On optimal allocation of redundancies in random weighted k $$ k $$ -out-of- n $$ n $$ systems

Random weighted $k$-out-of-$n$ systems are very useful in modeling the lifetimes of systems, wherein the success or failure of a system depends not only on its current operational status, but also on the contributions made by its components. In this paper, we consider random weighted $k$-out-of-$n$ systems with redundant components drawn randomly from a mixed population consisting of $m$ different subpopulations/substocks. We study different optimal allocation policies of active redundancies and minimal repair components in a random weighted $k$-out-of-$n$ system. Moreover, we investigate how the heterogeneity of subpopulations of items impacts the lifetime of a random weighted $k$-out-of-$n$ system. We also present some simulational results and a real data analysis for illustrative purpose.