Reliability Project 1 Team 9 Philippe Delelis Florian Brouet SungHyeok Lee

Data 1 N=21 2

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 Normal Log normal Weibull Bi-exponential

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

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

Data 1 : R (Correlation Coefficient Comparaison) Symmetric.S.C RSD Normal Log-Normal Weibull Bi-exponential Mean Rank RSD Median Rank RSD Normal Log-Normal Weibull Bi-exponential The Rest Method RSD

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

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

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

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

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

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

Data 2 N=26 16

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

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

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

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

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

Symmetric.S.C RSD Normal Log-Normal Weibull Bi-exponential Median Rank RSD Normal Log-Normal Weibull Bi-exponential The Rest Method RSD Mean Rank RSD Data 2 : R (Correlation Coefficient Comparaison) 22

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

K-S test : Symmetric Simple Cumulative Distribution µ = σ = m = ξ = ξ = 125 x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

Data 2 : Mean Rank µ = σ = m = ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

Data 2 : Median Rank µ = σ = m = 1.84 ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

Data 2 : The Rest Method µ = σ = m = 1.81 ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

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

Data 3 N=29 29

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

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

Data 3 : Median rank Normal Log normal Weibull Biexponential

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

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

Data 3 : R (Correlation Coefficient Comparaison) Symmetric.S.C RSD Normal Log-Normal Weibull Bi-exponential Mean Rank RSD Median Rank RSD Normal Log-Normal Weibull Bi-exponential The Rest Method RSD

Normal α = 0.05 Dn α = Weibull, Bi- exponential α = 0.05 Dn α = Normal α = 0.15 Dn α = Weibull, Bi- exponential α = 0.15 Dn α = n = 29 Data 3 : Value of D n α

K-S test : Symmetric Simple Cumulative Distribution Dash dot : α = 0.15 Line : α = 0.05 µ = σ = m = 0.80 ξ = ξ = x 0 = Normal Weibull Bi-exponential

Mean Rank µ = σ = m = 0.80 ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

Median Rank Dash dot : α = 0.15 Line : α = 0.05 µ = σ = m = 0.86 ξ = ξ = x 0 = Normal Weibull Bi-exponential

The Rest Method µ = σ = m = 0.87 ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = 0.05 Normal Weibull Bi-exponential

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

Data 1+2 N=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 Normal Log normal Weibull Bi-exponential

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

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

Data 1+2 : R (Correlation Coefficient Comparaison) Symmetric.S.C RSD Normal Log-Normal Weibull Bi-exponential Median Rank RSD Normal Log-Normal Weibull Bi-exponential The Rest Method RSD Mean Rank RSD

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

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

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

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

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

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

Data 2+3 N=55 55

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

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

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

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

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

Symmetric.S.C RSD Normal Log-Normal Weibull Bi-exponential Median Rank RSD Normal Log-Normal Weibull Bi-exponential The Rest Method RSD Mean Rank RSD Data 2+3 : R (Correlation Coefficient Comparaison) 61

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

Data 2+3 : K-S Test (Symmetric Simple Cumulative Distribution) µ = σ = m = ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

Data 2+3 : K-S Test (Mean Rank) µ = σ = 200 m = ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

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

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

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

Data N=76

Data : Symmetric Simple Cumulative Distribution 69 Log-Normal Normal Weibull Bi-Exponential

Data : Mean Rank 70 Log-Normal Normal Weibull Bi-exponential

Data : Median Rank 71 Log-Normal Normal Weibull Bi-exponential

Data : The Rest Method 72 Log-Normal Normal Weibull Bi-exponential

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

Symmetric.S.C RSD Normal Log-Normal Weibull Bi-exponential Median Rank RSD Normal Log-Normal Weibull Bi-exponential The Rest Method RSD Mean Rank RSD Data : R (Correlation Coefficient Comparaison) 74

n = 76 Normal α = 0.05 Dn α = Weibull, Bi- exponential α = 0.05 Dn α = Normal α = 0.15 Dn α = Weibull, Bi- exponential α = 0.15 Dn α = Data : Value of D n α 75

Data : K-S Test (Symmetric Simple Cumulative Distribution) µ = σ = m = 1.09 ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

Data : K-S Test (Mean Rank) µ = σ = m = 1.09 ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

Data : K-S Test (Median Rank) µ = σ = m = 1.14 ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

Data : K-S Test (The Rest Method) µ = σ = m = 1.15 ξ = ξ = x 0 = Dash dot : α = 0.15 Line : α = Normal Weibull Bi-exponential

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

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