On Optimal Operational Sequence of Components in a Warm Standby System

TL;DR

This paper investigates the optimal sequence for activating components in a warm standby system, demonstrating that ordering by increasing lifetime maximizes system reliability under certain models.

Contribution

It introduces a new optimal activation strategy based on the virtual age and cumulative exposure models, extending previous limited cases.

Findings

Activation in increasing lifetime order is optimal under the models used.

System lifetime comparisons are made using stochastic precedence order.

The approach generalizes prior specific case analyses.

Abstract

We consider an open problem of optimal operational sequence for the $1$-out-of-$n$ system with warm standby. Using the virtual age concept and the cumulative exposure model, we show that the components should be activated in accordance with the increasing sequence of their lifetimes. Lifetimes of the components and the system are compared with respect to the stochastic precedence order. Only specific cases of this optimal problem were considered in the literature previously.