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

2. Data 1 N=21 2

3. Probabiblity Distribution

4. Data 1 : Symmetric Simple cumulative Distribution Normal Bi-exponential Log normal Weibull

5. Data 1 : Mean Rank Normal Log normal Weibull Bi-exponential

6. Data 1 : Median rank Normal Log normal Weibull Bi-exponential

7. Data 1 : The rest method Normal Log normal Weibull Bi-exponential

8. Data 1 : Linearity Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Log-Normal XXXX Weibull 0000 Bi-exponential 0000

9. Data 1 : R (Correlation Coefficient Comparaison) Symmetric.S.C RSD Normal0.958830.20172 Log-Normal0.844150.3925 Weibull0.932510.32349 Bi-exponential0.856440.4718 Mean Rank RSD 0.964930.16754 0.839830.35807 0.921940.30615 0.886830.36864 Median Rank RSD Normal0.962250.18434 Log-Normal0.842550.37647 Weibull0.928660.31387 Bi-exponential0.871970.42048 The Rest Method RSD 0.958830.20172 0.96120.19002 0.84320.38198 0.930230.31675

10. Normal α = 0.05 Dn α =0,1882 Weibull, Bi- exponential α = 0.05 Dn α =0.1932 Normal α = 0.15 Dn α =0.1636 Weibull, Bi- exponential α = 0.15 Dn α =0.1668 n = 21 Data 1 : Value of D n α

11. K-S test : Symmetric Simple Cumulative Distribution Dash dot : α = 0.15 Line : α = 0.05 µ = 288,431 σ = 196,078 m = 1,166 ξ = 326,693 ξ = 163,934 x 0 = 378,885 Normal Weibull Bi-exponential

12. Mean Rank µ = 288,696 σ = 217,391 m = 1.021 ξ = 338.885 ξ = 188,185 x 0 = 386,741 Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

13. Median Rank Dash dot : α = 0.15 Line : α = 0.05 µ = 286,939 σ = 204,082 m = 1,099 ξ = 332,047 ξ = 171,527 x 0 = 378,851 Normal Weibull Bi-exponential

14. The Rest Method µ = 285,8 σ = 200 m = 1,112 ξ = 331,007 ξ = 169,492 x 0 = 380,339 Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

15. Data 1 : K-S Test Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Weibull xx00 Bi-exponential xxx0

16. Data 2 N=26 16

17. Log-Normal Normal Weibull Bi-Exponential Data 2 : Symmetric S. C. Distribution 17

18. Log-Normal Normal Weibull Bi-exponential Data 2 : Mean Rank 18

19. Log-Normal Normal Weibull Bi-exponential Data 2 : Median Rank 19

20. Log-Normal Normal Weibull Bi-exponential Data 2 : The Rest Method 20

21. Data 2 : Linearity Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Log-Normal XXXX Weibull 0000 Bi-exponential 0000 21

22. Symmetric.S.C RSD Normal0.981220.1364 Log-Normal0.895690.32143 Weibull0.96460.2353 Bi-exponential0.90050.39445 Median Rank RSD Normal0.96190.12848 Log-Normal0.894210.31095 Weibull0.96360.22677 Bi-exponential0.91200.35259 The Rest Method RSD 0.98180.13082 0.894820.3145 0.964210.22889 0.908320.36637 Mean Rank RSD 0.981620.1304 0.895690.32143 0.96460.2353 0.922360.35894 Data 2 : R (Correlation Coefficient Comparaison) 22

23. n = 26 Normal α = 0.05 Dn α =0.1702 Weibull, Bi- exponential α = 0.05 Dn α =0.175 Normal α = 0.15 Dn α =0.1474 Weibull, Bi- exponential α = 0.15 Dn α =0.1514 Data 2 : Value of D n α 23

24. K-S test : Symmetric Simple Cumulative Distribution µ = 330.367 σ = 166.667 m = 1.9055 ξ = 340.52 ξ = 125 x 0 = 368.75 Dash dot : α = 0.15 Line : α = 0.05 24 Normal Weibull Bi-exponential

25. Data 2 : Mean Rank µ = 301.54 σ = 160.527 m = 1.8251 ξ = 337.25 ξ = 145.85 x 0 = 384.26 Dash dot : α = 0.15 Line : α = 0.05 25 Normal Weibull Bi-exponential

26. Data 2 : Median Rank µ = 316.54 σ = 166.06 m = 1.84 ξ = 343.7 ξ = 142.85 x 0 = 405.28 Dash dot : α = 0.15 Line : α = 0.05 26 Normal Weibull Bi-exponential

27. Data 2 : The Rest Method µ = 321.53 σ = 166.6 m = 1.81 ξ = 342.87 ξ = 142.85 x 0 = 409.97 Dash dot : α = 0.15 Line : α = 0.05 27 Normal Weibull Bi-exponential

28. Data 2 : K-S Test Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal X000 Weibull 0000 Bi-exponential 00XX 28

29. Data 3 N=29 29

30. Data 3 : Symmetric Simple cumulative Distribution Normal Log normal Bi-exponential Weibull

31. Data 3 : Mean Rank Normal Log normal Weibull Bi-exponential

32. Data 3 : Median rank Normal Log normal Weibull Biexponential

33. Data 3 : The rest method Normal Log normal Weibull Bi-exponential

34. Data 3 : Linearity Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Log-Normal XXXX Weibull 0000 Bi-exponential 0000

35. Data 3 : R (Correlation Coefficient Comparaison) Symmetric.S.C RSD Normal0.987030.14944 Log-Normal0.860320.47444 Weibull0.927090.42972 Bi-exponential0.948460.36331 Mean Rank RSD 0.986050.15517 0.864530.4685 0.930190.42177 0.943770.37985 Median Rank RSD Normal0.984190.17302 Log-Normal0.869010.48339 Weibull0.940040.41502 Bi-exponential0.943770.37985 The Rest Method RSD 0.983520.17899 0.870370.48743 0.943030.41164 0.933430.44388

36. Normal α = 0.05 Dn α =0.1612 Weibull, Bi- exponential α = 0.05 Dn α =0.1660 Normal α = 0.15 Dn α =0.1486 Weibull, Bi- exponential α = 0.15 Dn α =0.1436 n = 29 Data 3 : Value of D n α

37. K-S test : Symmetric Simple Cumulative Distribution Dash dot : α = 0.15 Line : α = 0.05 µ = 262.55 σ = 178.23 m = 0.80 ξ = 306.43 ξ = 156.01 x 0 = 332.30 Normal Weibull Bi-exponential

38. Mean Rank µ = 262.78 σ = 180.17 m = 0.80 ξ = 334.45 ξ = 167.50 x 0 = 351.75 Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

39. Median Rank Dash dot : α = 0.15 Line : α = 0.05 µ = 263.04 σ = 182.68 m = 0.86 ξ = 316.02 ξ = 159.24 x 0 = 350.33 Normal Weibull Bi-exponential

40. The Rest Method µ = 260.89 σ = 175.52 m = 0.87 ξ = 331.82 ξ = 157.23 x 0 = 350.62 Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

41. Data 3 : K-S Test Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Weibull XXXX Bi-exponential 000X

42. Data 1+2 N=47

43. Data 1+2: Symmetric Simple Cumulative Distribution Normal Log normal Weibull Bi-exponential

44. Data 1+2 : Mean Rank Normal Log normal Weibull Bi-exponential

45. Data 1+2 : Median Rank Normal Log normal Weibull Bi-exponential

46. Data 1+2 : The Rest Method Normal Log normal Weibull Bi-exponential

47. Linearity Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Log-Normal XXXX Weibull 0000 Bi-exponential 0000

48. Data 1+2 : R (Correlation Coefficient Comparaison) Symmetric.S.C RSD Normal0.976090.15421 Log-Normal0.858850.37466 Weibull0.960440.25098 Bi-exponential0.879640.43778 Median Rank RSD Normal0.978280.14319 Log-Normal0.856440.36809 Weibull0.956230.25496 Bi-exponential0.891210.40196 The Rest Method RSD 0.97760.14675 0.857340.37037 0.957870.25323 0.887410.41395 Mean Rank RSD 0.979950.13307 0.853040.36025 0.949640.26211 0.902530.36467

49. Data 1+2 : Value of D n α Normal α = 0.05 Dn α = 0,1282 Weibull, Bi- exponential α = 0.05 Dn α = 0,1332 Normal α = 0.15 Dn α = 0,111 Weibull, Bi- exponential α = 0.15 Dn α = 0,1175 n = 47

50. 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 x 0 = 372,16 Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

51. Data 1+2 : K-S Test (Mean Rank) µ = 292,44 σ = 178,25 m = 1.35 ξ = 343,13 ξ = 149,25 x 0 = 374,04 Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

52. Data 1+2 : K-S Test (Median Rank) µ = 292,18 σ = 172,41 m = 1.42 ξ = 340,09 ξ = 143,88 x 0 = 372,86 Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

53. Data 1+2 : K-S Test (The Rest Method) µ = 292,30 σ = 170,94 m = 1,44 ξ = 339,24 ξ = 142,45 x 0 = 372,63 Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

54. Data 1+2 : K-S Test Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Weibull XXXX Bi-exponential XXXX

55. Data 2+3 N=55 55

56. Log-Normal Normal Weibull Bi-Exponential Data 2+3 : Symmetric Simple Cumulative Distribution 56

57. Log-Normal Normal Weibull Bi-exponential Data 2+3 : Mean Rank 57

58. Log-Normal Normal Weibull Bi-exponential Data 2+3 : Median Rank 58

59. Log-Normal Normal Weibull Bi-exponential Data 2+3 : The Rest Method 59

60. Linearity Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Log-Normal XXXX Weibull 0000 Bi-exponential 0000 60

61. Symmetric.S.C RSD Normal0.978010.14793 Log-Normal0.749310.4995 Weibull0.896120.40745 Bi-exponential0.882090.43411 Median Rank RSD Normal0.981090.13404 Log-Normal0.742880.49423 Weibull0.881340.42199 Bi-exponential0.893760.39929 The Rest Method RSD 0.98010.13863 0.745090.49619 0.886430.41743 0.88990.4110 Mean Rank RSD 0.983810.1204 0.735640.48649 0.864680.43368 0.905440.36254 Data 2+3 : R (Correlation Coefficient Comparaison) 61

62. n = 55 Normal α = 0.05 Dn α = 0.119 Weibull, Bi- exponential α = 0.05 Dn α = 0.124 Normal α = 0.15 Dn α = 0.1035 Weibull, Bi- exponential α = 0.15 Dn α = 0.107 Data 2+3 : Value of D n α 62

63. 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 x 0 = 360.27 Dash dot : α = 0.15 Line : α = 0.05 63 Normal Weibull Bi-exponential

64. Data 2+3 : K-S Test (Mean Rank) µ = 319.2 σ = 200 m = 1.0349 ξ = 349.87 ξ = 147.05 x 0 = 360.29 Dash dot : α = 0.15 Line : α = 0.05 64 Normal Weibull Bi-exponential

65. Data 2+3 : K-S Test (Median Rank) µ = 328.4 σ = 200 m = 1.0855 ξ = 344.94 ξ = 142.86 x 0 = 362 Dash dot : α = 0.15 Line : α = 0.05 65 Normal Weibull Bi-exponential

66. Data 2+3 : K-S Test (The Rest Method) µ = 330 σ = 200 m = 1.1 ξ = 342.53 ξ = 140.84 x 0 = 359.97 Dash dot : α = 0.15 Line : α = 0.05 66 Normal Weibull Bi-exponential

67. Data 2+3 : K-S Test Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0XXX Weibull XXXX Bi-exponential 0000 67

68. Data 1+2+3 N=76

69. Data 1+2+3 : Symmetric Simple Cumulative Distribution 69 Log-Normal Normal Weibull Bi-Exponential

70. Data 1+2+3 : Mean Rank 70 Log-Normal Normal Weibull Bi-exponential

71. Data 1+2+3 : Median Rank 71 Log-Normal Normal Weibull Bi-exponential

72. Data 1+2+3 : The Rest Method 72 Log-Normal Normal Weibull Bi-exponential

73. Linearity Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Log-Normal XXXX Weibull 0000 Bi-exponential 0000 73

74. Symmetric.S.C RSD Normal0.990560.13213 Log-Normal0.882920.45247 Weibull0.952820.36607 Bi-exponential0.948380.38246 Median Rank RSD Normal0.988810.14718 Log-Normal0.888670.45249 Weibull0.960720.34544 Bi-exponential0.944950.39482 The Rest Method RSD 0.988360.15108 0.889580.4537 0.962610.34023 0.937290.43776 Mean Rank RSD 0.990120.13519 0.885640.44766 0.954350.36040 0.944950.39482 Data 1+2+3 : R (Correlation Coefficient Comparaison) 74

75. n = 76 Normal α = 0.05 Dn α =0.1018 Weibull, Bi- exponential α = 0.05 Dn α =0.1058 Normal α = 0.15 Dn α = 0.0884 Weibull, Bi- exponential α = 0.15 Dn α =0.0914 Data 1+2+3 : Value of D n α 75

76. 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 x 0 = 357.04 Dash dot : α = 0.15 Line : α = 0.05 76 Normal Weibull Bi-exponential

77. Data 1+2+3 : K-S Test (Mean Rank) µ = 281.28 σ = 172.29 m = 1.09 ξ = 345.17 ξ = 150.15 x 0 = 364.86 Dash dot : α = 0.15 Line : α = 0.05 77 Normal Weibull Bi-exponential

78. Data 1+2+3 : K-S Test (Median Rank) µ = 281.65 σ = 174.42 m = 1.14 ξ = 329.72 ξ = 146.41 x 0 = 363.10 Dash dot : α = 0.15 Line : α = 0.05 78 Normal Weibull Bi-exponential

79. 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 x 0 = 363.38 Dash dot : α = 0.15 Line : α = 0.05 79 Normal Weibull Bi-exponential

80. Data 1+2+3 : K-S Test Results Symmetric.S.CMean RankMedian Rank The Rest Method Normal 0000 Weibull XXXX Bi-exponential XXXX 80

81. 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 distributionC. D. F Data 1Normal distributionMean rank Data 2Weibull distributionSymmetric.S.C Data 3Normal distributionMean rank Data 1+2Normal distributionMean rank Data 2+3Bi-Exponential distributionMean rank Data 1+2+3Normal distributionSymmetric.S.C