### 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.

Language | English (US) |
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Title of host publication | Springer Series in Reliability Engineering |

Publisher | Springer London |

Pages | 11-51 |

Number of pages | 41 |

DOIs | |

State | Published - Jan 1 2019 |

### Publication series

Name | Springer Series in Reliability Engineering |
---|---|

ISSN (Print) | 1614-7839 |

ISSN (Electronic) | 2196-999X |

### Fingerprint

### ASJC Scopus subject areas

- Safety, Risk, Reliability and Quality

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

TY - CHAP

T1 - Fundamentals of probability theory

AU - Hu, Chao

AU - Youn, Byeng D.

AU - Wang, Pingfeng

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-319-92574-5_2

DO - 10.1007/978-3-319-92574-5_2

M3 - Chapter

T3 - Springer Series in Reliability Engineering

SP - 11

EP - 51

BT - Springer Series in Reliability Engineering

PB - Springer London

ER -