On Component Redundancy Versus System Redundancy for a $k$-out-of-$n$ System

TL;DR

This paper compares component-level and system-level redundancy in $k$-out-of-$n$ systems, demonstrating that component redundancy generally offers superior reliability in terms of stochastic precedence order.

Contribution

It establishes that, for $k$-out-of-$n$ systems, component redundancy outperforms system redundancy regarding stochastic precedence, extending understanding of optimal redundancy placement.

Findings

Component redundancy is superior to system redundancy in stochastic precedence order.

Active and cold redundancy cases are analyzed.

Results align with existing literature on other stochastic orders.

Abstract

Precedence order is a natural type of comparison for random variables in numerous engineering applications (e.g., for the stress-strength modeling). In this note, we show that, for a $k$-out-of-$n$ system, redundancy at the component level is superior to that at the system level with respect to the stochastic precedence order. Cases of active and cold redundancy are considered. Similar results for other stochastic orders were intensively discussed in the literature.