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

Christian Tanguy (1)

1 Orange Labs [Issy les Moulineaux]

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.

Mots clés: network reliability; mean time to failure; generating function; moments; cumulants

Domaines: Performance et fiabilité [cs.PF]

Christian Tanguy. Asymptotic Mean Time To Failure and Higher Moments for Large, Recursive Networks. 2008. ⟨hal-00293225⟩