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 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 provides information on life assessment strategies and conceptually illustrates the interplay of nondestructive evaluation (NDE) and fracture mechanics in the damage tolerant approach. It presents information on probability of detection (POD) and probability of false alarm (PFA). The article describes the damage tolerance approach to life management of cyclic-limited engine components and lists the commonly used nondestructive evaluation methods. It concludes with an illustration on the role of NDE, as quantified by POD, in fully probabilistic life management.

This article provides an overview of the structural design process and discusses the life-limiting factors, including material defects, fabrication practices, and stress. It details the role of a failure investigator in performing nondestructive inspection. The article provides information on fatigue life assessment, elevated-temperature life assessment, and fitness-for-service life assessment.

Life assessment of structural components is used to avoid catastrophic failures and to maintain safe and reliable functioning of equipment. The failure investigator's input is essential for the meaningful life assessment of structural components. This article provides an overview of the structural design process, the failure analysis process, the failure investigator's role, and how failure analysis of structural components integrates into the determination of remaining life, fitness-for-service, and other life assessment concerns. The topics discussed include industry perspectives on failure and life assessment of components, structural design philosophies, the role of the failure analyst in life assessment, and the role of nondestructive inspection. They also cover fatigue life assessment, elevated-temperature life assessment, fitness-for-service life assessment, brittle fracture assessments, corrosion assessments, and blast, fire, and heat damage assessments.

Risk and hazard analysis can be effectively used during design reviews to provide valuable feedback to the design to avoid failures. This article discusses the types of risks, namely, real risk, statistical risk, predicted risk, and perceived risk. It describes the principle and technical methods of risk/hazard analysis practiced in the industry to identify possible hazards and the resources necessary to avoid or reduce risks. These methods include the failure mode and effect analysis, fault tree analysis, event tree analysis, risk/benefit analysis, safety analysis, and probabilistic estimates.

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.

Both nondestructive testing (NDT) and nondestructive evaluation (NDE) use noninvasive measurement techniques to gain information about defects and various properties of materials, components, and structures. This article begins with a discussion on the historical development of quantitative measurement techniques, evaluation reliability, and quantitative interpretation of nondestructive inspection methods. The common nondestructive evaluation methods, along with their uses and limitations, are summarized in a table. The article conceptually illustrates the interplay of NDE and fracture mechanics in the damage tolerant approach. It concludes with information on pressure vessel applications that can be separated into three protocols used by military nuclear power, commercial nuclear power, and non-nuclear pressure vessels and/or fired boilers.

This article discusses corrosion fatigue, its effects on the damage tolerance of aircraft, and its predictive modeling. A conceptual framework is presented that incorporates two distinctive cyclic-based life-prediction philosophies and expands them both to include the time domain in order to consider the effects of corrosion. These philosophies include crack initiation used for safe-life design and crack growth used for damage tolerance. The article presents the methodology for computing the effects of real-time age degradation on an aircraft structure for two different corrosion types: crevice and pitting corrosion. It describes the rationale and techniques needed to apply the age-based structural integrity processes to in-service structures in order to realize the benefits throughout the full structural life cycle.

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.

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.

Aging is a process where the structural and/or functional integrity of components will be continuously degraded by exposure to the environmental conditions under which they are operated. This article discusses aging mechanisms in various components of military systems such as structural parts, engines, and subsystems. It describes the aging management processes such as full-scale structural testing and practical life-enhancement methods. The article reviews control and prevention systems such as usage and health monitoring systems necessary to provide effective corrosion maintenance on military systems. Failure prediction techniques, namely, the equivalent pre-crack size approach, life-cycle cost modeling and simulation, and holistic life-prediction methodology are also discussed.

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.

Fatigue properties are an integral part of materials comparison activities and offer information for structural life estimation in many engineering applications. This article presents three general approaches to fatigue design, with a discussion on their respective attributes. These include infinite-life criterion, finite-life criterion, and damage tolerant criterion. The article describes the individual property requirements of these approaches. It also presents selected examples of properties that reflect some detail of these approaches.

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.

The principal types of elevated-temperature mechanical failure are creep and stress rupture, stress relaxation, low- and high-cycle fatigue, thermal fatigue, tension overload, and combinations of these, as modified by environment. This article briefly reviews the applied aspects of creep-related failures, where the mechanical strength of a material becomes limited by creep rather than by its elastic limit. The majority of information provided is applicable to metallic materials, and only general information regarding creep-related failures of polymeric materials is given. The article also reviews various factors related to creep behavior and associated failures of materials used in high-temperature applications. The complex effects of creep-fatigue interaction, microstructural changes during classical creep, and nondestructive creep damage assessment of metallic materials are also discussed. The article describes the fracture characteristics of stress rupture. Information on various metallurgical instabilities is also provided. The article presents a description of thermal-fatigue cracks, as distinguished from creep-rupture cracks.

This article reviews the applied aspects of creep and stress-rupture failures. It discusses the microstructural changes and bulk mechanical behavior of classical and nonclassical creep behavior. The article provides a description of microstructural changes and damage from creep deformation, including stress-rupture fractures. It also describes metallurgical instabilities, such as aging and carbide reactions, and evaluates the complex effects of creep-fatigue interaction. The article concludes with a discussion on thermal fatigue and creep fatigue failures.

This article focuses on the subject of proactive or predictive maintenance with particular emphasis on the control and prediction of corrosion damage for life extension and failure prevention. It discusses creep life assessment from the perspective of creep-rupture properties and creepcrack growth. Practical methods based on replication and parametric approaches are also discussed.

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 fundamental variables involved in fatigue-life assessment, which describe the effects and interaction of material behavior, geometry, and stress history on the life of a component. It compares the safe-life approach with the damage-tolerance approach, which employs the stress-life method of fatigue life assessment. The article examines the behavior of three different metallic materials used in the design and manufacture of structural components: steel, aluminum, and titanium. It also reviews the effects of retardation and spectrum load on component life. The article concludes with case studies of fatigue life assessment from the aerospace industry.