The six types of statistical distributions are normal distribution, log normal distribution, Weibull distribution, exponential distribution, binomial distribution, and Poisson distribution. This article discusses the applicability of each distribution, providing information on the probability density function, cumulative distribution function, population mean and variance, and parameter and percentile estimation.

This article details factors that have been used for evaluating the susceptibility of alloys to stress-corrosion cracking. Many considerations impacting the validity and accuracy of information gathered from laboratory testing programs are reviewed. The article highlights the main characteristics of probability distributions, such as normal distribution, log-normal distribution, exponential distribution, Poisson distribution, and extreme-value distribution. It also provides information on the statistical concepts to produce effective test programs.

Spray casting, also known as spray forming, is a niche casting process for the manufacture of preforms. This article lists commercial examples of alloys manufactured by spray casting and provides sequential steps of the spray casting process. Gas atomization is a chaotic, stochastic process that always produces a wide range of droplet diameters. The article schematically illustrates a typical log-normal droplet diameter probability density distribution on a mass or volume basis obtained by gas atomization. It also explains the changes in solid fraction during the spray casting process as a function of axial distance from the point of droplet atomization. The article concludes with information on the occurrence of macrosegregation and coarsening in spray cast preforms.

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 reviews the planning of fatigue experiments, including the structure of a test plan, randomization, and nuisance variables. The statistical characterization of the S/N (stress/life) or e/N (strain/life) response of a single material tested under a single condition is discussed. The techniques for defining a mean fatigue curve and evaluating scatter or variability about that mean are explained. The article presents the standard techniques for statistical characterization of the fatigue strength or fatigue limit of a single material by use of the Probit method, the up-and-down (staircase) method, and two-point procedures. Stress-level selection methods are also presented. The article discusses the comparison of the fatigue behavior of two or more materials for data generated at a single stress or strain level. Treatments to compare data generated over a range of stress or strain levels are included. The article also summarizes the consolidation of fatigue data generated at different conditions.

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 describes design factors for products used in engineering applications. The article groups these factors into three categories: functional requirements, analysis of total life cycle, and other major factors. These categories intersect and overlap, constituting a major challenge in engineering design. Performance specifications, risk and hazard analysis, design process, design for manufacture and assembly, design for quality, reliability in design, and redesign are considered for functional requirements. Life-cycle analysis considers raw-material extraction from the earth and product manufacture, use, recycling (including design for recycling), and disposal. The other major factors considered include evaluation of the current state of the art for a given design, designing to codes and standards, and human factors/ergonomics.

This article describes concepts and tools that can be used by the failure analyst to understand and address deformation, cracking, or fracture after a stress-related failure has occurred. Issues related to the determination and use of stress are detailed. Stress is defined, and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear elastic fracture mechanics analysis, with some mention of elastic-plastic fracture mechanics analysis. The article describes the probabilistic aspects of fatigue and fracture. Information on crack-growth simulation of the material is also provided.

The microstructure that develops during the solidification stage of cast iron largely influences the subsequent solid-state transformations and mechanical properties of the cast components. This article provides a brief introduction of methods that can be used for simulating the solidification microstructure of cast iron. Analytical as well as numerical models describing solidification phenomena at both macroscopic and microscopic scales are presented. The article introduces macroscopic transport equations and presents analytical microscopic models for solidification. These models include the dendrite growth models and the cooperative eutectic growth models. The article provides some solutions using numerical models to simulate the kinetics of microstructure formation in cast iron. It concludes with a discussion on cellular automaton (CA) technique that can handle complex topology changes and reproduce most of the solidification microstructure features observed experimentally.

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 describes the metallurgy and process specifics of subcritical annealing, which involves heating below the lower critical temperature such that austenite does not form during subcritical annealing. It provides information on the nominal subcritical annealing temperatures of plain carbon, low-alloy and high-alloy steels and temperature-time relations of subcritical annealing. Practical implications for induction annealing and induction normalizing are included. The article concludes by describing induction softening, which softens the threaded area on carburized components such as hypoid pinion gears, to prevent the occurrence of delayed fractures from occurring.

In the design of composite structures for durability and damage tolerance, the primary concerns are out-of-plane failures, such as delamination, material degradation associated with environment, stability under compression loading, large degree of scatter in fatigue life, and bearing failure of joints. This article presents an introductory discussion on the fatigue damage process, methodologies assessing fatigue behavior, and life prediction models. It describes the damage mechanisms introduced for a quasi-isotropic laminate under tension-compression fatigue loading. Delamination is a critical issue in fatigue and generally results from high interlaminar normal and shear stresses. The article schematically illustrates the structural elements in which high interlaminar stresses are common. It concludes with a discussion on the classification of fatigue models such as mechanistic or phenomenological, for composite materials under cyclic loading.

This article discusses the production of aluminum and aluminum alloy powders with emphasis on the gas atomization method and the atomizing nozzle. It illustrates the particle formation mechanism and details the requisites for particle size distribution, control, and morphology. The article presents information on the mean oxide thickness formed on atomized powders. It also describes the mechanical and physical properties of aluminum and aluminum alloy powders, as well as their applications.

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.

This article provides an overview of the general methods of metal powder production. It details the primary methods for particle sizing used in additive manufacturing: sieving, laser diffraction and scattering, and digital image analysis. Methods of interpreting and understanding particle size distribution (PSD) data are presented, with an emphasis on the differences between count- and volume-based PSDs. The article then outlines practices for both qualitative and quantitative assessment of particle morphology.