Discrete and Continuous Consecutive 2-Out-of-n:F System Reliability with Correlated Components

Abstract

A linear consecutive [Formula: see text]-out-of-[Formula: see text]:failed system, henceforth written consecutive [Formula: see text]-out-of-[Formula: see text]:F, is an [Formula: see text]-component system that fails if [Formula: see text] or more consecutive components in positions [Formula: see text] fail, where [Formula: see text]. The consecutive [Formula: see text]-out-of-[Formula: see text]: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 [Formula: see text]-out-of-[Formula: see text]: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.

Correlated reliability and an application: Propulsive landing on Mars

“…In another publication, Fiondella and Xing 38 consider correlated systems with two failure modes per component and conclude that ignoring correlation may lead to overstatement of system reliability. Lai, 39 Fiondella and colleagues, 40,41 and Jafary and colleagues 42,43 provide interesting numerical correlated reliability examples for systems that relate to the FEDS and the SEDS in varying degrees. Two additional publications by Fiondella and colleagues 44,45 investigate other aspects of correlated reliability including negative correlation.…”