Fundamentals of Probability Theory

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.