Download presentation
Presentation is loading. Please wait.
Published byGwendolyn Terry Modified over 9 years ago
1
MAE430 Reliability Engineering in ME Term Project II Jae Hyung Cho 20101103 Andreas Beckmann 20156476
2
Contents Project I results summary Results using theoretical probability distribution Results using the graphical procedure Conclusion 2
3
Contents Project I results summary Results using theoretical probability distribution Results using the graphical procedure Conclusion 3
4
Project I results summary Jae Hyung’s Data Set (n = 63) –Best fitting distribution: Biexponential Distribution –Best CDF estimation method: Median Rank Andreas’s Data Set (n = 59) –Best fitting distribution: Weibull Distribution –Best CDF estimation method: Symmetric S. C. D. 4
5
Contents Project I results summary Results using theoretical probability distribution Results using the graphical procedure Conclusion 5
6
Strength and Stress 6 42207371440 60225380449 96232386449 96233390461 114235393468 130239393473 132239399484 134259400490 150262405499 150268410506 159299412514 186305413527 187306414544 188315415546 194340422606 205345435 Strength 16139281428 27140292430 30151313441 30152314446 40154323450 49157325460 53168336463 81175360488 87189364513 89207384513 93209398547 99236408561 108238421573 123240423601 134242424 Stress
7
Calculation of PDF Using Wolfram Alpha 7 Strength: Biexponential CDF calculation: Median Rank ξ = 118.9061 X0 = 391.3413 Strength: Weibull CDF calculation: Symmetric S.C.D. m = 1.41297 ξ = 308.2052
8
Theoretical probability distribution 8 Strength Stress
9
Numerical Integration Using Matlab 9 >> f = @(x)(1-exp(-exp((x-391.3413)/118.9061))).*(0.000430008.*exp(-0.000304329.*( x.^1.41297)).*(x.^0.41297)); >> P_f = integral(f, 0, Inf) P_f = 0.3792 >> g = @(x)(1-exp(-(x/308.2052).^(1.41297))).*(0.000312936*exp(-0.0372099.*exp(0.0 0841*x)+0.00841*x)); >> R = integral(g, 0, Inf) R = 0.6208 Stress-basedStrength-based The two formulas yield the same result !
10
10 % f_stress_smaller0 = 0; % F_stress_smaller0 = 0; % f_stress_larger0 = 0.000430008.*exp(-0.000304329.*(x.^1.41297))*(x.^0.41297); % F_stress_larger0 = 1-exp(-(x./308.2052).^(1.41297)); % f_strength = 0.000312936.*exp(-0.0372099.*exp(0.00841.*x)+0.00841.*x); % F_strength = 1-exp(-exp((x-391.3413)/118.9061)); % term_for_R_smaller0 = (f_strength * F_stress_smaller0); % term_for_R_larger0 = (f_strength * F_stress_larger0); integrand_R_smaller0 = @(x) 0.000312936.*exp(-0.0372099.*exp(0.00841.*x)+0.00841.* x).* 0; integrand_R_larger0 = @(x) (0.000312936.*exp(-0.0372099.*exp(0.00841.*x)+0.00841.* x)).* (1-exp(-(x./308.2052).^(1.41297))); integrand_Pf_smaller0 = @(x) 0.* ( 1-exp(-exp((x-391.3413)./118.9061))); integrand_Pf_larger0 = @(x) (0.000430008.*exp(-0.000304329.*(x.^1.41297)).*(x.^0.4 1297)).* (1-exp(-exp((x-391.3413)./118.9061))); R = integral(integrand_R_smaller0, -inf, 0) + integral(integrand_R_larger0, 0, i nf) Pf = integral(integrand_Pf_smaller0, -inf, 0) + integral(integrand_Pf_larger0, 0, inf) R = 0.620773031855217 Pf = 0.379229034575878 0.6208 + 0.3792 = 1
11
Contents Project I results summary Results using theoretical probability distribution Results using the graphical procedure Conclusion 11
12
12
13
13
14
14
15
15
16
16
17
17
18
18
19
19
20
20 Theoretical LowerUpperTriangle Theoretical LowerUpperTriangle Most conservative values
21
Contents Project I results summary Results using theoretical probability distribution Results using the graphical procedure Conclusion 21
22
Conclusion 22
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.