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.

Reliability is a measure of the capacity of equipment or systems to operate without failure in the service environment. This article focuses on reliability in design and presents equations governing the instantaneous failure rate, general reliability function, mean time to failure, mean time between failures, and useful life period. The article describes the calculation of reliabilities for series and parallel arrangements of a complex system. It provides a comparison of probabilistic and deterministic design and concludes with a discussion on reliability growth.

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 presents definitions, equations, and notational conventions that are used widely in statistical analysis. It provides information on a basic framework for the selection of a statistical test. The article outlines the basic elements common to all statistical tests. Illustrations of specific statistical tests and the concept of confidence limits are introduced. The article provides an overview of sampling issues, with guidance on both selecting a sampling method and determining the number of units to sample. One-way analysis of the variance, correlation, and simple regression are also illustrated.

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.

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 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 primarily considers the problem of sampling bulk materials, including minerals, metals, environmentally important substances, and industrial raw materials and waste products. It provides useful information on sample types, sampling plan, optimizing sampling resources, practical aspects of sampling, and how to ensure the quality of sampling.

This article describes a scientific approach to the planning and evaluation of fatigue tests based on the determination of probabilities for detected fracture positions within the observed range of fatigue scatter. It schematically illustrates a constant-amplitude stress cycling about a possible mean load that leads to the fracture of a single part or specimen. The article discusses the evaluation of the range of transition and of the finite-endurance range for fatigue curves. It concludes with a discussion on extrapolation from the range of finite endurance into the range of transition.

Electron spin resonance (ESR), or electron paramagnetic resonance (EPR), is an analytical technique that can extract a great deal of information from any material containing unpaired electrons. This article explains how ESR works and where it applies in materials characterization. It describes a typical ESR spectrometer and explains how to tune it to optimize critical electromagnetic interactions in the test sample. It also identifies compounds and elements most suited for ESR analysis and explains how to extract supplementary information from test samples based on the time it takes electrons to return to equilibrium from their resonant state. Two of the most common methods for measuring this relaxation time are presented as are several application examples.

Nondestructive testing (NDT), also known as nondestructive evaluation (NDE), includes various techniques to characterize materials without damage. This article focuses on the typical NDE techniques that may be considered when conducting a failure investigation. The article begins with discussion about the concept of the probability of detection (POD), on which the statistical reliability of crack detection is based. The coverage includes the various methods of surface inspection, including visual-examination tools, scanning technology in dimensional metrology, and the common methods of detecting surface discontinuities by magnetic-particle inspection, liquid penetrant inspection, and eddy-current testing. The major NDE methods for internal (volumetric) inspection in failure analysis also are described.