10.26180/5b8375b2794a9 ARVIND RAJAN ARVIND RAJAN Moment-Based Uncertainty Propagation Using Multivariate Polynomials: Advances in Probabilistic Engineering Design Monash University 2018 Uncertainty Measurement Mellin Transform Polynomials Method of Moments Maximum Entropy Method Probability Density Function Reliability Analysis Robustness Analysis Reliability-Based Design Optimisation Reliability-Based Robust Design Optimisation Robust Design Optimisation Engineering Design Cumulative Distribution Function Random Variable Performance-Based Design Probability Theory Probability Statistics Manufacturing Safety and Quality Entropy Electrical and Electronic Engineering not elsewhere classified Optimisation Performance Evaluation; Testing and Simulation of Reliability Applied Statistics Design 2018-08-27 03:53:20 Thesis https://bridges.monash.edu/articles/thesis/Moment-Based_Uncertainty_Propagation_Using_Multivariate_Polynomials_Advances_in_Probabilistic_Engineering_Design/6998936 The research embarked on an adventurous journey five years ago to synthesise a novel and effective framework for the probabilistic analyses of engineering systems. The framework took the unpopular approach of using statistical moments to enable both better accuracy and much faster computation compared to the mainstream methods. Crucial theoretical developments in mathematical statistics became the key to unlock the full potential of the moment approach; which in turn, has led to the design of more economical yet safe real-world systems across multiple engineering disciplines, especially in the mission-critical projects where reliability and safety are the principal objectives.