Table 8 The run length characteristic (ARL, SDRL (in 2nd row) and MDRL (in 3rd row)) of the proposed Auxiliary HWMA-SR repetitive chart with \(n=15\), \(ARL_0=500\), different values of \(\omega\), and different values of \(\rho\) for different distributions.
\(\delta\) | \(\rho =0.25\) | \(\rho =0.5\) | \(\rho =0.75\) | ||||||
|---|---|---|---|---|---|---|---|---|---|
\(\omega =0.03\) | \(\omega =0.05\) | \(\omega =0.2\) | \(\omega =0.03\) | \(\omega =0.05\) | \(\omega =0.2\) | \(\omega =0.03\) | \(\omega =0.05\) | \(\omega =0.2\) | |
Normal (0,1) | |||||||||
0.0 | 499.3 | 501.5 | 502.9 | 500.2 | 499.0 | 499.1 | 502.2 | 501.2 | 501.9 |
452.4 | 439.8 | 387.7 | 566.2 | 268.7 | 578.5 | 503.7 | 447.8 | 581.9 | |
429.5 | 423 | 400.5 | 321.5 | 441 | 329 | 359.5 | 359.5 | 330.5 | |
0.1 | 23.4 | 29.3 | 31.9 | 20.6 | 24.9 | 27.2 | 19.8 | 21.2 | 25.7 |
15.9 | 20.9 | 39.1 | 12.1 | 21.5 | 19.5 | 13.4 | 13.4 | 30.3 | |
21 | 23 | 8 | 17 | 16.5 | 25.5 | 15.5 | 19 | 10 | |
0.5 | 1.7 | 1.9 | 1.9 | 1.5 | 1.9 | 2 | 1.3 | 1.6 | 2 |
0.9 | 1.1 | 0.9 | 1.1 | 1.3 | 0.8 | 0.9 | 0.8 | 1.3 | |
1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
Laplace (0,\(1/\sqrt{2}\)) | |||||||||
0.0 | 502.4 | 500.8 | 501 | 501.9 | 499.7 | 503.4 | 500.4 | 499.6 | 502.4 |
405.3 | 331.5 | 324.3 | 372.3 | 399.9 | 346.8 | 413.4 | 322.2 | 323.3 | |
439.5 | 499 | 457.5 | 481 | 445.5 | 496.5 | 422 | 415 | 478.5 | |
0.1 | 15.3 | 16.4 | 19.1 | 13.8 | 14.8 | 18.5 | 11.7 | 12.4 | 17.3 |
15.1 | 17.8 | 17.1 | 15.2 | 11.5 | 25.5 | 9.5 | 13.9 | 12.9 | |
10.5 | 7 | 14 | 6 | 14 | 10 | 8 | 5.5 | 16 | |
0.5 | 1.4 | 1.5 | 1.6 | 1.2 | 1.4 | 1.6 | 1.2 | 1.3 | 1.5 |
0.8 | 1.1 | 0.8 | 0.6 | 0.8 | 0.9 | 0.6 | 0.6 | 0.8 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
LG (0,\(\sqrt{3}/\pi\)) | |||||||||
0.0 | 501.8 | 504.3 | 503.2 | 506.6 | 499.1 | 500.7 | 500.2 | 499.8 | 500.5 |
368.3 | 418.8 | 439.2 | 530.8 | 402.7 | 404.9 | 429.7 | 291.4 | 474.6 | |
452 | 415.5 | 490 | 358 | 434 | 380.5 | 441.5 | 487 | 254 | |
0.1 | 17.5 | 21.3 | 29.9 | 16.1 | 19.4 | 25.8 | 13.7 | 18.1 | 24.4 |
16.9 | 27.7 | 45.1 | 21.7 | 17.9 | 15.9 | 15.9 | 16.3 | 15.2 | |
15.5 | 11.5 | 12.5 | 5.5 | 16 | 21.5 | 7 | 12 | 23.5 | |
0.5 | 1.5 | 1.7 | 1.9 | 1.4 | 1.6 | 1.8 | 1.3 | 1.4 | 1.7 |
1.1 | 1.1 | 0.9 | 0.9 | 0.9 | 1.0 | 0.9 | 0.8 | 0.9 | |
1 | 1.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1.5 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
Student’s t-Distribution (4) | |||||||||
0.0 | 505.9 | 503 | 499.1 | 501.8 | 503.2 | 502 | 503.7 | 503.6 | 501.3 |
353.9 | 324.1 | 384.2 | 485.6 | 359.6 | 387.8 | 490.4 | 503.7 | 502.3 | |
492.5 | 479.5 | 468 | 369.5 | 486 | 459.5 | 352.2 | 422.5 | 456.1 | |
0.1 | 20.2 | 21.8 | 22.5 | 17.4 | 20.6 | 21.1 | 15.3 | 19.1 | 20.2 |
17.4 | 20.7 | 36.0 | 13.1 | 17.8 | 13.3 | 16.2 | 20.6 | 14.2 | |
15 | 16.5 | 7.5 | 14 | 14 | 20 | 8.5 | 11 | 14 | |
0.5 | 1.5 | 1.6 | 1.7 | 1.4 | 1.5 | 1.6 | 1.3 | 1.4 | 1.5 |
1.1 | 1.2 | 0.8 | 0.8 | 1.1 | 1.1 | 0.6 | 0.8 | 0.8 | |
1 | 1 | 1.5 | 1 | 1 | 1 | 1 | 1 | 1 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
Student’s t-Distribution (8) | |||||||||
0.0 | 505.5 | 500.0 | 503.7 | 499.7 | 498.0 | 501.9 | 507.2 | 502.0 | 502.8 |
284.1 | 310.4 | 350.8 | 384.6 | 413.1 | 521.1 | 335.7 | 162.3 | 271.5 | |
490.5 | 456.5 | 447.5 | 493.0 | 401.5 | 394.0 | 459.5 | 425.0 | 435.0 | |
0.1 | 21.3 | 28.2 | 29 | 19.1 | 25.4 | 26.8 | 18 | 23.5 | 24.9 |
23.5 | 30.5 | 34.4 | 17.3 | 21.1 | 17.3 | 15.5 | 21.3 | 13.5 | |
7.5 | 22 | 13.5 | 14 | 24 | 22.5 | 13 | 16.5 | 22 | |
0.5 | 1.6 | 1.7 | 1.8 | 1.5 | 1.6 | 1.7 | 1.4 | 1.5 | 1.6 |
0.9 | 1.1 | 1.1 | 0.8 | 1.3 | 0.9 | 0.8 | 0.8 | 0.9 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
