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 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.

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.

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).

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.

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.

This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering, selection of a probability distribution, the failure model definition, and a definition of the probability of failure. The article also explains the solution techniques for special cases and general solution techniques, such as first-second-order reliability methods, the advanced mean value method, the response surface method, and Monte Carlo sampling. A brief introduction to importance sampling, time-variant reliability, system reliability, and risk analysis and target reliabilities is also provided. The article examines the various application problems for which probabilistic analysis is an essential element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis.

The process of fatigue failure consists of three stages: initial fatigue damage leading to crack initiation; crack propagation to some critical size; and final, sudden fracture of the remaining cross section. Variations in mechanical properties, composition, microstructure, and macrostructure, along with their subsequent effects on fatigue life, have been studied extensively to aid in the appropriate selection of steel to meet specific end-use requirements. The metallurgical variables having the most pronounced effects on the fatigue behavior of carbon and low-alloy steels are strength, ductility, cleanliness, residual stresses, surface conditions, and aggressive environments. The article discusses the stress-based and strain-based approach to fatigue. The application of fatigue data in engineering design is complicated by the characteristic scatter of fatigue data; variations in surface conditions of actual parts; variations in manufacturing processes such as bending, forming, and welding; and the uncertainty of environmental and loading conditions in service.

Probability of detection (POD) assesses the performance of a non-destructive evaluation (NDE)-based inspection, which is a method used to determine the capability of an inspection as a function of defect type and defect size. This article provides an overview of the concept of POD, why it is needed, the history behind the development of POD, how POD assessments are performed, and how modeling and simulation can be integrated into the execution of a POD assessment. It describes the methods by which POD is determined. This includes detail on the experimental process to acquire the needed data, the mathematical methods to obtain a POD curve, and techniques to assess uncertainty in the POD curve as it is obtained from a limited data set. The concept of model-assisted POD (MAPOD) is introduced, with additional details and representative examples of MAPOD.

This article is a detailed account of the principles of electron-excited X-ray microanalysis. It begins by discussing the physical basis of electron-excited X-ray microanalysis and the advantages and limitations of energy dispersive spectrometry (EDS) and wavelength dispersive spectrometry for electron probe microanalysis. Key concepts for performing qualitative analysis and quantitative analysis by electron-excited X-ray spectrometry are then presented. Several sources that lead to measurement uncertainties in the k-ratio/matrix corrections protocol are provided, along with the significance of the raw analytical total. Sections on accuracy of the standards-based k-ratio/matrix corrections protocol with EDS and processes of analysis when severe peak overlap occurs are also included. The article provides information on low-atomic-number elements, iterative qualitative-quantitative analysis for complex compositions, and significance of standardless analysis in the EDS software. It ends with a section on the processes involved in elemental mapping for major and minor constituents.