Failures of engineered systems (e.g., vehicle, aircraft, and material) lead to significant maintenance/quality-control costs, human injuries, and fatalities. Examples of such system failures can be found in various engineering fields: the Chernobyl disaster in Russia (1986), the collapse of the I-35 W Mississippi River Bridge in the U.S. (2007), the explosion of a compressed natural gas (CNG) bus in the Republic of Korea (2010), and the lithium-ion battery fire/smoke on Boeing 787 Dreamliners in the U.S. and Japan (2013). Many system failures can be traced back to various difficulties in evaluating and designing complex systems under highly uncertain manufacturing and operational conditions. One of the greatest challenges in design of engineered system is to ensure high reliability and maintainability of a system during its life-cycle. Our attempt to address this challenge begins with the discussion of the fundamentals of reliability analysis. This discussion will be separately conducted for time-independent and time-dependent reliability analyses, with an aim to facilitate more in-depth discussions in later chapters.