Table 2 ATS values for Gamma AEWMA VSI charts with \(\alpha = \left\{ {1,3,5,10} \right\}\) for various \(h_{{2}}\) with fixed \(h_{1} = 1.25\).

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

 

α=1

 

α=3

\(H = 0.707\)

\(H = 0.7{11}\)

\(K\)

0.372

0.361

0.315

0.218

\(K\)

0.371

0.360

0.313

0.217

\(c/h_{{2}}\)

0.1

0.2

0.5

0.8

\(c/h_{{2}}\)

0.1

0.2

0.5

0.8

0.5

2.18

2.20

2.25

2.37

0.5

1.31

1.29

1.24

1.28

0.6

3.29

3.34

3.49

3.71

0.6

1.61

1.62

1.63

1.72

0.7

5.92

6.04

6.44

6.97

0.7

2.48

2.51

2.63

2.82

0.8

13.94

14.25

15.30

16.72

0.8

5.17

5.31

5.75

6.33

0.9

52.97

53.62

55.90

59.29

0.9

21.36

21.91

23.75

26.49

1.0

369.64

369.85

370.24

370.14

1.0

369.79

370.00

369.71

370.12

1.1

137.51

138.96

144.44

154.50

1.1

39.96

41.08

44.98

51.39

1.2

45.58

46.99

52.13

60.57

1.2

11.21

11.73

13.45

15.80

1.3

22.73

23.79

27.48

32.85

1.3

5.30

5.55

6.32

7.28

1.4

13.24

13.98

16.51

19.87

1.4

3.35

3.49

3.91

4.46

1.5

8.69

9.22

10.95

13.10

1.5

2.43

2.52

2.79

3.19

 

α=5

 

α=10

\(H = 0.7{11}\)

\(H = 0.7{12}\)

\(K\)

0.374

0.362

0.316

0.221

\(K\)

0.373

0.362

0.315

0.221

\(c/h_{{2}}\)

0.1

0.2

0.5

0.8

\(c/h_{{2}}\)

0.1

0.2

0.5

0.8

0.5

1.23

1.18

1.08

1.09

0.5

1.20

1.12

0.99

0.97

0.6

1.32

1.30

1.26

1.31

0.6

1.21

1.15

1.03

1.04

0.7

1.78

1.80

1.84

1.96

0.7

1.31

1.29

1.24

1.30

0.8

3.45

3.51

3.76

4.09

0.8

2.05

2.09

2.18

2.35

0.9

13.61

13.96

15.32

17.18

0.9

7.06

7.29

7.99

8.94

1.0

370.26

369.66

369.78

369.95

1.0

369.75

369.91

369.44

370.13

1.1

23.16

23.87

26.68

30.82

1.1

10.72

11.16

12.60

14.59

1.2

6.22

6.47

7.33

8.41

1.2

3.11

3.21

3.53

3.96

1.3

3.17

3.27

3.63

4.09

1.3

1.77

1.81

1.91

2.13

1.4

2.12

2.17

2.36

2.65

1.4

1.35

1.34

1.32

1.45

1.5

1.63

1.65

1.73

1.93

1.5

1.20

1.15

1.05

1.13

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