Table 3: Approximated performance of the Phase I EWMA chart with λI = 0.6 obtained from randomly generated sets of k = 50 normal samples of size n for both the formulations of the ESEM and a nominal 1% FAR level.
Approach |
n |
TAP |
FAP |
|||||||
d |
d |
|||||||||
0.4 |
1.0 |
1.6 |
2.0 |
0.0 |
0.4 |
1.0 |
1.6 |
2.0 |
||
Localized shifting pattern |
||||||||||
Shen’s formulation |
5 |
3.3 |
26.1 |
72.5 |
91.3 |
1.0 |
1.1 |
1.2 |
1.6 |
2.1 |
10 |
6.5 |
58.1 |
97.0 |
99.9 |
1.0 |
1.1 |
1.4 |
2.8 |
4.1 |
|
Zwetsloot’s formulation |
5 |
3.2 |
25.8 |
69.0 |
89.3 |
1.0 |
1.1 |
1.2 |
1.3 |
1.4 |
10 |
6.1 |
57.3 |
96.7 |
99.9 |
1.0 |
1.1 |
1.2 |
1.3 |
1.4 |
|
Diffuse shifting pattern |
||||||||||
Shen’s formulation |
5 |
1.3 |
1.4 |
2.1 |
3.0 |
0.9 |
1.0 |
1.0 |
1.0 |
1.1 |
10 |
1.0 |
1.3 |
1.5 |
2.1 |
1.0 |
1.0 |
1.0 |
1.1 |
1.1 |
|
Zwetsloot’s formulation |
5 |
1.2 |
1.2 |
1.5 |
2.3 |
1.0 |
0.9 |
1.0 |
0.9 |
0.9 |
10 |
1.0 |
1.2 |
1.3 |
1.5 |
1.1 |
1.0 |
1.1 |
1.0 |
1.0 |
|
Single step shifting pattern |
||||||||||
Shen’s formulation |
5 |
7.0 |
56.5 |
91.9 |
97.9 |
0.9 |
1.0 |
1.1 |
1.2 |
1.2 |
10 |
15.9 |
87.3 |
99.3 |
100.0 |
1.0 |
1.0 |
1.2 |
1.2 |
1.2 |
|
Zwetsloot’s formulation |
5 |
6.8 |
57.1 |
91.8 |
97.5 |
1.0 |
1.0 |
1.2 |
1.3 |
1.3 |
10 |
16.3 |
87.2 |
99.3 |
99.9 |
1.0 |
1.1 |
1.2 |
1.3 |
1.3 |
|
Multiple step shifting pattern |
||||||||||
Shen’s formulation |
5 |
5.8 |
47.9 |
86.8 |
95.9 |
1.0 |
1.2 |
1.6 |
2.0 |
2.3 |
10 |
12.7 |
80.9 |
98.2 |
99.8 |
1.0 |
1.3 |
1.7 |
3.2 |
3.6 |
|
Zwetsloot’s formulation |
5 |
5.7 |
44.3 |
78.7 |
93.7 |
1.0 |
1.5 |
3.7 |
4.9 |
5.3 |
10 |
11.6 |
79.7 |
96.1 |
99.6 |
1.0 |
1.6 |
4.9 |
5.4 |
5.9 |