This article provides an outline of the issues to consider in performing a probabilistic life assessment. It begins with an historical background and introduces the most common methods. The article then describes those methods covering subjects such as the required random variable definitions, how uncertainty is quantified, and input for the associated random variables, as well as the characterization of the response uncertainty. Next, it focuses on specific and generic uncertainty propagation techniques: first- and second-order reliability methods, the response surface method, and the most frequently used simulation methods, standard Monte Carlo sampling, Latin hypercube sampling, and discrete probability distribution sampling. Further, the article discusses methods developed to analyze the results of probabilistic methods and covers the use of epistemic and aleatory sampling as well as several statistical techniques. Finally, it illustrates some of the techniques with application problems for which probabilistic analysis is an essential element.

Most modern instrumental techniques produce an output or signal that is not absolute. To obtain quantitative information, the raw output from an instrument must be converted into a physical quantity. This is done by standardizing or calibrating the raw response from an instrument and subsequently analyzing the uncertainty from both the calibration process and the measurement process. This article briefly summarizes the most common calibration and uncertainty analysis methods, namely external standard methods, abbreviated external standard methods, internal normalization, internal standard, standard addition, and serial dilution methods. In addition, it includes information on the traceability of true value of a measured quantity.

This article provides a comprehensive review and critical assessment of numerical modeling of heat and mass transfer in fusion welding. The different fusion welding processes are gas tungsten arc welding, gas metal arc welding, laser welding, electron beam welding, and laser-arc hybrid welding. The article presents the mathematical equations of mass, momentum, energy, and species conservation. It reviews the applications of heat transfer and fluid flow models for different welding processes. Finally, the article discusses the approaches to improve reliability of, and reduce uncertainty in, numerical models.

This article presents an approach to manage the uncertainty present in materials design. It describes inductive and deductive approaches to deal with uncertainty. The article focuses on providing an understanding of the opportunities for managing uncertainty and the decisions that influence the accuracy of the results. A design of experiments (DOE) represents a sequence of experiments to be performed, expressed in terms of factors set at specified levels. The article discusses the two types of DOEs: the full factorial design and the fractional factorial design. It explains the factors to be considered when selecting a procedure for propagating uncertainty. The article lists the categories of the popular types of uncertainty propagation methods, including simulation-based methods, local expansion methods, and numerical integration-based methods.

Neural networks permit the discovery of fundamental relationships and quantitative structure within vast arrays of ill-understood data. This article provides an overview of neural network modeling method, describing its overfitting nature. It discusses the use of neural networks in modeling noise and uncertainties in conducting experiments. The article also presents examples of the application of neural-network modeling to the behavior of metals.

This article discusses some of the statistical aspects of design from an engineer's perspective. It reviews the commonly used statistical terms and distributions for providing some guidance on the practical engineering applications of these distributions. The article describes the basic statistical procedures that can be used to address variability and uncertainty in an engineering analysis. It contains a table that lists the relevant statistics standards published by the American Society of Testing and Materials.

There are two parts to deal with uncertainty in fatigue design: determining the distributions of possible values for all uncertain inputs and calculating the probability of failure due to all the uncertain inputs. This article discusses the sources of uncertainty in a fatigue analysis, such as the material properties, distribution of applied stress levels within a given environment, environments or loading intensities, and modeling or prediction. It presents a probabilistic approach for analyzing the uncertainties and determining the level of reliability (probability of failure).