Reliability of systems with identically distributed correlated components

The vast majority of reliability engineers and many researchers continue to base their models on the assumption that components fail in a statistically independent manner. This assumption is generally untenable because correlated failures can lower the reliability of a fault tolerant system. A simple method that quantifies the impact of correlation among the components of a system is needed to eliminate this widespread practice. Previous approaches to model correlated component failures have not gained popularity because they rely on excessively sophisticated mathematical approaches, making them cumbersome to apply in practice. This paper proposes a method to model the reliability of systems with correlated identical components, where the components exhibit the same average reliability and also possess a common failure correlation parameter. The method is applicable to the class of coherent systems commonly modelled by reliability block diagrams and fault trees. The utility of the approach is demonstrated through a series of examples, including the derivation of several commonly used structures such as the k-out-of-n and parallel systems. The examples illustrate how the method facilitates the assessment of component correlation on system reliability.