Fundamentals of Probability Theory

Chao Hu (), Byeng D. Youn () and Pingfeng Wang ()
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Chao Hu: Iowa State University
Byeng D. Youn: Seoul National University
Pingfeng Wang: University of Illinois at Urbana–Champaign

Chapter Chapter 2 in Engineering Design under Uncertainty and Health Prognostics, 2019, pp 11-51 from Springer

Abstract: 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.

Keywords: Time-dependent Reliability; Discrete Random Variables; Probability Density Function (PDF); Marginal PMFs; Reliability-based Robust Design Optimization (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:ssrchp:978-3-319-92574-5_2

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DOI: 10.1007/978-3-319-92574-5_2

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