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Table 3 TDI simulation results

From: The Total Deviation Index estimated by Tolerance Intervals to evaluate the concordance of measurement devices

    

Mean

MSE × 1000

EC

 

p

n

log(κ p )

Lin

Ch.

PI

Lin

Ch.

PI

Lin

Ch.

TI

μ D = 0

0.80

20

1.981

2.014

1.977

1.985

10.409

8.492

8.496

95.7

94.7

98.5

σ D = 5.65

 

100

 

1.997

1.980

1.981

2.040

1.617

1.615

97.4

94.8

98.5

 

0.85

20

2.097

2.131

2.093

2.102

10.425

8.491

8.498

95.7

94.7

98.3

  

100

 

2.133

2.096

2.098

2.048

1.616

1.615

97.4

94.8

98.3

 

0.90

20

2.231

2.264

2.227

2.235

10.381

8.496

8.491

95.7

94.7

97.9

  

100

 

2.246

2.229

2.231

2.027

1.618

1.615

97.3

94.4

97.9

 

0.95

20

2.406

2.439

2.402

2.410

10.399

8.495

8.491

95.7

94.7

97.6

  

100

 

2.421

2.405

2.406

2.036

1.617

1.615

97.3

94.7

97.6

μ D = 2.174

0.80

20

2.052

2.076

2.047

2.054

10.286

9.216

9.135

95.2

94.9

97.4

σ D = 5.65

 

100

 

2.061

2.048

2.050

2.167

1.983

1.971

95.5

93.4

95.4

 

0.85

20

2.167

2.192

2.161

2.169

10.347

9.109

9.030

95.2

94.9

96.9

  

100

 

2.178

2.163

2.165

2.192

1.961

1.951

95.7

93.3

95.0

 

0.90

20

2.300

2.326

2.293

2.300

10.364

8.998

8.902

95.3

94.8

96.6

  

100

 

2.311

2.296

2.297

2.199

1.943

1.930

95.8

93.1

94.2

 

0.95

20

2.473

2.501

2.465

2.472

10.487

8.834

8.735

95.6

94.9

96.2

  

100

 

2.486

2.469

2.470

2.253

1.904

1.892

96.1

93.3

93.8

μ D = 5

0.80

20

2.287

2.281

2.276

2.281

8.736

9.211

9.061

91.9

94.6

91.0

σ D = 5.65

 

100

 

2.278

2.286

2.287

1.954

1.890

1.886

91.9

94.7

92.6

 

0.85

20

2.391

2.398

2.378

2.383

8.748

8.658

8.505

93.6

95.0

91.4

  

100

 

2.395

2.390

2.390

1.890

1.751

1.747

95.3

94.5

92.8

 

0.90

20

2.508

2.531

2.495

2.500

9.231

8.114

7.965

94.9

94.6

91.9

  

100

 

2.528

2.507

2.508

2.272

1.616

1.613

97.7

94.5

92.8

 

0.95

20

2.662

2.706

2.647

2.652

10.660

7.624

7.463

97.2

94.1

92.0

  

100

 

2.703

2.660

2.661

3.569

1.485

1.481

99.1

94.4

93.2

μ D = 0

0.80

20

2.579

2.618

2.581

2.589

10.282

7.911

8.011

97.1

96.7

99.1

σ D = 10.28

 

100

 

2.595

2.577

2.579

2.121

1.647

1.639

97.2

94.3

98.5

 

0.85

20

2.695

2.734

2.697

2.705

10.301

7.911

8.014

97.1

96.7

98.7

  

100

 

2.711

2.693

2.695

2.128

1.642

1.639

97.2

94.4

98.2

 

0.90

20

2.828

2.868

2.830

2.839

10.327

7.912

8.018

97.1

96.7

98.3

  

100

 

2.844

2.827

2.828

2.139

1.641

1.640

97.2

94.4

97.8

 

0.95

20

3.003

3.043

3.006

3.014

10.349

7.911

8.020

97.1

96.7

98.0

  

100

 

3.020

3.002

3.004

2.148

1.640

1.640

97.2

94.5

97.5

μ D = 2.174

0.80

20

2.601

2.627

2.593

2.601

9.833

8.595

8.502

95.3

95.2

97.9

σ D = 10.28

 

100

 

2.613

2.597

2.599

2.171

1.819

1.809

96.3

93.5

96.9

 

0.85

20

2.717

2.743

2.709

2.717

9.846

8.567

8.473

95.3

95.3

97.8

  

100

 

2.729

2.713

2.715

2.177

1.816

1.806

96.3

93.6

96.9

 

0.90

20

2.850

2.877

2.842

2.849

9.864

8.529

8.435

95.4

95.2

97.3

  

100

 

2.862

2.847

2.848

2.185

1.812

1.802

96.3

93.6

96.4

 

0.95

20

3.025

3.052

3.016

3.024

9.879

8.848

8.379

95.5

95.3

97.1

  

100

 

3.038

3.022

3.023

2.192

1.807

1.797

96.4

93.7

95.8

μ D = 5

0.80

20

2.689

2.706

2.682

2.689

9.727

9.684

9.550

93.6

94.1

95.8

σ D = 10.28

 

100

 

2.698

2.688

2.689

2.103

1.994

1.988

95.8

93.8

95.1

 

0.85

20

2.803

2.823

2.795

2.802

9.810

9.444

9.313

94.0

94.2

95.7

  

100

 

2.814

2.802

2.803

2.147

1.947

1.942

95.9

94.0

94.5

 

0.90

20

2.934

2.956

2.925

2.932

9.907

9.175

9.037

94.0

94.4

95.2

  

100

 

2.947

2.933

2.934

2.204

1.890

1.886

96.0

93.8

94.0

 

0.95

20

3.105

3.131

3.095

3.102

10.112

8.826

8.684

94.1

94.1

94.7

  

100

 

3.123

3.104

3.105

2.335

1.812

1.808

96.5

94.1

93.6

  1. Simulation results. log(κ p ) refers to the actual log-transformed Total Deviation Index (TDI) simulated, whereas Mean and MSE correspond to the mean value and mean squared error of the log-transformed TDI estimates from each of the scenarios considered, based on Lin, Choudhary and our Probability Interval (PI) approaches respectively. EC refers to the empirical confidence based on the 95% confidence level based on Lin, Choudhary (Ch.) and our Tolerance Interval (TI) upper bounds of the log-transformed TDI estimates respectively.