Failure analysis can sometimes involve considerations of statistics and probability. This chapter reviews some of the basic types of statistical distributions in order to understand some basic principles in their use. The main focus is on the uses of the normal distribution, which is the most commonly used statistical distribution. The chapter also includes a section discussing the reliability and probability of passing.

This chapter provides an introduction to statistical process control and the concept of total quality management. It begins with a review of quality improvement efforts in the extrusion industry and the considerations involved in developing sampling plans and interpreting control charts. It then lays out the steps that would be followed in order to implement statistical testing for billet casting, die performance, or any other process or variable that impacts extrusion quality. The chapter concludes with an overview of the fundamentals of total quality management.

Statistics, data analysis, root cause analysis, and problem-solving processes play a key role in failure investigations. This chapter explains how to collect failure investigation data, how to build and maintain a database for company-related failures, and how to use corresponding statistics including type of failure, material, and root cause. It describes the purpose and benefits of conducting a root cause analysis and the factors, namely relative failure importance and company value, that determine when an investigation should be performed. The chapter also discusses the four-step problem-solving process as it applies to failure investigation, how to assemble an investigation team, and the details of organization and planning. It concludes with a case history of the Firestone 500 steel-belted tire failure, stressing the importance of a systematic approach to failure investigations.

A successful heat treating operation is determined by the ability to satisfy the customer's quality requirements consistently and economically. This chapter reviews the steps that are important to produce quality parts in heat treating with a brief practical explanation of each. The steps include selecting proper material and design of the part being treated; determining whether the process is capable of heat treatment; using statistical process control, control charting, and in-process inspection and testing; and applying statistical quality control and final testing (sampling) to verify the results.

This chapter surveys both basic quality and basic reliability concepts as an introduction to the failure analysis professional. It begins with a section describing the distinction between quality and reliability and moves on to provide an overview of the concept of experiment design along with an example. The chapter then discusses the purposes of reliability engineering and introduces four basic statistical distribution functions useful in reliability engineering, namely normal, lognormal, exponential, and Weibull. It also provides information on three fundamental acceleration models used by reliability engineers: Arrhenius, Eyring, and power law models. The chapter concludes with information on failure rates and mechanisms and the two techniques for uncovering reliability issues, namely burn-in and outlier screening.

Fatigue fractures are generally considered the most serious type of fracture in machinery parts simply because fatigue fractures can and do occur in normal service, without excessive overloads, and under normal operating conditions. This chapter first discusses the three stages (initiation, propagation, and final rupture) of fatigue fracture followed by a discussion of its microscopic and macroscopic characteristics. The relationship between stress and strength in fatigue is explained. The next section provides information that may help the uninitiated to appreciate some of the problems of laboratory fatigue testing and of the fatigue process itself. Finally, information on types and statistical aspects of fatigue is provided along with examples.

This chapter discusses the factors that play a role in fatigue failures and how they affect the service life of metals and structures. It describes the stresses associated with high-cycle and low-cycle fatigue and how they differ from the loading profiles typically used to generate fatigue data. It compares the Gerber, Goodman, and Soderberg methods for predicting the effect of mean stress from bending data, describes the statistical nature of fatigue measurements, and explains how plastic strain causes cyclic hardening and softening. It discusses the work of Wohler, Basquin, and others and how it led to the development of a strain-based approach to fatigue and the use of fatigue strength and ductility coefficients. It reviews the three stages of fatigue, beginning with crack initiation followed by crack growth and final fracture. It explains how fracture mechanics can be applied to crack propagation and how stress concentrations affect fatigue life. It also discusses fatigue life improvement methods and design approaches.

This chapter covers the failure modes and mechanisms associated with boiler components and the tools and techniques used to assess damages and predict remaining component life. It begins with a review of the design and operation of a utility boiler and the materials used in construction. It then describes the various causes of failure in boiler tubes, headers, and steam pipes, explaining how and why they occur, how they are diagnosed, and how to mitigate their effects. The final and by far largest section in the chapter is a tutorial on damage and life assessment techniques for boiler components and assemblies. It demonstrates the use of various methods, including analytical techniques that estimate life expenditure based on operating history, component geometry, and material properties; predictive methods based on the extrapolation of failure statistics; methods that predict life based on dimensional measurements; methods based on metallographic studies; methods based on temperature estimates; and a method for estimating remaining life under creep conditions based on stress-rupture testing of service-exposed material samples. The chapter also discusses the use of fracture mechanics and presents a number of cases in which life assessments are made based on the integration of several methods.

This chapter discusses the role of standards and specifications for steel castings. It defines specifications and discusses how certification, testing, examination, methods, practices, procedures, compositions, properties, facilities, statistical process control, and documentation relate to codes and standards. The chapter describes processes involved in the selection of specifications for steel castings. Further, it provides information on the cost of specifications.