Allocating hot standbys to randomly weighted k-out-of-n: G systems

Abstract

In industrial engineering applications, randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems can model many reliability systems whose components may contribute unequally and randomly to the systems’ performance. This paper investigates optimal allocations of hot standbys for [Formula: see text]-out-of-[Formula: see text]: G systems with random weights. First, optimal allocation policies are presented by maximizing the total capacity according to the usual stochastic ordering and the expectation ordering when the system is constituted by independent and heterogeneous components accompanied with independent random weights. Second, we investigate hot standbys allocation for randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems with right [left] tail weakly stochastic arrangement increasing random weights in the sense of the usual stochastic ordering [increasing concave ordering]. Simulation studies are provided to illustrate our theoretical findings as well. These established results can provide useful guidance for system designers on how to introduce hot standbys in randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems in order to enhance their total capacities.