Table 6. The RL characteristics of the EWMA-MA sign control chart under various distributions for η = 0.05, w = 5, n = 10, and L = 2.305 at ARL0≅370.
Distribution | Characteristic | δ | AEQL | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0.05 | 0.10 | 0.25 | 0.50 | 0.75 | 1.00 | 1.50 | 2.00 | 2.5 | 3.0 | |||
N(0,1) |
ARL | 368.7 | 170.2 | 66.3 | 15.7 | 5.8 | 3.1 | 1.9 | 1.2 | 1.0 | 1.0 | 1.0 | 9.7 |
SDRL | 357.3 | 160.9 | 55.1 | 10.4 | 3.6 | 2.1 | 1.3 | 0.5 | 0.2 | 0.0 | 0.0 | ||
MRL | 260 | 122 | 52 | 14 | 6 | 3 | 1 | 1 | 1 | 1 | 1 | ||
Weibull(2,1) |
ARL | 369.2 | 192.5 | 81.7 | 21.3 | 8.6 | 5.4 | 3.9 | 2.5 | 1.9 | 1.5 | 1.4 | 15.6 |
SDRL | 358.7 | 180.7 | 72.5 | 15.0 | 5.3 | 3.3 | 2.5 | 1.7 | 1.2 | 0.9 | 0.7 | ||
MRL | 262 | 137 | 59 | 18 | 8 | 5 | 4 | 2 | 1 | 1 | 1 | ||
Weibull(3.5,1) |
ARL | 371.7 | 178.6 | 72.4 | 19.1 | 7.6 | 4.6 | 3.2 | 2.0 | 1.5 | 1.3 | 1.2 | 13.2 |
SDRL | 358.0 | 171.9 | 65.6 | 13.0 | 4.6 | 2.9 | 2.1 | 1.3 | 0.8 | 0.6 | 0.4 | ||
MRL | 261 | 125 | 53 | 16 | 7 | 4 | 3 | 1 | 1 | 1 | 1 | ||
|
ARL | 368.5 | 149.7 | 54.2 | 13.4 | 4.9 | 2.6 | 1.7 | 1.1 | 1 | 1 | 1 | 9.3 |
SDRL | 361.4 | 137.8 | 43.7 | 8.6 | 3.1 | 1.8 | 1.1 | 0.4 | 0.2 | 0.1 | 0 | ||
MRL | 259 | 108 | 43 | 12 | 5 | 2 | 1 | 1 | 1 | 1 | 1 | ||
CN |
ARL | 370.1 | 152.8 | 67.1 | 13.8 | 5.1 | 2.8 | 1.8 | 1.1 | 1.0 | 1.0 | 1.0 | 9.4 |
SDRL | 364.1 | 143.7 | 48.7 | 9.0 | 3.2 | 1.9 | 1.1 | 0.4 | 0.1 | 0.0 | 0.0 | ||
MRL | 258 | 114 | 43 | 12 | 5 | 2 | 1 | 1 | 1 | 1 | 1 | ||
t(5) |
ARL | 369.8 | 133.6 | 49.2 | 11.8 | 4.3 | 2.4 | 1.6 | 1.1 | 1.0 | 1.0 | 1.0 | 9.1 |
SDRL | 365.7 | 121.6 | 30.1 | 7.5 | 2.8 | 1.6 | 0.9 | 0.4 | 0.2 | 0.1 | 0.0 | ||
MRL | 256 | 95 | 39 | 11 | 4 | 2 | 1 | 1 | 1 | 1 | 1 | ||
t(10) |
ARL | 371.3 | 155.5 | 58.2 | 14.1 | 5.1 | 2.7 | 1.8 | 1.2 | 1.0 | 1.0 | 1.0 | 95 |
SDRL | 364.1 | 144.3 | 49.8 | 9.2 | 3.2 | 1.8 | 1.1 | 0.4 | 0.2 | 0.1 | 0.0 | ||
MRL | 260 | 112 | 44 | 12 | 5 | 2 | 1 | 1 | 1 | 1 | 1 | ||
ARL | 372.7 | 87.2 | 29.8 | 8.6 | 3.6 | 2.1 | 1.5 | 1.1 | 1.0 | 1.0 | 1.0 | 8.8 | |
SDRL | 362.8 | 74.8 | 22.4 | 5.2 | 2.3 | 1.4 | 0.9 | 0.4 | 0.2 | 0.1 | 0.0 | ||
MRL | 260 | 65 | 25 | 8 | 3 | 2 | 1 | 1 | 1 | 1 | 1 | ||
gamma(2,1) | ARL | 369.4 | 153.0 | 58.8 | 14.5 | 5.5 | 3.1 | 2.0 | 1.2 | 1.0 | 1.0 | 1.0 | 9.6 |
SDRL | 365.1 | 144.5 | 51.2 | 9.4 | 3.4 | 2.0 | 1.3 | 0.5 | 0.2 | 0.1 | 0.0 | ||
MRL | 261 | 112 | 45 | 13 | 5 | 3 | 2 | 1 | 1 | 1 | 1 | ||
gamma(5,1) | ARL | 370.1 | 165.7 | 64.4 | 15.3 | 5.7 | 3.2 | 2.0 | 1.2 | 1.0 | 1.0 | 1.0 | 9.7 |
SDRL | 354.9 | 153.4 | 55.2 | 10.0 | 3.5 | 2.1 | 1.3 | 0.5 | 0.2 | 0.1 | 0.0 | ||
MRL | 264 | 119 | 48 | 14 | 6 | 3 | 2 | 1 | 1 | 1 | 1 |