Discrete and continuous reliability models for systems with identically distributed correlated components

•Reliability of systems with identical but correlated components are studied.•Correlation lowers the reliability and mean time to failure of fault tolerant systems.•Correlation lowers the availability and mean residual life of fault tolerant systems.

Many engineers and researchers base their reliability models on the assumption that components of a system fail in a statistically independent manner. This assumption is often violated in practice because environmental and system specific factors contribute to correlated failures, which can lower the reliability of a fault tolerant system. A simple method to quantify the impact of correlation on system reliability is needed to encourage models explicitly incorporating correlated failures. Previous approaches to model correlation are limited to systems consisting of two or three components or assume that the majority of the subsets of component failures are statistically independent. This paper proposes a method to model the reliability of systems with correlated identical components, where components possess the same reliability and also exhibit a common failure correlation parameter. Both discrete and continuous models are proposed. The method is demonstrated through a series of examples, including derivations of analytical expressions for several common structures such as k-out-of-n: good and parallel systems. The continuous models consider the role of correlation on reliability and metrics, including mean time to failure, availability, and mean residual life. These examples illustrate that the method captures the impact of component correlation on system reliability and related metrics.