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Fundamentals of Probability and Statistics for Reliability Analysis ∗

By P Rakesh

Abstract

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 a random phenomenon cannot be predicted with absolute accuracy. The entirety of all possible outcomes of an experiment constitutes the sample space. Anevent is any subset of outcomes contained in the sample space, and hence an event could be an empty (or null) set, a subset of the sample space, or the sample space itself. Appropriate operators for events are union, intersection, and complement. The occurrence of events A and B is denoted as A ∪ B (the union of A and B), whereas the joint occurrence of events A and B is denoted as A ∩ B or simply (A, B) (the intersection of A and B). Throughout the book, the complement of event A is denoted as A ′. When two events A and B contain no common elements, then the two events are mutually exclusive or disjoint events, which is expressed as ( A, B) =∅, where ∅ denotes the null set. Venn diagrams illustrating the union and intersection of two events are shown in Fig. 2.1. When the occurrence of event Adepends on that of event B, then they are conditional events, ∗ Most of this chapter, except Secs. 2.5 and 2.7, is adopted from Tung and Yen (2005)

Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.189.5126
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