Two redundancy mechanisms in series and parallel systems with heterogeneous dependent components

In this paper, we study two redundancy mechanisms in series and parallel systems with possibly dependent heterogeneous components. The purpose is to determine where two redundant components should be located in series and parallel systems, according to their structures. In the series system, 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. Similar results are obtained for parallel system. In the parallel system, 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 present some results for other system structures as well and show that these properties also depend on the copula (dependence structure).