Table 5 ATS values between Gamma EWMA VSI and AEWMA VSI charts for \(\alpha = \left\{ {1,3,5,10} \right\}\) under various \(h_{1}\) with fixed \(h_{2} { = 0}{\text{.1}}\) and \(c = 0.9\).

From: Considering AEWMA control chart applied to Gamma-distributed data with fixed and variable sampling intervals

 

α=1

 

α=3

EWMA

AEWMA

EWMA

AEWMA

\(h_{1} /\lambda\)

0.05

0.1

0.2

\(\phi = 0.1\)

\(h_{1} /\lambda\)

0.05

0.1

0.2

\(\phi = 0.1\)

1.25

75.97

84.21

93.89

52.97

1.25

29.26

32.80

42.17

21.36

1.5

73.37

81.97

92.18

49.83

1.5

27.31

30.69

40.09

19.36

1.75

72.18

80.96

91.36

48.37

1.75

26.54

29.77

39.12

18.44

2

71.57

80.36

90.95

47.41

2

26.16

29.22

38.56

18.10

2.5

71.07

79.69

90.46

47.07

2.5

25.77

28.71

37.99

18.14

3

70.80

79.45

90.31

47.11

3

25.63

28.46

37.66

18.21

4

70.50

79.28

90.21

47.44

4

25.50

28.21

37.35

18.40

 

α=5

 

α=10

EWMA

AEWMA

EWMA

AEWMA

\(h_{1} /\lambda\)

0.05

0.1

0.2

\(\phi = 0.1\)

\(h_{1} /\lambda\)

0.05

0.1

0.2

\(\phi = 0.1\)

1.25

18.88

19.73

25.28

13.61

1.25

10.80

9.70

11.48

7.06

1.5

17.37

18.16

23.30

12.49

1.5

9.93

9.13

10.31

6.71

1.75

16.83

17.46

22.49

11.99

1.75

9.58

8.72

9.79

6.59

2

16.58

17.09

22.03

11.82

2

9.40

8.50

9.50

6.67

2.5

16.34

16.73

21.55

12.06

2.5

9.25

8.25

9.20

6.98

3

16.25

16.54

21.34

12.19

3

9.14

8.14

9.05

7.11

4

16.19

16.38

21.14

12.60

4

9.08

8.04

8.93

7.53

  1. Bold values indicate that the minimum out-of-control ARL values of proposed charts at various process shifts.
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