Reliability Project 1 Team 9 Philippe Delelis Florian Brouet SungHyeok Lee.

Reliability Project 1

Team 9

Philippe DelelisFlorian BrouetSungHyeok Lee

2

Data 1N=21

Probabiblity Distribution

Data 1 : Symmetric Simple cumulative Distribution

Normal

Bi-exponential

Log normal

Weibull

Data 1 : Mean Rank

Normal Log normal

Weibull Bi-exponential

Data 1 : Median rank

NormalLog normal

WeibullBi-exponential

Data 1 : The rest method

Normal Log normal


Data 1 : Linearity Results

Symmetric .S.C Mean Rank Median Rank The Rest Method

Normal 0 0 0 0Log-Normal X X X X

Weibull 0 0 0 0Bi-exponential 0 0 0 0

Data 1 : R (Correlation Coefficient Comparaison)

Symmetric .S.C

R SD

Normal 0.95883 0.20172

Log-Normal 0.84415 0.3925

Weibull 0.93251 0.32349

Bi-exponential 0.85644 0.4718

Mean Rank

R SD

0.96493 0.16754

0.83983 0.35807

0.92194 0.30615

0.88683 0.36864

Median Rank

R SD

Normal 0.96225 0.18434

Log-Normal 0.84255 0.37647

Weibull 0.92866 0.31387


The Rest Method

R SD

0.95883 0.20172

0.9612 0.19002

0.8432 0.38198

0.93023 0.31675

Normal α = 0.05 Dnα =0,1882

Weibull, Bi-exponential α = 0.05 Dn

α =0.1932

Normal α = 0.15 Dnα =0.1636


α =0.1668

n =

21Data 1 : Value of Dn

α

K-S test : Symmetric Simple Cumulative Distribution

Dash dot : α = 0.15Line : α = 0.05

• µ = 288,431• σ = 196,078

• m = 1,166• ξ = 326,693

• ξ = 163,934• x0= 378,885

Normal WeibullBi-exponential

Mean Rank

• µ = 288,696• σ = 217,391

• m = 1.021• ξ = 338.885

• ξ = 188,185• x0= 386,741

Dash dot : α = 0.15Line : α = 0.05


Median Rank

Dash dot : α = 0.15Line : α = 0.05

• µ = 286,939• σ = 204,082

• m = 1,099• ξ = 332,047

• ξ = 171,527• x0= 378,851


The Rest Method

• µ = 285,8• σ = 200

• m = 1,112• ξ = 331,007

• ξ = 169,492• x0= 380,339

Dash dot : α = 0.15Line : α = 0.05


Data 1 : K-S Test Results


Normal 0 0 0 0Weibull x x 0 0

Bi-exponential x x x 0

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Data 2N=26

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Log-NormalNormal

Weibull Bi-Exponential

Data 2 : Symmetric S. C. Distribution

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Log-NormalNormal


Data 2 : Mean Rank

19

Log-NormalNormal


Data 2 : Median Rank

20

Log-NormalNormal


Data 2 : The Rest Method

21





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Symmetric .S.C

R SD

Normal 0.98122 0.1364

Log-Normal 0.89569 0.32143

Weibull 0.9646 0.2353


Median Rank

R SD

Normal 0.9619 0.12848

Log-Normal 0.89421 0.31095

Weibull 0.9636 0.22677


The Rest Method

R SD

0.9818 0.13082

0.89482 0.3145

0.96421 0.22889

0.90832 0.36637

Mean Rank

R SD

0.98162 0.1304

0.89569 0.32143

0.9646 0.2353

0.92236 0.35894


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n =

26

Normal α = 0.05 Dnα =0.1702


α =0.175

Normal α = 0.15 Dnα =0.1474


α =0.1514

Data 2 : Value of Dnα

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• µ = 330.367• σ = 166.667

• m = 1.9055• ξ = 340.52

• ξ = 125• x0= 368.75

Dash dot : α = 0.15Line : α = 0.05

Normal Weibull Bi-exponential

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Data 2 : Mean Rank

• µ = 301.54• σ = 160.527

• m = 1.8251• ξ = 337.25

• ξ = 145.85• x0= 384.26

Dash dot : α = 0.15Line : α = 0.05


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Data 2 : Median Rank

• µ = 316.54• σ = 166.06

• m = 1.84• ξ = 343.7

• ξ = 142.85• x0= 405.28

Dash dot : α = 0.15Line : α = 0.05


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Data 2 : The Rest Method

• µ = 321.53• σ = 166.6

• m = 1.81• ξ = 342.87

• ξ = 142.85• x0= 409.97

Dash dot : α = 0.15Line : α = 0.05


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Normal X 0 0 0Weibull 0 0 0 0

Bi-exponential 0 0 X X

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Data 3N=29

Data 3 : Symmetric Simple cumulative Distribution

Normal Log normal

Bi-exponential

Weibull

Data 3 : Mean Rank

Normal Log normal


Data 3 : Median rank

Normal

Log normal

WeibullBiexponential

Data 3 : The rest method

Normal

Log normal



Symmetric .S.C

R SD

Normal 0.98703 0.14944

Log-Normal 0.86032 0.47444

Weibull 0.92709 0.42972


Mean Rank

R SD

0.98605 0.15517

0.86453 0.4685

0.93019 0.42177

0.94377 0.37985

Median Rank

R SD

Normal 0.98419 0.17302

Log-Normal 0.86901 0.48339

Weibull 0.94004 0.41502


The Rest Method

R SD

0.98352 0.17899

0.87037 0.48743

0.94303 0.41164

0.93343 0.44388

Normal α = 0.05 Dnα =0.1612


α =0.1660

Normal α = 0.15 Dnα =0.1486


α =0.1436

n =

29Data 3 : Value of Dn

α


Dash dot : α = 0.15Line : α = 0.05

• µ = 262.55• σ = 178.23

• m = 0.80• ξ = 306.43

• ξ = 156.01• x0= 332.30


Mean Rank

• µ = 262.78• σ = 180.17

• m = 0.80• ξ = 334.45

• ξ = 167.50• x0= 351.75

Dash dot : α = 0.15Line : α = 0.05


Median Rank

Dash dot : α = 0.15Line : α = 0.05

• µ = 263.04• σ = 182.68

• m = 0.86• ξ = 316.02

• ξ = 159.24• x0= 350.33


The Rest Method

• µ = 260.89• σ = 175.52

• m = 0.87• ξ = 331.82

• ξ = 157.23• x0= 350.62

Dash dot : α = 0.15Line : α = 0.05




Normal 0 0 0 0Weibull X X X X

Bi-exponential 0 0 0 X

Data 1+2N=47

Data 1+2: Symmetric Simple Cumulative Distribution

Normal Log normal

Weibull

Bi-exponential

Data 1+2 : Mean Rank

Normal Log normal

Weibull

Bi-exponential

Data 1+2 : Median Rank

NormalLog normal

Weibull

Bi-exponential

Data 1+2 : The Rest Method

Normal Log normal

Weibull

Bi-exponential

Linearity Results




Data 1+2 : R (Correlation Coefficient Comparaison)

Symmetric .S.C

R SD

Normal 0.97609 0.15421

Log-Normal 0.85885 0.37466

Weibull 0.96044 0.25098


Median Rank

R SD

Normal 0.97828 0.14319

Log-Normal 0.85644 0.36809

Weibull 0.95623 0.25496


The Rest Method

R SD

0.9776 0.14675

0.85734 0.37037

0.95787 0.25323

0.88741 0.41395

Mean Rank

R SD

0.97995 0.13307

0.85304 0.36025

0.94964 0.26211

0.90253 0.36467

Data 1+2 : Value of Dnα

Normal α = 0.05 Dnα = 0,1282


α = 0,1332

Normal α = 0.15 Dnα = 0,111


α = 0,1175

n =

47

Data 1+2 : K-S Test (Symmetric Simple Cumulative Distribution)

• µ = 292,04• σ = 168,06

• m = 1,45• ξ = 348,25

• ξ = 139,86• x0= 372,16

Dash dot : α = 0.15Line : α = 0.05


Data 1+2 : K-S Test (Mean Rank)

• µ = 292,44• σ = 178,25

• m = 1.35• ξ = 343,13

• ξ = 149,25• x0= 374,04

Dash dot : α = 0.15Line : α = 0.05


Data 1+2 : K-S Test (Median Rank)

• µ = 292,18• σ = 172,41

• m = 1.42• ξ = 340,09

• ξ = 143,88• x0= 372,86

Dash dot : α = 0.15Line : α = 0.05


Data 1+2 : K-S Test (The Rest Method)

• µ = 292,30• σ = 170,94

• m = 1,44• ξ = 339,24

• ξ = 142,45• x0= 372,63

Dash dot : α = 0.15Line : α = 0.05


Data 1+2 : K-S Test Results



Bi-exponential X X X X

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Data 2+3N=55

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Log-NormalNormal

WeibullBi-Exponential

Data 2+3 : Symmetric Simple Cumulative Distribution

57

Log-NormalNormal


Data 2+3 : Mean Rank

58

Log-NormalNormal


Data 2+3 : Median Rank

59

Log-NormalNormal


Data 2+3 : The Rest Method

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Linearity Results




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Symmetric .S.C

R SD

Normal 0.97801 0.14793

Log-Normal 0.74931 0.4995

Weibull 0.89612 0.40745


Median Rank

R SD

Normal 0.98109 0.13404

Log-Normal 0.74288 0.49423

Weibull 0.88134 0.42199


The Rest Method

R SD

0.9801 0.13863

0.74509 0.49619

0.88643 0.41743

0.8899 0.4110

Mean Rank

R SD

0.98381 0.1204

0.73564 0.48649

0.86468 0.43368

0.90544 0.36254

Data 2+3 : R (Correlation Coefficient Comparaison)

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n =

55

Normal α = 0.05 Dnα = 0.119


α = 0.124

Normal α = 0.15 Dnα = 0.1035


α = 0.107

Data 2+3 : Value of Dnα

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Data 2+3 : K-S Test (Symmetric Simple Cumulative Distribution)

• µ = 279.55• σ = 166.667

• m = 1.1293• ξ = 341.3

• ξ = 138.8• x0= 360.27

Dash dot : α = 0.15Line : α = 0.05


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Data 2+3 : K-S Test (Mean Rank)

• µ = 319.2• σ = 200

• m = 1.0349• ξ = 349.87

• ξ = 147.05• x0= 360.29

Dash dot : α = 0.15Line : α = 0.05


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Data 2+3 : K-S Test (Median Rank)

• µ = 328.4• σ = 200

• m = 1.0855• ξ = 344.94

• ξ = 142.86• x0= 362

Dash dot : α = 0.15Line : α = 0.05


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Data 2+3 : K-S Test (The Rest Method)

• µ = 330• σ = 200

• m = 1.1• ξ = 342.53

• ξ = 140.84• x0= 359.97

Dash dot : α = 0.15Line : α = 0.05


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Data 2+3 : K-S Test Results


Normal 0 X X XWeibull X X X X

Bi-exponential 0 0 0 0

Data 1+2+3N=76

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Data 1+2+3 : Symmetric Simple Cumulative Distribution

Log-NormalNormal

WeibullBi-Exponential

70

Data 1+2+3 : Mean Rank

Log-NormalNormal

Weibull

Bi-exponential

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Data 1+2+3 : Median Rank

Log-NormalNormal


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Data 1+2+3 : The Rest Method

Log-NormalNormal


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Linearity Results




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Symmetric .S.C

R SD

Normal 0.99056 0.13213

Log-Normal 0.88292 0.45247

Weibull 0.95282 0.36607


Median Rank

R SD

Normal 0.98881 0.14718

Log-Normal 0.88867 0.45249

Weibull 0.96072 0.34544


The Rest Method

R SD

0.98836 0.15108

0.88958 0.4537

0.96261 0.34023

0.93729 0.43776

Mean Rank

R SD

0.99012 0.13519

0.88564 0.44766

0.95435 0.36040

0.94495 0.39482

Data 1+2+3 : R (Correlation Coefficient Comparaison)

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n =

76

Normal α = 0.05 Dnα =0.1018


α =0.1058

Normal α = 0.15 Dnα = 0.0884


α =0.0914

Data 1+2+3 : Value of Dnα

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Data 1+2+3 : K-S Test (Symmetric Simple Cumulative Distribution)

• µ = 280.89• σ = 170.05

• m = 1.09• ξ = 342.02

• ξ = 145.14• x0= 357.04

Dash dot : α = 0.15Line : α = 0.05


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Data 1+2+3 : K-S Test (Mean Rank)

• µ = 281.28• σ = 172.29

• m = 1.09• ξ = 345.17

• ξ = 150.15• x0= 364.86

Dash dot : α = 0.15Line : α = 0.05


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Data 1+2+3 : K-S Test (Median Rank)

• µ = 281.65• σ = 174.42

• m = 1.14• ξ = 329.72

• ξ = 146.41• x0= 363.10

Dash dot : α = 0.15Line : α = 0.05


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Data 1+2+3 : K-S Test (The Rest Method)

• µ = 280.46• σ = 171.83

• m = 1.15• ξ = 333.18

• ξ = 145.35• x0= 363.38

Dash dot : α = 0.15Line : α = 0.05


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Data 1+2+3 : K-S Test Results



Bi-exponential X X X X

Conclusion

• R value comparison - Normal > Weibull > Bi-Exponential > Lognormal but R value and C.D.F doesn’t guarantee optimal distribution• The best distribution

Data The fittest distribution C. D. FData 1 Normal distribution Mean rank

Data 2 Weibull distribution Symmetric .S.C

Data 3 Normal distribution Mean rank

Data 1+2 Normal distribution Mean rank

Data 2+3 Bi-Exponential distribution Mean rank

Data 1+2+3 Normal distribution Symmetric .S.C

Reliability Project 1 Team 9 Philippe Delelis Florian Brouet SungHyeok Lee.

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Transcript of Reliability Project 1 Team 9 Philippe Delelis Florian Brouet SungHyeok Lee.