Table 7 Simulation results of AEWMA FSI and AEWMA VSI charts with \(\alpha = 5\), \(\phi = 0.1\) and \(c = 0.9\).

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

 

\(X\)

\(Y\)

\(T\)

\(\hat{\delta }^{*}\)

\(\hat{\delta }^{{**}}\)

\(\tilde{\delta }\)

\(g{(}\tilde{\delta }{)}\)

\(W\)

\(h_{FSI}\)

\(h\)

\(h_{VSI}\)

1

2.897

1.425

− 0.768

− 0.077

− 0.768

0.768

0.2

− 0.154

0

1.25

0

2

5.825

1.799

0.752

0.006

0.032

0.032

0.015

− 0.140

1

1.25

1.25

3

6.479

1.864

1.017

0.107

0.395

0.395

0.1

− 0.024

2

1.25

2.5

4

6.173

1.834

0.895

0.186

0.541

0.541

0.1

0.068

3

1.25

3.75

5

4.114

1.602

− 0.049

0.162

0.397

0.397

0.1

0.056

4

1.25

5

6

3.082

1.455

− 0.647

0.082

0.174

0.174

0.015

0.045

5

1.25

6.25

7

5.598

1.776

0.656

0.139

0.266

0.266

0.1

0.106

6

1.25

7.5

8

5.373

1.751

0.558

0.181

0.318

0.318

0.1

0.152

7

1.25

8.75

9

7.555

1.962

1.415

0.304

0.497

0.497

0.1

0.278

8

1.25

10

10

5.709

1.787

0.703

0.344

0.528

0.528

0.1

0.320

9

1.25

11.25

11

3.558

1.527

− 0.357

0.274

0.399

0.399

0.1

0.253

10

1.25

12.5

12

2.305

1.321

− 1.193

0.127

0.178

0.178

0.015

0.231

11

1.25

13.75

13

2.806

1.410

− 0.829

0.032

0.043

0.043

0.015

0.215

12

1.25

15

14

6.961

1.909

1.200

0.149

0.193

0.193

0.015

0.230

13

1.25

16.25

15

9.933

2.150

2.177

0.351

0.443

0.443

0.1

0.425

14

0.1

17.5

16

5.708

1.787

0.703

0.387

0.475

0.475

0.1

0.453

15

0.1

17.6

17

1.991

1.258

− 1.449

0.203

0.244

0.244

0.015

0.424

16

0.1

17.7

18

7.294

1.939

1.322

0.315

0.371

0.371

0.1

0.514

17

0.1

17.8

19

3.813

1.562

− 0.212

0.262

0.303

0.303

0.1

0.441

18

0.1

17.9

20

3.870

1.570

− 0.180

0.218

0.248

0.248

0.015

0.432

19

0.1

18

21

6.851

1.899

1.159

0.312

0.350

0.350

0.1

0.505

20

0.1

18.1

22

6.129

1.830

0.877

0.369

0.409

0.409

0.1

0.542

21

0.1

18.2

23

7.725

1.977

1.474

0.479

0.526

0.526

0.1

0.635

22

0.1

18.3

24

1.383

1.114

− 2.034

0.228

0.248

0.248

0.015

0.595

23

0.1

18.4

25

3.502

1.519

− 0.389

0.166

0.179

0.179

0.015

0.580

24

0.1

18.5

26

4.602

1.663

0.199

0.169

0.181

0.181

0.015

0.575

25

0.1

18.6

27

2.378

1.335

− 1.137

0.039

0.041

0.041

0.015

0.549

26

0.1

18.7

28

7.751

1.979

1.484

0.183

0.193

0.193

0.015

0.563

27

0.1

18.8

29

4.719

1.677

0.256

0.191

0.200

0.200

0.015

0.558

28

0.1

18.9

30

4.447

1.644

0.123

0.184

0.192

0.192

0.015

0.552

29

0.1

19

31

5.780

1.795

0.733

0.239

0.248

0.248

0.015

0.555

30

0.1

19.1

32

6.491

1.865

1.021

0.317

0.328

0.328

0.1

0.601

31

0.1

19.2

33

10.128

2.164

2.234

0.509

0.525

0.525

0.1

0.765

32

**

19.3

34

4.225

1.617

0.009

0.459

0.472

0.472

0.1

0.689

   

35

7.299

1.940

1.324

0.545

0.559

0.559

0.1

0.753

   

36

4.535

1.655

0.167

0.507

0.519

0.519

0.1

0.694

   

37

7.076

1.920

1.243

0.581

0.593

0.593

0.1

0.749

   

38

7.794

1.983

1.498

0.673

0.685

0.685

0.1

0.824

   

39

6.591

1.875

1.060

0.711

0.723

0.723

0.1

0.847

   

40

8.351

2.029

1.686

0.809

0.821

0.821

0.2

1.015

   

41

7.328

1.942

1.334

0.861

0.873

0.873

0.2

1.079

   

42

5.100

1.721

0.435

0.819

0.829

0.829

0.2

0.950

   

43

3.162

1.468

− 0.596

0.677

0.685

0.685

0.1

0.795

   

44

6.173

1.834

0.895

0.699

0.706

0.706

0.1

0.805

   

45

11.816

2.278

2.698

0.899

0.907

0.907

0.2

1.184

   

46

7.537

1.961

1.409

0.950

0.957

0.957

0.2

1.229

   

47

7.413

1.950

1.365

0.991

0.998

0.998

0.2

1.256

   

48

6.217

1.839

0.913

0.984

0.990

0.990

0.2

1.187

   

49

7.568

1.963

1.420

1.027

1.033

1.033

0.25

1.246

   

50

4.084

1.598

− 0.065

0.918

0.923

0.923

0.2

0.983

   
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