Fundamentals of probability theory

Chao Hu, Byeng D. Youn, Pingfeng Wang

Research output: Chapter in Book/Report/Conference proceedingChapter


Probability theory is a mathematical discipline that investigates possible outcomes of repeated experiments and a long-run relative frequency of these outcomes. The word “probability” generally refers to the chance of a specific event occurring, taking values between zero (impossible) and one (certain). Probability theory enables the analysis of reliability, i.e. the probability that a system performance meets its marginal value (or requirement) under uncertainty at the very beginning of operation (time-independent reliability) or during its lifetime (time-dependent reliability). In this chapter, we briefly summarize fundamental probability theory with the aim of providing a sufficient background in probability to enable understanding and use of techniques and methods found in later chapters.

Original languageEnglish (US)
Title of host publicationSpringer Series in Reliability Engineering
Number of pages41
StatePublished - 2019

Publication series

NameSpringer Series in Reliability Engineering
ISSN (Print)1614-7839
ISSN (Electronic)2196-999X

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality


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