The Book Starts With The Basic Theory In Uncertainty Propagation Using Monte Carlo Methods And The Generation Of Random Variables And Stochastic Processes For Some Common Distributions Encountered In Engineering Applications. It Then Introduces A Class Of Powerful Simulation Method Called Markov Chain Monte Carlo Method (Mcmc), An Important Machinery Behind Subset Simulation That Allows One To Generate Samples For Investigating Rare Scenarios In A Probabilistically Consistent Manner. The Theory Of Subset Simulation Is Then Presented, Addressing Related Practical Issues Encountered In The Actual Implementation. A Number Of Variants Of Subset Simulation That Can Lead To Improved Performance For Specific Classes Of Problems Will Also Be Covered. The Second Half The Book Introduces The Reader To Probabilistic Failure Analysis And Reliability - Based Design, Which Are Laid Out In A Context That Can Be Efficiently Tackled Within The Context Of Subset Simulation Or Monte Carlo Simulation In General. The Result Is A General Framework That Allows The Practitioner To Investigate Reliability Sensitivity To Uncertain Parameters And To Explore Possible Design Scenarios Systematically For Selection Of The Final Design In A Convenient But Computationally Efficient Manner Via Simulation. A Unique Feature Of This Book Is That It Is Complemented With A Vba (Visual Basic For Applications) That Implements Subset Simulation In The Excel Spreadsheet Environment. This Allows The Reader To Experiment With The Examples In The Book And Get Hands - On Experience With Simulation. A Chapter Is Devoted To The Software Framework That Allows A Practical Solution By Resolving The Risk Assessment Problem Into Three Uncoupled Procedures, Namely, Deterministic Modeling, Uncertainty Modeling And Uncertainty Propagation