Category Hydrosystems Engineering Reliability Assessment and Risk Analysis

Brief History of Engineering Reliability Analysis

Development of engineering reliability analysis started with the desire for prod­uct quality control in manufacturing engineering three-quarters of a century ago (Shewart, 1931). World War II considerably accelerated its advancement. During the war, over 60 percent of airborne equipment shipped to the Far East arrived damaged. About half the spares and equipment in storage became un­serviceable before use. Mean service time before requiring repair or replace­ment for bomber electronics was less than 20 hours. The cost of repair and maintenance exceeded 10 times the original cost of procurement. About two – thirds of radio vacuum tubes in communications devices failed. In response to the high failure rates and damage to military airborne and electronic equip­ment, the U. S. Joint Army-Navy Committees on Parts Standards and on Vac­uum Tube Development were established in June 1943 to improve military equipment reliability. However, when the Korean War began, about 70 percent of Navy electronic equipment did not function properly. In 1950, the U. S. Department of Defense (DOD) established an Ad Hoc Group on Reliability that was upgraded in November 1952 as the Advisory Group on the Reliability of Electronic Equipment (AGREE) to monitor and promote military-related reli­ability evaluation and analysis.

Meanwhile, the civilian-side activities on reliability engineering also became active in aeronautical engineering (Tye, 1944) and in communications. In 1949-1953, Bell Laboratories and Vitro Laboratories investigated the relia­bility of communications electronic parts. Carhart (1953) conducted an early state-of-the-art study of reliability engineering. He divided the reliability prob­lems into five groups, namely, electronics, vacuum tubes, other components, system personnel, and organization. He listed seven factors that determined the worth of manufactured systems: (1) performance capacity, (2) reliability, (3) accuracy, (4) vulnerability, (5) operability, (6) maintainability, and (7) procur­ability. In 1953, RCA established the first civilian-organized industrial reliabil­ity program.

Contributions to reliability engineering through development of missiles be­gan with a DOD project to General Dynamics in 1954. Bell Aircraft Corporation issued the first industrial reliability handbook (LeVan, 1957). In the following decades, reliability engineering played important roles in aerospace and air­craft engineering.

Henney (1956) edited the first commercial reliability book. Chorafas (1960) published a textbook combining statistics with reliability engineering. More comprehensive textbooks on reliability related to manufacturing engineering started to appear in the early 1960s (Bazovsky, 1961; Calabro, 1962). The first reliability engineering course was offered in 1963 by Kececioglu at the Uni­versity of Arizona. In 1955, the Institute of Radio Engineers [IRE, now the Institute of Electrical and Electronic Engineers (IEEE)] initiated the Reliabil­ity and Quality Control Society, and in 1978, IEEE established its Reliability Society.

The American Institute of Aeronautics and Astronautics (AIAA), the Soci­ety of Automotive Engineers (SAE), and the American Society of Mechanical Engineers (ASME) initiated the Annual Reliability and Maintainability Con­ferences in 1962. It became the Annual Symposium on Reliability in 1966 and Annual Reliability and Maintainability Symposium in 1972, the year that the Society of Reliability Engineers was founded at Buffalo, New York.

Beyond manufacture-related reliability engineering, on the infrastructural side, Freudenthal (1947, 1956) was among the first to develop reliability anal­ysis for structural engineering. Public attention on the safety of nuclear power plants and earthquake hazards has provoked significant development on re­liability engineering for infrastructures, leading to publication of a series of comprehensive textbooks on the subject (Benjamin and Cornell, 1970; Ang and Tang, 1975, 1984; Yao, 1985; Madsen et al., 1986; Marek et al., 1995; Harr, 1996; Ayyub and McCuen, 1997; Kottagoda and Rosso, 1997; Melchers, 1999; Haldar and Mahadevan, 2000).

Reliability of Hydrosystem Engineering Infrastructure

The performance of a hydrosystem engineering infrastructure, function of an engineering project, or completion of an operation all involve a number of con­tributing components, and most of them, if not all, are subject to various types of uncertainty (Fig. 1.1). Detailed elaboration of uncertainties in hydrosystem engineering and their analysis are given in Tung and Yen (2005). Reliability and risk, on the other hand, generally are associated with the system as a whole. Thus methods to account for the component uncertainties and to combine them are required to yield the system reliability. Such methods usually involve the use of a logic tree, which is discussed in Chap. 5. A typical logic tree for culvert design is shown in Fig. 1.2 as an example.

The reliability of an engineering system may be considered casually, such as through the use of a subjectively decided factor of safety (see Sec. 1.6). Today, reliability also may be handled in a more comprehensive and system­atic manner through the aid of probability theory. Factors that contribute to the slow development and application of analyses of uncertainty and reliabil­ity in hydrosystem engineering infrastructure design and analysis include the following:

1. Those who understand the engineering processes well often are not trained adequately and are uncomfortable with probability. Contrarily, those who are good in probability theory and statistics seldom have sufficient knowledge of the details of the engineering process involved.

Natural variability Knowledge deficiency






Model Operational Data




Construction Procedure Deterioration Maintenance & manufacturing or process і









Handling and







of data


Подпись: Sampling Sampling Sampling Spatial period duration frequency representativeness (resolution)

Sources of uncertainty. (After Tung and Yen, 2005.)

Failure of culvert




Reliability of Hydrosystem Engineering InfrastructureReliability of Hydrosystem Engineering InfrastructureReliability of Hydrosystem Engineering Infrastructure


2. Many factors contribute to the reliability of an engineering system. Only recently have advances in techniques and computers rendered the combina­tion and integration of these contributions feasible to evaluate the system reliability. Nevertheless, some of the factors are still beyond the firm grasp of engineers and statisticians. Furthermore, these factors usually require the work of experts in different disciplines, whereas interdisciplinary communi­cation and cooperation often are a problem.

3. Engineers have a tendency to focus on components affecting their problem most while ignoring other contributing elements. For instance, hydrologists as a group perhaps have contributed more than any other discipline to fre­quency analysis and also have made major contributions to related proba­bility distributions. Yet their devotion and accomplishment are a blessing as well as a curse, in that they hinder the vision to see beyond to a broader view of uncertainty and reliability analyses. As noted by Cornell (1972):

It is important to engineering applications that we avoid the tendency to model only those probabilistic aspects that we think we know how to analyze. It is far better to have an approximate model of the whole problem than an exact model of only a portion of it.

Only more recently, uncertainties other than natural randomness of floods/ rainfalls are considered in reliability-based design of flood mitigation schemes (U. S. National Research Council, 2000).

4. Inconsistent definitions of risk and risk analysis cause considerable con­fusion and doubt about the subject. For example, in flood protection engi­neering, hydraulic engineers tend to accept the definition used by struc­tural, aerospace, and electronic engineers that risk analysis is the analysis of the probability of failure to achieve the intended objectives. Hydrologists often consider risk in terms of the return period, which is considered as the reciprocal of the annual exceedance probability of the hydrologic events (i. e., flood, storm, or drought). Water resources planners and decision makers mostly adopt the definition used in economics and the health science fields, regarding risk analysis as the analysis of risk costs, assessment of the eco­nomic and social consequence of a failure, and risk management. For exam­ple, the United Nations Department of Humanitarian Affairs (1992) defines risk as

The expected losses (of lives, persons injured, property damaged and economic activity disrupted) due to a particular hazard for a given area and reference period. Based on mathematical calculations, risk is the product of hazard and vulnerability.

Further, hazard is defined as “a threatening event or the probability of occurrence of a potentially damaging phenomenon within a given time period and area.” Hence, in the United Nations terminology, hazard is what engi­neers define as risk. The problem of confusion probably would be minimized if the experts in these subdisciplines worked separately, each responsible for his or her own specialty. However, the trend of the past decades, expecting jack-of-all-trades water resources engineers to be experts in all these sub­disciplines, bears significant undesirable consequences, a small one ofwhich is the confusion concerning the definition of risk.

Practically all hydrosystem engineering infrastructures placed in a natu­ral environment are subject to various external stresses and loads. The resis­tance, strength, capacity, or supply of the system is its ability to accomplish the intended mission satisfactorily without failure when subjected to demands or external stresses. Loads, stresses, and demands tend to cause failure of the system. Failure occurs when the demand exceeds the supply or the load exceeds the resistance. Owing to the existence of uncertainties, the capacity of an infrastructural system and the imposed loads more often than not are random and subject to some degrees of uncertainty. Hence the design and oper­ation of engineering systems are always subject to uncertainties and potential failures.

Nevertheless, engineers always face the dilemma of decision making or design with imperfect information. It is the engineer’s responsibility to obtain a solu­tion with limited information, guided by experience and judgment, considering the uncertainties and probable ranges of variability of the pertinent factors, as well as economic, social, and environmental implications, and assessing a reasonable level of safety.


1.1 Reliability Engineering

Occasionally, failures of engineering systems catch public attention and raise concern over the safety and performance of the systems. The cause of the mal­function and failure could be natural phenomena, human error, or deficiency in design and manufacture. Reliability engineering is a field developed in recent decades to deal with such safety and performance issues.

Based on their setup, engineering systems can be classified loosely into two types, namely, manufactured systems and infrastructural systems. Manufac­tured systems are those equipment and assemblies, such as pumping stations, cars, computers, airplanes, bulldozers, and tractors, that are designed, fabri­cated, operated, and moved around totally by humans. Infrastructural systems are the structures or facilities, such as bridges, buildings, dams, roads, levees, sewers, pipelines, power plants, and coastal and offshore structures, that are built on, attached to, or associated with the ground or earth. Most civil, en­vironmental, and agricultural engineering systems belong to infrastructural systems, whereas the great majority of electronic, mechanical, industrial, and aeronautical/aerospace engineering systems are manufactured systems.

The major causes of failure for these two types of systems are different. Fail­ure of infrastructures usually is caused by natural processes, such as geophys­ical extremes of earthquakes, tornadoes, hurricanes or typhoons, heavy rain or snow, and floods, that are beyond human control. Failure of such infrastruc­tural systems seldom happens, but if a failure occurs, the consequences often are disastrous. Replacement after failure, if feasible, usually involves so many changes and improvements that it is essentially a different, new system.

On the other hand, the major causes of failure for manufactured systems are wear and tear, deterioration, and improper operation, which could be dealt with by human abilities but may not be economically desirable. Their failures usually do not result in extended major calamity. If failed, they can be repaired or replaced without affecting their service environment. Their reliability anal­yses are usually for production, quality control, or for maintenance service and warranty planning. Thus failures of manufactured systems often are classified into repairable and nonrepairable types. Conversely, failures of infrastructural systems can be classified as structural failures and functional failures, as will be explained in Sec. 1.5.

The approaches and purposes of reliability analysis for these two types of systems are related but different. As described in Sec. 1.3, reliability analysis for manufactured systems has a history of more than 70 years and is relatively more developed than reliability analysis for civil engineering infrastructural systems. Many books and papers have been published on reliability engineer­ing for manufactured systems. One can refer to Ireson and Coombs (1988), Kececioglu (1991), Ushakov (1994), Pecht (1995), Birolini (1999), and Modarres et al. (1999) for extensive lists of the literature. Conversely, this book deals mainly with reliability issues for hydrosystem engineering infrastructures. Nonetheless, it should be noted that many of the basic theories and methods are applicable to both systems.


Through my academic career, I have spent most of research efforts on problems relating to probabilistic hydrosystem engineering. I am truly thankful to my advisor, Larry W. Mays, who first introduced me to this fascinating area when I was a Ph. D. student. Over the years, both Larry and the late Ben C. Yen have been my unflagging supporters and mentors. In the process of putting together the book, the use of materials from some of my former students (Drs. Wade Hathhorn, Yixing Bao, and Bing Zhao) brought many fond memories back about the time we spent together burning midnight oil, cutting fire wood, and fishing. Many of my more recent students (Chen Xingyuan, Lu Zhihua, Wang Ying, Eddy Lau, and Wu Shiang-Jen) have contributed their kind assistance in preparing figures and tables, reading manuscripts and offering their criticisms from a student’s perspective. I am also grateful to Ms. Queenie Tso for skillful typing of numerous equations and painstakingly performing necessary corrections in the book. Especially, I would like to express sincere gratitude to my dear friend Ms. Joanne Lam for her prayers and encouragements during the course of writing this book.

Although writing this book has been a very rewarding experience, it never­theless has occupied many hours and attention that I should have spent with my family. I am grateful to my wife Be-Ling and daughters (Fen, Wen, Fei, and Ting) for their understanding and support without which the completion of this book would not have been possible. By the time the final manuscript was submitted, I felt an overwhelming sense of sadness and loss since I wished Prof. Yen would have lived to see the completion of this book. I want to thank Ruth Yen for her encouragement to continue with the work. Also I am much obliged to Steve Melching for his willingness to work with me on the book. Look­ing back, I see how kind God has been to me. He blesses me by surrounding me with so many people who do not hold back their support, kindness, and love. I praise the Lord that through His mercy and grace the book is completed.

Last, but not the least, I am thankful to McGraw-Hill for supporting the publication of the book, to Mr. Larry Hager for his advice in preparing the book, and, in particular, to Samik Roy Choudhury (Sam) and his team at International Typesetting and Composition for editorial and production efforts.

Yeou-Koung Tung

I would like to take this opportunity to most sincerely thank my coauthors. The late Prof. Ben C. Yen was my Ph. D. advisor, mentor, and friend, and the greatest influence on my life after my parents and my Lord Jesus Christ. Professor Yen led me down the path of the study of uncertainty and reliability in hydrosystems engineering in my Ph. D. work and we worked together on many related projects throughout my professional life. Professor Y. K. Tung invited me to get involved in this book after Prof. Yen’s untimely death, initially to be a second pair of eyes to ensure that the concepts were clear, concise, and correct. Eventually my small contribution grew enough that Y. K. honored me with a coauthorship.

I also would like to thank my wife, Qiong, and my children, Christine and Brian, for their patience while I hide in the basement on evenings and week­ends working on this book. I also thank my former students, Satvinder Singh, Sharath Anmangandla, Chun Yoon, and Gemma Manache, whose work on un­certainty analysis gave me additional insight that is part of my contribution to this book.

Charles S. Melching

Hydrosystems Engineering Reliability Assessment and Risk Analysis

Failures of major engineering systems always raise public concern on the safety and reliability of engineering infrastructure. Decades ago quantitative evalua­tions of the reliability of complex infrastructure systems were not practical, if not impossible. Engineers had to resort to the use of a safety factor mainly de­termined through experience and judgment. The contribution of human factors to structural safety still remains elusive for analytical treatment. The main areas of concern and application in this book are hydrosystems and related environmental engineering.

Without exception, failures of hydrosystem infrastructure (e. g., dams, levees, and storm sewers) could potentially pose significant threats to public safety and inflict enormous damage on properties and the environment. The tra­ditional approach of considering occurrence frequency of heavy rainfalls or floods, along with an arbitrarily chosen safety factor, has been found inadequate for assessing the reliability of hydrosystem infrastructure and for risk-based cost analysis and decision making. In the past two decades or so, there has been a steady growth in the development and application of reliability analysis in hydrosystems engineering and other disciplines. The main objective ofthe book is to bring together some of these developments and applications in one volume and to present them in a systematic and understandable manner to the water resource related engineering profession. Through this book it is hoped to demon­strate how to integrate involved physical processes, along with some knowledge in mathematics, probability, and statistics, to perform reliability assessment and risk analysis of hydrosystem engineering problems. An accompanying book, Hydrosystems Engineering Uncertainty Analysis, provides treatments and quantifications of various types of uncertainty, which serve as essential infor­mation needed for the reliability assessment and risk analysis of hydrosystems.

Hydrosystems is the term used to describe collectively the technical areas of hydrology, hydraulics, and water resources. The term has now been widely used to encompass various water resource systems including surface water storage, groundwater, water distribution, flood control, drainage, and others. In many hydrosystem infrastructural engineering and management problems, both quantity as well as quality aspects of water and other environmental issues have to be addressed simultaneously. Due to the presence of numerous uncertainties, the ability of the system to achieve the goals of design and man­agement decisions cannot be assessed definitely. It is almost mandatory for an engineer involved in major hydrosystem infrastructural design or hazardous waste management to quantify the potential risk of failure and the associated consequences.

Application of reliability analysis to hydrosystems engineering covers a wide scope of subfields, ranging from data collection and gauging network design to turbulence loading on structures; and from inland surface water to groundwa­ter to coastal water. In terms of the system scale, it could involve entire river basins containing many components, or a large dam and reservoir, or a single culvert or pipe. Depending on the objective, the application could be for design­ing the geometry and dimension of hydraulic facilities, for planning of a hy­draulic project, for determining operation procedure or management strategy, for risk-cost analysis, or for risk-based decision making.

The book is not intended to be a review of literature, but is an introduction for upper level undergraduate and graduate students to methods applicable for reliability analysis of hydrosystem infrastructure. Most of the principles and methodologies presented in the book can equally be applied to other civil engi­neering disciplines. The book presents relevant theories of reliability analysis in a systematic fashion and illustrates applications to various hydrosystem engi­neering problems. Although more advanced statistical and mathematical skills are occasionally required, the great majority of the problems can be solved with basic knowledge of probability and statistics. Illustrations in the book bring to­gether the use of probability and statistics, along with knowledge of hydrology, hydraulics, water resources, and operations research for the reliability analysis and optimal reliability-based design of various hydrosystem engineering prob­lems. The book provides added dimensions to water resource engineers beyond conventional frequency analysis.

The book consists of eight chapters. In each chapter of the book, ample exam­ples are given to illustrate the methodology for enhancing the understanding of the materials. The book can serve as an excellent reference book not only for engineers, planners, system analysts, and managers in area of hydrosystems, but also other civil engineering disciplines. In addition, end-of-chapter problems are provided for practice and homework assignments for classroom teaching.

The book focuses on integration of reliability analysis with knowledge in hydrosystems engineering with applications made to hydraulics, hydrology, water resources, and occasionally, to environmental and water quality manage­ment related problems. Since many good books on basic probability, statistics, and hydrologic frequency analysis have been written, background in proba­bility, statistics, and frequency analysis that are relevant to reliability anal­ysis are summarized in Chapters 2 and 3, respectively. The book, instead of dwelling on the subject of data analysis, focuses on how to perform relia­bility analysis of hydrosystem engineering problems once relevant statistical data analysis has been conducted. As real-life hydrosystems generally involve various uncertainties other than just inherent natural randomness of hydro­logic events, the book goes beyond conventional frequency analysis by consider­ing reliability issues in a more general context of hydrosystems engineering and management. Chapter 4 elaborates the reliability analysis methods consider­ing load-resistance interaction under the static and time-dependent conditions. First-order and second-order reliability methods, with the emphasis given to the former, are derived. For many hydrosystem infrastructures, it is sometimes practical to treat the system as a whole and analyze its performance over time without considering detailed load-resistance interaction. Chapter 5 is devoted to time-to-failure analysis that is particularly useful for dealing with systems that are repairable. Chapter 6 provides a detailed treatment of using Monte Carlo simulation and its variations applicable to reliability analysis. The sub­ject, in most books, is covered in the context of univariate problems in which stochastic variables are treated as independent and uncorrelated. In reality, the great majority of the hydrosystem infrastructural engineering problems involve multiple stochastic variables, which are correlated. Treatment of such problems is emphasized. Chapter 7 focuses on the evaluation of system reliabil­ity by integrating load-resistance reliability analysis methods or time-to-failure analysis, along with system configuration, for assessing system reliability. Different methods for system reliability analysis are presented and demon­strated through examples. Chapter 8 presents the framework that integrates uncertainties, risk, reliability, and economics for an optimal design of hydrosys­tem infrastructure. A brief description of system optimization is also given.

The intended uses and audiences for the book are: (1) as a textbook for an intermediate course at the undergraduate senior level or graduate level in wa­ter resources engineering on the risk and reliability related subjects; (2) as a textbook for an advanced course in risk and reliability analysis of hydrosystem engineering; and (3) as a reference book for researchers and practicing engi­neers dealing risk and reliability issues in hydrosystems engineering, planning, management, and decision making.

The expected background for the readers of this book is a minimum of 12 credits of mathematics including calculus, matrix algebra, probability, and statistics; a one-semester course in elementary fluid mechanics; and a one- semester course in elementary water resources covering basic principles in hydrology and hydraulics. Additional knowledge on engineering economics, water-quality models, and optimization would be desirable.

Two possible one-semester courses could be taught from this book depend­ing on the background of the students and the type of course designed by the instructor. Instructors can also refer to the accompanying book Hydrosystems Engineering Uncertainty Analysis for other relevant materials to compliment this book. The possible course outlines are presented below.

Outline 1. (For students who have taken a one-semester probability and statis­tics course). The objective of this outline aims at achieving higher level of capability to perform reliability analysis. The optimal risk-based design concept can be introduced without having to formally cover subjects on opti­mization techniques. The subject materials could include Chapter 1, Chapter 2 (2.7), Chapter 3, Chapter 4 (4.1—4.4), Chapter 5 (5.1-5.3), Chapter 6 (6.1-6.4, 6.6), Chapter 7 (7.1-7.3), and Chapter 8 (8.1-8.4).

Outline 2. (For water resource engineers or students who have a good under­standing in basic statistics, probability, and operations research.) The aim of this outline is for readers to achieve higher level and deeper appreciation of the applications of reliability assessment techniques in hydrosystems engineering. The topics might include Chapters 1, 4, 5, 6, 7, and 8.

The uncertainty and reliability issues in hydrosystem engineering problems have been attracting a lot of attention of engineers and researchers. A tremen­dous amount of progress has been made in the area. This book, and the accompa­nying book Hydrosystems Engineering Uncertainty Analysis, merely represent our humble offer to the hydrosystem engineering community. We hope that readers will find this book useful and enjoyable. Due to our limited knowledge and exposure in the exciting area of stochastic hydraulics, we are unable to incorporate many brilliant works in this book. It is our sincere wish that this effort will bring out much greater works from others to improve and enhance our contribution to society and mankind.