Redundancy in systems with heterogeneous dependent components

Abstract

We study different redundancy mechanisms in coherent systems with possibly dependent heterogeneous components. The dependence is modelled through copulas. We use distortion functions to obtain general results for different redundancy procedures. This model includes the popular active redundancy and minimal repair procedures. The purpose is to determine where these redundant components should be located in the system, according to its structure. We study series and parallel systems in detail. In the first case (series systems), it is well known that active and minimal repair redundancies should be assigned to the weakest component. However, we show that, surprisingly, this is not always the case for all the redundancy mechanisms. Moreover, we give a condition on the redundancy mechanism to get this expected property. Similar results are obtained for parallel systems. In these systems one can think that the best option is to assign the redundancy to the strongest component. However, we prove that this is not always the case. We include results for other system structures as well and we show that these properties also depend on the copula (dependence structure).