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

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