Intro -- Acknowledgements -- Author biographies -- Melanie Po-Leen Ooi -- Arvind Rajan -- Ye Chow Kuang -- Serge Demidenko -- Nomenclature -- Outline placeholder -- Greek symbols -- Other symbols -- Acronyms/abbreviations -- Chapter 1 Introduction -- References -- Chapter 2 Uncertainty propagation -- 2.1 Averaging methods for estimating the measurand in nonlinear models -- 2.2 First-order linearisation and the normality assumption -- 2.3 The Monte Carlo method -- 2.4 The use of a mathematical representation of the probability density function -- 2.5 Uncertainty evaluation using moments -- 2.5.1 The normal distribution -- 2.5.2 The Cornish-Fisher expansion -- 2.5.3 The extended generalised lambda distribution -- 2.5.4 Tukey's gh distribution -- 2.5.5 The Pearson distribution -- 2.5.6 The Johnson distribution -- 2.5.7 The maximum entropy method -- 2.6 Summary -- References -- Chapter 3 Probabilistic design optimisation -- 3.1 Robust design optimisation -- 3.1.1 The univariate dimension reduction method -- 3.1.2 The performance moment integration method -- 3.2 Reliability-based design optimisation -- 3.2.1 Most probable point-based methods -- 3.2.2 The Monte Carlo method -- 3.2.3 Metamodels with direct sampling methods -- 3.2.4 Moment-based methods for RBDO -- 3.3 Reliability-based robust design optimisation -- 3.4 Summary -- References -- Chapter 4 Moment-based standard uncertainty in design optimisation -- 4.1 The derivation of the analytical moments of multivariate polynomials -- 4.1.1 The Mellin transform and the product of independent random variables -- 4.1.2 Applying the Mellin transform to analytical moments of multivariate polynomials -- 4.1.3 Moment calculation for positive-order variables, m∈Z+ -- 4.1.4 Moment calculation for negative-order variables, m∉Z+ -- 4.1.5 Extension to high-dimensional correlated variables.

4.2 A toolbox for moment-based standard uncertainty evaluation -- 4.3 Case studies for moment-based analytical standard uncertainty evaluation -- 4.3.1 Case study 1-monomial: magnetic force microscope -- 4.3.2 Case study 2-simple polynomial: microwave meter calibration -- 4.3.3 Case study 3-high-order Taylor series approximation: eddy current measurement -- 4.4 A general framework for analytical moment-based reliability and robustness analysis -- 4.5 Summary -- References and further reading -- Chapter 5 Moment-based expanded uncertainty evaluation in design optimization -- 5.1 The improved moment-constrained maximum entropy method -- 5.1.1 Setting the zero mean and unit variance -- 5.1.2 Finding integral limits -- 5.1.3 The modified Gram-Schmidt algorithm for polynomial orthogonalisation -- 5.2 Test distributions for benchmarking and performance analysis -- 5.2.1 Unimodal distributions -- 5.2.2 Multimodal distributions -- 5.2.3 A performance assessment framework that uses the benchmark test distributions -- 5.3 Reliability analysis of parametric distribution-fitting techniques: from unimodal to multimodal distributions -- 5.3.1 Unimodal distributions with four moments -- 5.3.2 Unimodal distributions with more than four moments -- 5.3.3 Multimodal distributions -- 5.3.4 Reliable regions for Tukey's gh method and the Cornish-Fisher technique -- 5.4 A toolbox for the MaxEnt algorithm -- 5.5 Summary -- References -- Chapter 6 Real-world design optimisation problems: applications and usefulness -- 6.1 The framework for probabilistic design optimisation -- 6.1.1 Local response surface modelling using multivariate polynomials -- 6.1.2 The selective sampling technique -- 6.2 Lithium-ion batteries: a reliability-based design optimisation framework -- 6.2.1 The finite element model of the lithium-ion battery.

6.2.2 Incorporating moment-based uncertainty evaluation -- 6.2.3 The resultant design -- 6.3 Vehicle design based on side-impact crashworthiness: the application of a reliability-based robust design optimisation problem -- 6.3.1 Problem formulation -- 6.3.2 Resultant design -- 6.4 Fuel cells: parameter optimisation for reliable and robust operation -- 6.4.1 Problem formulation -- 6.4.2 Sensitivity analysis -- 6.4.3 Determination of the optimal operating conditions for RBDO and RBRDO -- 6.5 Magnetic sensor module design -- 6.5.1 Problem formulation -- 6.5.2 The results of the PolyMoment-based RBDO method -- 6.6 A multistorey three-dimensional steel structure: reliability analysis and optimisation -- 6.6.1 Problem formulation -- 6.6.2 The resultant design and benchmarking -- 6.7 Summary -- References -- Chapter -- Reference -- Chapter -- References.