Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Determination of MPFP of each kernel analysis in the original design space

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Estimation of MPFP of each kernel reliability analysis in the original design space

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Using EoGRA with N=50,000 to solve example 3 with Pf=30% and (a) normal, (b) uniform, (c) heart-shaped, (d) like-shaped, (e) star-shaped, and (f) corona-shaped distributions

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Using EoGRA with N=50,000 to solve example 3 with Pf=1% and (a) normal and (b) uniform distributions

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Using EoGRA with N=50,000 to solve example 2 with Pf=30% and (a) normal, (b) uniform, (c) heart-shaped, (d) like-shaped, (e) star-shaped, and (f) corona-shaped distributions

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Using EoGRA with N=50,000 to solve example 2 with Pf=1% and (a) normal, (b) uniform, (c) heart-shaped, (d) like-shaped, (e) star-shaped, and (f) corona-shaped distributions

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Using EoGRA with N=50,000 to solve example 1 with Pf=30% and (a) normal, (b) uniform, (c) heart-shaped, (d) like-shaped, (e) star-shaped, and (f) corona-shaped distributions

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Using EoGRA with N=50,000 to solve example 1 with Pf=1% and (a) normal, (b) uniform, (c) heart-shaped, (d) like-shaped, (e) star-shaped, and (f) corona-shaped distributions

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Iteration path of solving example 3 with like-shaped distribution and Pf=30% using EoGRA with N=50,000

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Iteration path of solving example 2 with corona-shaped distribution and Pf=30% using EoGRA with N=50,000

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Generated random distributions: (a) a heart-shaped distribution, (b) a like-shaped distribution, (c) a star-shaped distribution, and (d) a corona-shaped distribution. (Small dots represent the sampling points; the circle at the center represents the mean value of randomly distributed points; and dashed ellipses represent the ranges of 1σ, 2σ, and 3σ if treating the random points as normal distributions).

Date of download: 10/7/2017 Copyright © ASME. All rights reserved. From: An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses J. Mech. Des. 2016;138(7):071403-071403-14. doi:10.1115/1.4033548 Figure Legend: Results of photo enhancements: (a) original photo, (b) pixel distribution in CIELAB, (c) enhanced photo by treating image pixels as normally distributed (Pnorm  = 0.2811%), and (d) enhanced photo by EoGRA (PEoGRA  = 4.9485%)