Most systems involve many subsystems and components whose performances affect the performance of the system as a whole. The reliability of the entire system is affected not only by the reliability of individual subsystems and components but also by the interactions and configurations of the subsystems and components. Many engineering systems involve multiple failure paths or modes; that is, there are several potential paths and modes of failure in which the occurrence, either individually or in combination, would constitute system failure. As mentioned in Sec. 1.3, engineering system failure can be structural failure such that the system can no longer function, or it can be performance failure, for which the objective is not achieved but the functioning of the system is not damaged. In terms of their functioning configuration and layout pattern, engineering systems can be classified into series systems or parallel systems, as shown schematically in Figs. 7.1 and 7.2, respectively.
A formal quantitative reliability analysis for an engineering system involves a number of procedures, as illustrated in Fig. 7.3. First, the system domain is defined, the type of the system is identified, and the conditions involved in the problem are defined. Second, the kind offailure is identified and defined. Third, factors that contribute to the working and failure of the system are identified. Fourth, uncertainty analysis for each of the contributing component factors or subsystems is performed. Chapters 4 and 5 of Tung and Yen (2005) and Chap. 6 of this book describe some of the methods that can be used for this step. Fifth, based on the characteristics of the system and the nature of the failure, a logic tree is selected to relate the failure modes and paths involving different components or subsystems. Fault trees, event trees, and decision trees are the logic trees often used. Sixth, identify and select an appropriate method or methods that can combine the components or subsystems following the logic of the tree to facilitate computation of system reliability. Some of the computational
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methods are described in Chaps. 4, 5, and 6. Seventh, perform the computation following the methods selected in the sixth step to determine the system failure probability and reliability. Eighth, if the cost of the damage associated with the system failure is desired and the failure damage cost function is known or can be determined, it can be combined with the system failure probability function determined in step 7 to yield the expected damage cost.
The different contributing factors or parameters may have different measurement units. In quantitative combination for reliability analysis, these statistical parameters or factors are normalized through their respective mean or standard deviation to become nondimensional, such as coefficients of variation, to facilitate uncertainty combination.
Real-life hydrosystems engineering infrastructural systems often are so large and complex that teams of experts of different disciplines are required to conduct the reliability analysis and computation. Logic trees are tools that permit division of team work and subsequent integration for the system result. Information on the logic trees and types of systems related to steps 5 and 6 are discussed in this chapter.
