Signatures of Repairable Systems

Abstract

The literature related to system signatures is briefly discussed. In short, computing a “signature” is associated with the fact of capturing the essence of a coherent system to simplify the quantification of its reliability. In this context, a representation of the reliability function of a repairable coherent system of components is addressed. It is assumed that each component can individually fail and be minimally repaired up to a fixed number of times. Failures occur at any component according to a nonhomogeneous Poisson process with a common intensity function. First, it is shown that the reliability function of a series system can be written in terms of the intensity function and a distribution‐free measure based on the probabilities of the number of repairs until system failure. Secondly, the utility of this result in the comparative study of system performance is illustrated through a “preservation” theorem. Finally, the results for series systems lead to an explicit expression for computing the reliability function of any repairable coherent system that depends on a distribution‐free measure of the system's design.

Discussion of signature‐based models of preventive maintenance

“…After the general view of PM actions, the main purpose of the paper is focusing on describing recent optimal PM models on complex multi‐component coherent systems where the reliability function is expressed in terms of the signature of the system. As described in Reference 3 “computing a signature is associated with the fact of capturing the essence of a coherent system to simplify the quantification of its reliability that leads us to better understand the nature of each system”. Here the authors start by describing the classical signature introduced by Samaniego 4 and after that also the two more recent concepts of survival signatures and $$$ t $$$‐signatures.…”