Table 3 Comparative of existing Bayesian Max-EWMA control chart and proposed Adaptive Bayesian Max-EWMA control chart under SELF, with \(\lambda\) = 0.15.

From: An adaptive Bayesian approach for improved sensitivity in joint monitoring of mean and variance using Max-EWMA control chart

α

0.00

0.10

0.25

0.50

1.00

2.00

3.00

β

n

Type

ARL

SDRL

ARL

SDRL

ARL

SDRL

ARL

SDRL

ARL

SDRL

ARL

SDRL

ARL

SDRL

1.00

3

Existing

370.0950

365.2474

209.9108

201.1163

54.0980

46.5065

14.1483

8.4748

4.9633

1.7631

2.3219

0.5266

1.7192

0.2783

Proposed

370.8369

360.4711

117.6749

87.4265

35.3488

23.6503

11.2035

7.1431

3.7337

1.6922

1.5963

0.5744

1.0552

0.2283

5

Existing

370.2356

364.1423

159.6950

152.5825

32.5425

25.4189

9.2319

4.5814

3.6589

1.0929

1.9308

0.3448

1.1773

0.3819

Proposed

370.6832

368.6289

86.7464

60.6099

23.9619

15.5557

7.5019

4.1790

2.7061

1.1737

1.1096

0.3161

1.0002

0.0155

7

Existing

370.2879

363.4935

126.6313

119.0586

23.2994

16.7468

7.1665

3.1000

3.0334

0.8171

1.6825

0.4681

1.0150

0.1215

Proposed

370.5644

356.1078

70.2331

47.8194

18.1380

11.5507

5.8326

2.9831

2.1104

0.9869

1.0132

0.1144

1.0000

0.0000

1.50

3

Existing

11.9084

7.8667

11.6904

7.6825

10.5982

6.6942

8.2143

4.6934

4.7135

2.1296

2.3871

0.7419

1.6709

0.5207

Proposed

9.1807

7.3751

9.0332

7.2040

8.1454

6.3377

6.1360

4.4775

3.4105

2.0014

1.6575

0.7279

1.1429

0.3575

5

Existing

7.3073

3.9265

7.2076

3.8278

6.8140

3.4989

5.6582

2.6500

3.5234

1.3296

1.9076

0.5443

1.2691

0.4441

Proposed

5.5847

3.7696

5.5130

3.7158

5.1509

3.4086

4.1497

2.5970

2.4595

1.3684

1.2074

0.4499

1.0100

0.0995

7

Existing

5.5734

2.6158

5.5318

2.5680

5.2939

2.3824

4.5478

1.8702

2.9553

1.0103

1.6433

0.5167

1.0735

0.2609

Proposed

4.2187

2.6401

4.1949

2.6142

3.9712

2.4645

3.2431

1.9485

1.9479

1.0877

1.0633

0.2530

1.0004

0.0205

2.00

3

Existing

5.0767

2.6626

5.0556

2.6606

4.9461

2.5796

4.6197

2.3474

3.7112

1.7207

2.3528

0.8943

1.6745

0.5974

Proposed

3.5588

2.4692

3.5263

2.4468

3.4498

2.3755

3.2142

2.1626

2.5628

1.5582

1.6160

0.7879

1.1988

0.4291

5

Existing

3.3971

1.4363

3.3972

1.4320

3.3553

1.4030

3.2148

1.3167

2.7468

1.0419

1.8542

0.6364

1.3135

0.4716

Proposed

2.3204

1.4087

2.3011

1.4066

2.2769

1.3934

2.1546

1.2987

1.7892

1.0081

1.2139

0.4774

1.0295

0.1720

7

Existing

2.7436

1.0182

2.7401

1.0246

2.7204

1.0088

2.6335

0.9469

2.3144

0.7915

1.5984

0.5548

1.1361

0.3435

Proposed

1.8000

1.0449

1.7945

1.0396

1.7687

1.0230

1.6804

0.9546

1.4413

0.7382

1.0789

0.2870

1.0038

0.0617

3.00

3

Existing

2.5667

1.2163

2.5594

1.2097

2.5406

1.2033

2.5079

1.1894

2.3680

1.0969

1.9643

0.8628

1.5976

0.6626

Proposed

1.7506

1.0054

1.7405

0.9905

1.7399

0.9877

1.7154

0.9717

1.6284

0.8836

1.4004

0.6686

1.2007

0.4519

5

Existing

1.8523

0.7359

1.8546

0.7384

1.8492

0.7393

1.8380

0.7327

1.7579

0.6991

1.5210

0.5905

1.2842

0.4692

Proposed

1.2649

0.5563

1.2634

0.5562

1.2603

0.5484

1.2510

0.5390

1.2102

0.4885

1.1103

0.3437

1.0390

0.1995

7

Existing

1.5460

0.5870

1.5515

0.5906

1.5423

0.5871

1.5313

0.5831

1.4792

0.5610

1.3027

0.4759

1.1268

0.3343

Proposed

1.1015

0.3336

1.0989

0.3285

1.0961

0.3256

1.0954

0.3244

1.0766

0.2882

1.0299

0.1765

1.0071

0.0856

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