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

Abstract Random weighted ‐out‐of‐ 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 ‐out‐of‐ systems with redundant components drawn randomly from a mixed population consisting of different subpopulations/substocks. We study different optimal allocation policies of active redundancies and minimal repair components in a random weighted ‐out‐of‐ system. Moreover, we investigate how the heterogeneity of subpopulations of items impacts the lifetime of a random weighted ‐out‐of‐ system. We also present some simulational results and a real data analysis for illustrative purpose.