Essentials of Reliability Engineering

Inhaltsverzeichnis

1. Frontmatter

2. Chapter 1. Introduction and Concepts

   Fuqing Yuan

   Abstract

   Developing an immortal product has long been a human aspiration. However, the frequent accidents caused by engineering systems remind us that this dream remains a formidable challenge. We must live with inherently unreliable systems and learn to manage their limitations to gain the greatest benefit. This chapter first outlines the historical development of reliability engineering and highlights several notable practical applications. It then introduces key concepts and definitions fundamental to the field.

3. Chapter 2. Reliability Mathematics

   Fuqing Yuan

   Abstract

   Probability and statistics are the primary mathematical approaches applied in the field of reliability. This chapter begins by introducing the fundamental concepts of probability. Then, starting from empirical data distributions, it presents several important theoretical statistical distributions. Finally, key statistical properties and categories of distribution parameters relevant to reliability are discussed.

4. Chapter 3. Essential Elements of Statistics for Reliability

   Fuqing Yuan

   Abstract

   Many methods are used in reliability engineering for both quantitative and qualitative analysis, among which statistical methods are undoubtedly among the most important. This chapter presents key statistical concepts and methods that are essential for reliability analysis. Statistics, as a fundamental branch of mathematics, is well developed with mature theories. However, applying statistical methods to reliability problems without a proper understanding of their fundamentals and limitations can be risky. Misconceptions and misuse of statistical methods are common in state-of-the-art applications of reliability engineering. This hchapter introduces statistics from a practical perspective for reliability. It begins with parameter estimation, including discussions on confidence interval derivation, consistency, and asymptotic normality. It then addresses parameter bias, methods for goodness-of-fit test, and approaches for approximating cumulative distribution functions.

5. Chapter 4. Statistical Exponential Distribution

   Fuqing Yuan

   Abstract

   Exponential distribution is the most used distribution in reliability engineering. It is widely applied to model life data for non-repairable systems or the time between failures for repairable systems. Two forms of Exponential distribution can have: the one-parameter Exponential and the two-parameter Exponential. In the one-parameter Exponential distribution, the single parameter represents the failure rate, which characterizes the system’s reliability. The simplicity of having just one parameter makes parameter estimation straightforward. Unless otherwise specified, this chapter refers to Exponential distribution as the one-parameter one.

6. Chapter 5. Weibull Distribution

   Fuqing Yuan

   Abstract

   The Exponential distribution, discussed in the previous chapter, assumes a constant failure rate that sometimes fails to represent field data. In practice, failure rates can vary—decreasing, increasing, or exhibiting complex patterns with multiple peaks. A non-constant failure rate is more realistic, as many products, especially in the wear-out phase, typically show an increasing failure rate. Consequently, a more flexible statistical distribution is needed to model such behavior. The Weibull distribution, widely used in reliability engineering, meets this need due to its versatility. This chapter examines the statistical properties of the Weibull distribution and explains how it can be effectively applied to reliability analysis.

7. Chapter 6. System Reliability

   Fuqing Yuan

   Abstract

   System reliability considers the reliability of a system containing dependent or interdependent units, components, or subsystems. It concerns how the reliability of the whole system is related to its constituent parts. For instance, the reliability of an airplane can be assessed based on the reliability of its engines, avionics, navigation system, communication systems, and more. Similarly, the reliability of a laptop can be evaluated from that of its hard drive, screen, memory, power supply, battery, etc. The interactions among these subsystems, components, or units—referred to hereafter simply as “units” for simplicity—may not follow straightforward patterns but instead form a complex stochastic process. This chapter discusses methods for evaluating the reliability of an entire system based on the reliability of its constituent units.

8. Chapter 7. Reliability Evaluation from Limit-State Function

   Fuqing Yuan

   Abstract

   Reliability evaluation we have discussed before has been focusing on methods of using event data analysis, mainly by using failure data to find out the reliability level. This method is essentially analyzing reliability from management perspective and statistic perspective, while less from the engineering perspective. Data from fields contain noise, outlier, inaccuracy. The resultant evaluation accuracy is thus compromised. With the growing concern of reliability issue for the modern equipment’s such as cellphone, smart home, autonomous drone, the reliability evaluation has gone beyond the original domain. In the industries, reliability evaluation from field data might be too rough in its accuracy or infeasible as it often lacks data. There is another domain of reliability analysis which analyzes the probabilistic behavior of the system, where the reliability level is evaluated from a probabilistic analysis, for example, evaluating reliability from thermal models where some parameters and measurements are uncertain for electronic units; evaluating the probability of bridge collapsing by mechanical analysis where operating condition is uncertain in structural engineering. This kind of analysis is also named probabilistic design. This Chapter addresses this method. We start from the simplest stress-strength analysis then to the more general limit-state analysis.

9. Chapter 8. Multivariate Distribution for Reliability Dependency Analysis

   Fuqing Yuan

   Abstract

   Classical life data analysis typically focuses on a single variable, usually failure time, using statistical distributions such as the Exponential and Weibull distributions, which have been discussed earlier in this book. However, in many applications, life data often involves multiple variables. For example, the lifespan of a car is determined by both age and mileage, the lifespan of an aircraft is influenced by both calendar years and total flying hours. This necessitates the use of multivariate distributions to address such cases. In statistics, a multivariate distribution refers to a method that incorporates more than one variable, making it suitable for analyzing complex relationships between multiple factors. This chapter explores the application of multivariate distributions in reliability analysis. Since multivariate distributions are less familiar in reliability engineering, the chapter begins with an introduction to the basic concepts of Normal multivariate distributions. Later, we will discuss using the Copula function to develop some special multivariate distributions for reliability dependency analysis.

10. Chapter 9. Proportional Hazard Model

    Fuqing Yuan

    Abstract

    Accounting for operating conditions that have a significant impact on failure time in the life distribution model can improve the accuracy of reliability analysis. The Proportional Hazard Model (PHM) is one of such popular models that can account for these operating conditions. The PHM was initially introduced by Cox as a regression method. It combines the hazard rate—also known as the failure rate in reliability engineering—with other variables, known as covariates, into a single model using a form of linear regression [1]. The strength of the PHM lies in its partial likelihood estimation approach, which allows estimation of covariate coefficients without requiring knowledge of the underlying failure rate. This advantage makes it useful in both medical and engineering applications. This chapter presents the fundamentals of the PHM and addresses the key issues relevant to reliability data analysis.

11. Chapter 10. Reliability Simulation

    Fuqing Yuan

    Abstract

    Obtaining analytical solutions to complex problems is often preferable; however, it requires substantial mathematical effort, and in some cases, analytical solutions may not be available. Simulation methods, by contrast, are relatively simple yet highly effective, especially for solving complex problems, as they usually require fewer assumptions to obtain solutions. With the widespread availability of computers and significant advances in their processing power, simulation has become a popular approach in engineering analysis, for example, in modeling dynamic systems, performing uncertainty analyses, and analyzing failure data. This chapter introduces the fundamentals of simulation, highlights its limitations, and discusses various methods for applying simulation to reliability data analysis.

12. Chapter 11. Reliability Physics

    Fuqing Yuan

    Abstract

    Failure is undesirable in engineering. Explaining the root causes of failure and predicting them through mathematical models based on physical principles provides a convincing and solid basis for decision making. Using physics to explain failure can help overcome the shortcomings of life data analysis, which is sometimes criticized for lacking a solid physical foundation. In general, engineering systems consist of mechanical, electrical, electronic, and software components. This chapter addresses fundamental physical principles related only to mechanical and electronic systems, while omitting software, as it is not governed by physical laws. The concepts discussed in this chapter may be less familiar to some engineers and may not directly explain specific failures, but they can enhance the understanding of the fundamental nature of failures.

13. Chapter 12. Accelerated Life Test

    Fuqing Yuan

    Abstract

    In industrial reliability analysis, life data obtained solely from field information may not be sufficient for a reliable evaluation of system reliability. Consequently, reliability engineers have increasingly focused on experimental approaches. The Accelerated Life Test (ALT) is one of the major experimental methods used in reliability analysis. This chapter discusses the principles of ALT and demonstrates several ALT models for mechanical and electronic systems.