Fundamentals of probability theory

Chao Hu, Byeng D. Youn, Pingfeng Wang

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.

LanguageEnglish (US)
Title of host publicationSpringer Series in Reliability Engineering
PublisherSpringer London
Pages11-51
Number of pages41
DOIs
StatePublished - Jan 1 2019
Externally publishedYes

Publication series

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

Fingerprint

Experiments
Uncertainty

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality

Cite this

Hu, C., Youn, B. D., & Wang, P. (2019). Fundamentals of probability theory. In Springer Series in Reliability Engineering (pp. 11-51). (Springer Series in Reliability Engineering). Springer London. https://doi.org/10.1007/978-3-319-92574-5_2

Fundamentals of probability theory. / Hu, Chao; Youn, Byeng D.; Wang, Pingfeng.

Springer Series in Reliability Engineering. Springer London, 2019. p. 11-51 (Springer Series in Reliability Engineering).

Research output: Chapter in Book/Report/Conference proceedingChapter

Hu, C, Youn, BD & Wang, P 2019, Fundamentals of probability theory. in Springer Series in Reliability Engineering. Springer Series in Reliability Engineering, Springer London, pp. 11-51. https://doi.org/10.1007/978-3-319-92574-5_2
Hu C, Youn BD, Wang P. Fundamentals of probability theory. In Springer Series in Reliability Engineering. Springer London. 2019. p. 11-51. (Springer Series in Reliability Engineering). https://doi.org/10.1007/978-3-319-92574-5_2
Hu, Chao ; Youn, Byeng D. ; Wang, Pingfeng. / Fundamentals of probability theory. Springer Series in Reliability Engineering. Springer London, 2019. pp. 11-51 (Springer Series in Reliability Engineering).
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