|
Tabular CUSUM (TC)
|
Standardized CUSUM (SC)
|
EWMA (E)
| | | | |
---|
|
TC
|
RSb
|
RAc
|
RSRAd
|
SC
|
RSb
|
RAc
|
RSRAd
|
E
|
RSb
|
RAc
|
RSRAd
|
Average number of false positive alerts per week
| |
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
T
r
S
a
|
0.01
|
0.04
|
0.06
|
0.08
|
0.10
|
0.04
|
0.04
|
0.04
|
0.19
|
0.16
|
0.10
|
0.03
|
0.09
|
0.02
|
0.19
|
0.14
|
0.00
|
0.00
|
0.14
|
0.08
|
0.00
|
0.00
|
0.03
|
0.06
|
T
r
U
|
0.06
|
0.08
|
0.09
|
0.06
|
0.11
|
0.08
|
0.15
|
0.12
|
0.13
|
0.11
|
0.15
|
0.11
|
0.07
|
0.05
|
0.18
|
0.17
|
0.00
|
0.00
|
0.20
|
0.15
|
0.00
|
0.00
|
0.05
|
0.06
|
T
r
SU
|
0.04
|
0.02
|
0.01
|
0.02
|
0.07
|
0.04
|
0.03
|
0.04
|
0.06
|
0.05
|
0.05
|
0.03
|
0.05
|
0.02
|
0.08
|
0.07
|
0.01
|
0.02
|
0.06
|
0.04
|
0.03
|
0.02
|
0.08
|
0.05
|
T
r
US
|
0.02
|
0.03
|
0.02
|
0.02
|
0.05
|
0.03
|
0.04
|
0.04
|
0.04
|
0.04
|
0.08
|
0.08
|
0.04
|
0.03
|
0.06
|
0.06
|
0.02
|
0.04
|
0.09
|
0.08
|
0.02
|
0.03
|
0.08
|
0.04
|
T
r
SUS
|
0.03
|
0.02
|
0.01
|
0.01
|
0.05
|
0.03
|
0.02
|
0.02
|
0.03
|
0.02
|
0.02
|
0.01
|
0.05
|
0.03
|
0.05
|
0.04
|
0.01
|
0.01
|
0.05
|
0.03
|
0.03
|
0.02
|
0.01
|
0.04
|
T
r
USU
|
0.01
|
0.02
|
0.03
|
0.03
|
0.03
|
0.03
|
0.04
|
0.02
|
0.02
|
0.03
|
0.03
|
0.03
|
0.03
|
0.02
|
0.03
|
0.03
|
0.01
|
0.02
|
0.08
|
0.07
|
0.02
|
0.02
|
0.08
|
0.04
|
Detection rate
| |
T
r
SU
|
10 %
|
95 %
|
100 %
|
100%
|
40 %
|
0 %
|
100 %
|
25 %
|
85 %
|
100 %
|
100 %
|
100 %
|
T
r
US
|
70 %
|
85 %
|
95 %
|
100%
|
65 %
|
25 %
|
45 %
|
60 %
|
85 %
|
100 %
|
65 %
|
100 %
|
T
r
SUS
| | | | | | | | | | | | |
S →U
|
10 %
|
95 %
|
95 %
|
95%
|
30 %
|
0 %
|
95 %
|
35 %
|
75 %
|
100 %
|
95 %
|
100 %
|
U →S
|
0 %
|
0 %
|
95 %
|
75%
|
0 %
|
0 %
|
0 %
|
0 %
|
0 %
|
0 %
|
35 %
|
100 %
|
T
r
USU
| | | | | | | | | | | | |
S →U
|
60 %
|
70 %
|
100 %
|
100%
|
55 %
|
25 %
|
35 %
|
60 %
|
85 %
|
95 %
|
55 %
|
95 %
|
U →S
|
0 %
|
0 %
|
100 %
|
100%
|
0 %
|
0 %
|
60 %
|
0 %
|
5 %
|
40 %
|
65 %
|
100 %
|
Average Run Length [days]
| |
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
mean
|
sd
|
T
r
SU
|
2.50
|
2.12
|
17.47
|
4.56
|
10.30
|
3.40
|
16.25
|
2.99
|
6.38
|
4.34
|
/
|
/
|
13.75
|
4.00
|
7.20
|
4.60
|
2.94
|
2.36
|
10.20
|
3.53
|
15.85
|
3.05
|
10.10
|
3.39
|
T
r
US
|
5.29
|
5.38
|
16.41
|
3.39
|
14.89
|
3.96
|
14.00
|
4.53
|
14.08
|
5.89
|
7.80
|
7.29
|
16.89
|
4.78
|
12.00
|
5.41
|
11.18
|
4.39
|
14.05
|
6.55
|
23.38
|
2.79
|
14.85
|
6.10
|
T
r
SUS
| | | | | | | | | | | | | | | | | | | | | | | | |
S →U
|
4.00
|
1.41
|
18.95
|
2.68
|
13.00
|
5.42
|
16.21
|
5.14
|
4.33
|
3.14
|
/
|
/
|
13.58
|
4.60
|
6.29
|
1.98
|
2.93
|
2.25
|
9.20
|
4.27
|
15.79
|
3.60
|
10.80
|
4.27
|
U →S
|
/
|
/
|
/
|
/
|
15.63
|
3.68
|
11.20
|
4.38
|
/
|
/
|
/
|
/
|
/
|
/
|
/
|
/
|
/
|
/
|
/
|
/
|
24.14
|
2.14
|
13.15
|
5.90
|
T
r
USU
| | | | | | | | | | | | | | | | | | | | | | | | |
U →S
|
6.50
|
6.79
|
14.64
|
6.06
|
16.85
|
6.06
|
12.60
|
5.45
|
12.27
|
4.58
|
10.40
|
9.34
|
12.57
|
4.61
|
8.58
|
5.62
|
11.29
|
6.57
|
21.37
|
5.91
|
21.55
|
4.11
|
14.05
|
5.35
|
S →U
|
/
|
/
|
/
|
/
|
10.95
|
3.66
|
15.65
|
4.22
|
/
|
/
|
/
|
/
|
15.08
|
3.48
|
/
|
/
|
6.00
|
0.00
|
13.88
|
6.75
|
20.77
|
3.14
|
13.25
|
4.84
|
- Notes
-
aTraining simulation scenarios as described in Table 3
-
bControl chart with rational subgroups implemented
-
cControl chart with a reinitialization after three consecutive alarm days
-
dControl chart with rational subgroups and a reinitialization after three consecutive alarm days