Correlated consecutive 2-out-of-n failed systems

Most methods to model system reliability assume component failures are statistically independent in order to simplify analysis. In many cases, however, the components of a system can experience correlated failures. This is especially true of consecutive k-out-of-n: F systems because the failure of consecutive components can be geospatially correlated due to events such as natural disasters and power outages. A method to quantify the reliability of a consecutive k-out-of-n: F system that does not assume statistically independent component failures is needed to explicitly consider the impact of correlated failures on the reliability of such systems. This paper presents a method to model the reliability of a consecutive 2-out-of-n failed system composed of correlated components. The approach produces analytical expressions for the reliability of discrete and continuous systems in terms of the component reliabilities and the correlation between the failures of the components. We demonstrate our approach through examples, which illustrate the impact of correlated component failures on system reliability and metrics such as mean time to failure. These examples illustrate that correlated failures can negatively influence the reliability of a consecutive k-out-of-n:F system. Thus, the approach can quantify the improvements to system reliability that could be achieved by lowering the correlation between the failures of a system´s components.