Reliability Engineering and Risk Analysis

Fault tree analysis: A survey of the state-of-the-art in modeling, analysis and tools

“…Similar to fault trees, reliability block diagrams (RBDs) [9] decompose systems into subsystems to show the effects of (combinations of) faults. Similar to FTs, RBDs are attractive to users because the blocks can often map directly to physical components, and because they allow quantitative analysis (computation of reliability and availability) and qualitative analysis (determination of cut sets).…”

Optimal loading of system with random repair time

“…While different types of distributions have been used to model system time-to-failure and the numerical algorithm suggested in Section 4 has no limitation on the distribution types, the Weibull distribution is selected due to its broad application in the reliability area and its flexibility for modeling diverse failure rate behavior (Modarres, Kaminskiy, & Krivtsov, 2010;Weibull, 1951 distribution parameters corresponding to the different loading conditions can be obtained using accelerated life testing analysis (Amari, Misra, & Pham, 2008;Nelson, 1990). Refer to (Levitin, Xing, Amari, & Dai, 2013) for a specific example of parameter estimation.…”

Using Copula Functions in Bayesian Analysis: A Comparison of the Lognormal Conjugate

“…In these instances, Kaufman (1963) has shown that the lognormal distribution provides a reasonable fit in empirical data on reported oil field sizes instead of a normal distribution. Other examples can be found in applications including the discovery of gold ore in a mining environment (Kirge 2004), reliability engineering (Modarres et al 2010), and stock price returns (Gemmill 1992), among others. Luenberger (1998, p. 302) has demonstrated that the observed distribution of the logarithm of stock prices is larger in the tails ("fatter tails") than a normal distribution with the same variance.…”