Asymptotic Mean Time To Failure and Higher Moments for Large, Recursive Networks

TL;DR

This paper derives asymptotic formulas for the mean time to failure and higher moments of large recursive systems, extending classical reliability results to more complex configurations and non-exponential component failures.

Contribution

It provides new asymptotic expressions for MTTF and higher moments in large recursive systems, including non-exponential failure distributions, broadening reliability analysis scope.

Findings

Asymptotic expressions for MTTF in large systems

Power-law behavior in system reliability

Impact of non-exponential failure distributions

Abstract

This paper deals with asymptotic expressions of the Mean Time To Failure (MTTF) and higher moments for large, recursive, and non-repairable systems in the context of two-terminal reliability. Our aim is to extend the well-known results of the series and parallel cases. We first consider several exactly solvable configurations of identical components with exponential failure-time distribution functions to illustrate different (logarithmic or power-law) behaviors as the size of the system, indexed by an integer n, increases. The general case is then addressed: it provides a simple interpretation of the origin of the power-law exponent and an efficient asymptotic expression for the total reliability of large, recursive systems. Finally, we assess the influence of the non-exponential character of the component reliability on the n-dependence of the MTTF.