The Superposition of Renewal Process (SRP) is often encountered in neuro science, queueing theory and reliability engineering. For example, the failure times of an industrial system composed of independent components in a series configuration can be modelled by an SRP if, after each breakdown, only the failed component is instantaneously repaired. In this context, we present an approximation method of SRP based on virtual age model, namely Arithmetic Reduction of Age with infinite memory (ARA). Using only three parameters, this auto correlated approximating process gives a more accurate estimation of systems lifetime and of the failure rate, compared to traditional approximations based on renewal process. An industrial application is presented, showing how to fit an ARA model to the observed failure times as well as the advantages and disadvantages of a such approximation.