On Stochastic Comparisons for Load-Sharing Series and Parallel Systems

TL;DR

This paper investigates optimal strategies for allocating redundant components in load-sharing series and parallel systems to maximize reliability, demonstrating that allocating to the weakest or strongest components is optimal under certain models.

Contribution

It establishes new stochastic comparison results for load-sharing systems and identifies optimal redundancy allocation strategies under the cumulative exposure model.

Findings

Allocating redundancy to the weakest component in series systems maximizes reliability.

Allocating redundancy to the strongest component in parallel systems maximizes reliability.

Results are valid under the cumulative exposure model and general scenarios.

Abstract

We study the allocation strategies for redundant components in the load-sharing series/parallel systems. We show that under the specified assumptions, the allocation of a redundant component to the stochastically weakest (strongest) component of a series (parallel) system is the best strategy to achieve its maximal reliability. The results have been studied under cumulative exposure model and for a general scenario as well. They have a clear intuitive meaning, however, the corresponding additional assumptions are not obvious, which can be seem from the proofs of our theorems