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.

The influence of friction and wear on the function and structure of tribological systems is determined by various types of tribological tests. This article introduces the general categories of tribological testing and describes the basic objectives of testing. It reviews the results of tribological tests, where the system-dependent characteristics of friction and wear data can be expressed in different forms, such as tribographs, transition diagrams, and tribomaps. A summary of various methods of surface analysis is presented in a table. The article discusses the relationship between wear and reliability in terms of exponential distribution, Weibull distribution, and gamma distribution. It concludes with information on the effects of interaction on failure probability.

Brittle materials, such as ceramics, intermetallics, and graphites, are increasingly being used in the fabrication of lightweight components. This article focuses on the design methodologies and characterization of certain material properties. It describes the fundamental concepts and models associated with performing time-independent and time-dependent reliability analyses for brittle materials exhibiting scatter in ultimate strength. The article discusses the two-parameter and three-parameter Weibull distribution for representing the underlying probability density function for tensile strength. It reviews life prediction reliability models used for predicting the life of a component with complex geometry and loading. The article outlines reliability algorithms and presents several applications to illustrate the utilization of these reliability algorithms in structural applications.

Knowledge of fatigue behavior at the laminate level is essential for understanding the fatigue life of a laminated composite structure. This article describes fatigue failure of composite laminates in terms of layer cracking, delamination, and fiber break and interface debonding. It discusses the fatigue behavior of composite laminates in the form of a relation between applied maximum fatigue stress and fatigue life. The article explains Weibull distribution and parameters estimation for fatigue data analysis and life prediction of composite laminates. It analyzes the fatigue properties and damage tolerance of fiber-metal laminates such as ARALL and GLARE laminates. The article concludes with a discussion on the effects of fatigue on notched and unnotched specimens.

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 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.

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 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.

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.

Contact fatigue is a surface-pitting-type failure commonly found in ball or roller bearings. This article discusses the mechanisms of contact fatigue found in gears, cams, valves, rails, and gear couplings. It discusses the statistical analysis of rolling contact bearing-life tests. The article concludes with information on various approaches that improve the contact fatigue resistance of rolling contact systems.

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 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 discusses the need for design allowables, development of design allowables, and important factors that affect the selection of the allowable. It provides a comparison between lamina and laminate allowables. The article discusses laminate results and specific techniques used in the statistical development of allowable values.

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.

Corrosion, fatigue, and their synergistic interactions are among the principal causes of damage to aircraft structures. This article describes aircraft corrosion fatigue assessment in the context of different approaches used to manage aircraft structural integrity, schedule aircraft inspection intervals, and perform repair and maintenance of aircraft in service. It illustrates the types of corrosive attack observed in aircraft structures, including uniform, galvanic, pitting, filiform, fretting, intergranular, exfoliation corrosion, and stress-corrosion cracking. The article discusses geometric parameters such as pit dimensions, surface roughness, loss of metal thickness, and volume increase due to pillowing to quantitatively characterize the types of corrosion. It also explains the two most common fatigue life assessment methods used in the military aerospace industry: fatigue crack initiation and crack growth analysis.

The design process for ceramic materials is more complex than that of metals because of low-strain tolerance, low fracture toughness and brittleness. The application of structural ceramics to engineering systems hinges on the functional benefits to be derived and is manifested in the conceptual design for acceptable reliability. This article discusses the design considerations for the use of structural ceramics for engineering applications. It describes the conceptual design and deals with fast fracture reliability, lifetime reliability, joints, attachments, interfaces, and thermal shock in detailed design procedure. The article provides information on the proof testing of ceramics, and presents a short note on public domain software that helps determine the reliability of a loaded ceramic component. The article concludes with several design scenarios for gas turbine components, turbine wheels, ceramic valves, and sliding parts.

This article provides an overview of the steps that are used in ceramics processing and related mechanical design considerations. It discusses various design approaches, such as the empirical design, the deterministic design, and the probabilistic design. The article presents a general process design flowchart for ceramic processing. Information on traditional ceramics and advanced ceramics is also provided. The article describes various ceramic forming processes, such as wet processing, plastic forming, dry processing, and machining. The factors for evaluating different ceramic forming processes are summarized in a table. The article discusses vitrification and sintering that generally pertain to ceramic firing and concludes with a discussion on firing process factors.

This article provides information on the nominal compositions of high-carbon bearing steels and carburizing bearing steels. It discusses the bearing fundamentals with emphasis on surface contact, stresses, and fatigue life of bearings. The article describes bearing life prediction using three factors, namely, reliability, material, and application. It analyzes the bearing damage modes and concludes with information on fatigue failure considerations.

Rolling-element bearings, also called rolling bearings and antifriction bearings, tend to have very low friction characteristics compared to plain bearings or simple sliding bearings. This article discusses the types of rolling-element bearings, namely, ball bearings and roller bearings. It provides information on the bearing component materials. The article describes the lubrication requirements and lubrication methods, namely, elastohydrodynamic lubrication and grease lubrication. It reviews the adjustment factors influencing fatigue life of the bearing. The article also provides information on bearing load ratings, standard bearing geometries, rolling bearing friction factors, and wear and its control methods. It concludes with a discussion on damage modes of bearings.