Abstract
A linear consecutive k-out-of-n: failed system, henceforth written consecutive k-out-ofn: F, is an n-component system that fails if k or more consecutive components in positions i, (i + 1),..., (i + k - 1) fail, where 1 <= i <= n - (k - 1). The consecutive k-out-ofn: F system model is particularly valuable for characterizing critical infrastructures such as telecommunications that provide essential services to society. However, events that impact critical infrastructures such as natural disasters often produce geospatially correlated failures, necessitating reliability models that can accommodate these scenarios where component failures may be correlated.
This paper presents a method to explicitly model the correlation between component failures of a consecutive 2-out-of-n:F system. The approach produces analytical expressions for the reliability of discrete and continuous systems in terms of component reliabilities and correlation between the component failures. The explicit correlation parameter simplifies sensitivity analysis for a variety of measures of interest, including reliability, density function, hazard rate, mean time to failure (MTTF), availability, and mean residual life (MRL). It is illustrated through examples where correlated failures can negatively influence system reliability. Thus, the approach can quantify improvements to system reliability that could be achieved by lowering the correlation between failures of system components.