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In analyzing the statistical features of infrastructural system responses, many events of interest can be defined by the related random variables. A random variable is a real-value function defined on the sample space. In other words, a random variable can be viewed as a mapping from the sample space to the real line, as shown […]

The probability of the occurrence of an event E, in general, cannot be deter­mined directly or easily. However, the event E may occur along with other attribute events Ak. Referring to Fig. 2.2, event E could occur jointly with K mutually exclusive (Aj П Ak — 0 for j — k) and collectively exhaustive (A1 […]

The conditional probability is the probability that a conditional event would occur. The conditional probability P (A | B) can be computed as P(AI B) = PAA <2.6) in which P (A | B) is the occurrence probability of event A given that event B has occurred. It represents a reevaluation of the occurrence probability […]

If two events are statistically independent of each other, the occurrence of one event has no influence on the occurrence of the other. Therefore, events A and B are independent if and only if P (A, B) = P (A) P (B). The probability of joint occurrence of K independent events can be generalized as […]

2.1.1 Basic axioms of probability The three basic axioms of probability computation are (1) nonnegativity: P (A) > 0, (2) totality: P (S) = 1, with S being the sample space, and (3) additivity: For two mutually exclusive events A and B, P(A U B) = P(A) + P(B). As indicated from axioms (1) and […]

Assessment of the reliability of a hydrosystems infrastructural system or its components involves the use of probability and statistics. This chapter reviews and summarizes some fundamental principles and theories essential to relia­bility analysis. 2.1 Terminology In probability theory, an experiment represents the process of making obser­vations of random phenomena. The outcome of an observation from […]

There are two basic probabilistic approaches to evaluate the reliability of an in­frastructural system. The most direct approach is a statistical analysis of data of past failure records for similar systems. The other approach is through relia­bility analysis, which considers and combines the contribution of each factor po­tentially influencing failure. The former is a lumped-system […]

In engineering design and analysis, loads usually arise from natural events, such as floods, storms, or earthquakes, that occur randomly in time and in space. The conventional practice for measuring the reliability of a hydrosystems engineering infrastructure is the return period or recurrence interval. The return period is defined as the long-term average (or expected) […]

In view of the lack of generally accepted rigorous definitions for risk and reliability, it will be helpful to define these two terms in a manner amenable to mathematical formulation for their quantitative evaluation for engineering systems. The unabridged Webster’s Third New World International Dictionary gives the following four definitions of risk: 1. “the possibility […]

The basic idea of reliability engineering is to determine the failure probability of an engineering system, from which the safety of the system can be assessed or a rational decision can be made on the design, operation, or forecasting of the system, as depicted in Fig. 1.3. For example, Fig. 1.4 schematically illus­trates using reliability […]