Approximation of Superimposed Renewal Processes

A Superimposed Renewal Process (SRP) consists in the observation of inter-arrival times formed by the superposition of multiple independent renewal processes. In imperfect maintenance analysis, a repairable series system is commonly modelled by an SRP when maintenance actions consist of renewing the failed components while leaving the other components unchanged. An SRP involves a large number of parameters and in practice, the identification of the renewed components is often unrecorded. Therefore, an SRP is often reduced to a simpler process, usually a Homogeneous Poisson Process. This paper presents two new approximations of an SRP, one based on virtual ages, the other based on copulas. Both approximation methods make it possible to model the dependency between two successive inter-arrival times and to obtain a precise assessment of the Remaining Useful Life. The performance of the approximation methods is discussed when the parameters of the models are assumed to be known.