Reliability and Risk Models: Setting Reliability Requirements

This book presents new approaches for setting quantitative reliability requirements based on the cost of failure and specified minimum failure-free operation periods (MFFOPs). The cost-of-failure–based reliability analysis provides a real alternative to the current reliability analysis approach by considering the cost of the failures when setting reliability requirements. After an introduction to the reliability and risk analysis based on random variables, the author examines a new method for problem solving in the context of real reliability engineering applications and case studies and supplies algorithms that can be used for reliability analyses and for setting quantitative reliability requirements. The author also gives a comprehensive overview of basic Monte Carlo simulation techniques and algorithms for solving reliability engineering problems. In addition, the book provides a comprehensive introduction to loadstrength interference models for reliability and risk analysis by introducing the overstress reliability integral, a generalization of the load-strength interference integral with the time included. It also presents an efficient model for determining the probability of failure of loaded components and structures with integral flaws. The book comprises 16 chapters. Chapter 1 provides a general introduction to reliability (survival) functions, cumulative distributions and probability density functions of times to failure, and random events in reliability and risk modeling. Chapter 2 provides a general framework of the common reliability and risk models and their applications. Chapter 3 discusses reliability and risk models based on mixture distributions. Chapter 4 discusses general rules for reliability data analysis and also explores construction of reliability and risk models and estimation of the model parameters. Chapter 5 discusses load-strength (demand capacity) models and numerical methods for calculating the load-strength integral. Chapter 6 discusses Monte Carlo simulation algorithms for solving reliability and risk models, and Chapter 7 covers analysis of the properties of inhomogeneous media using Monte Carlo simulations. Chapter 8 discusses mechanisms of failure, including overstress failures, such as brittle fracture and ductile fracture; wear-out failures, such as fatigue and corrosion; and early-life failures, such as influence of the design. Chapter 9 discusses reliability associated with overstress failure mechanisms and damage factorization law. Chapter 10 introduces general equations related to the probability of failure of a stressed component with internal flaws and the individual probability of triggering failure with a single flaw. It also presents a stochastic model related to the fatigue life distribution of a component containing defects. Chapter 11 discusses the uncertainty and risk assessment associated with the location of the ductile-to-brittle transition region. Chapter 12 discusses modeling the kinetics of deterioration of protective coatings due to corrosion. Chapter 13 discusses physics-of-failure concepts that help improve the reliability of automotive suspension springs by delaying the fatigue failure mode. Chapter 14 discusses reliability governed by the relative locations of random variables in a finite domain. Chapter 15 discusses reliability based on minimum critical interval (MCI) and MFFOPs. It gives general equations related to random variables following a homogeneous Poisson process in a finite interval and some application examples. Chapter 16 provides a new methodology and models for reliability analysis and setting reliability requirements based on the cost of failure. Models and algorithms are introduced for determining the value from the reliability investment, the risk of premature failure, optimization models for minimizing the total losses, and models for limiting the risk of failure below a maximum acceptable level and for guaranteeing a minimum availability level. It is proved that the expected losses from failures of a repairable system in a specified time interval are equal to the expected number of failures times the expected cost given failure. Overall, this book examines the theory of reliability and risk analysis based on random variables. It also provides new methods for problem solving in the context of real reliability engineering problems. The book is ideal reading material for practicing engineers and consultants dealing with reliability and risk assessment. It also can be used as a reference by researchers and graduate students in reliability engineering and other quantitative disciplines such as actuarial science, economy, and applied probability and statistics.