Stochastic Comparisons of Two-Units Repairable Systems

TL;DR

This paper compares the lifetimes of two-unit repairable systems, including cold and warm standby configurations, using stochastic orders, and extends analysis to non-exponential distributions.

Contribution

It introduces stochastic comparison methods for repairable systems with exponential and non-exponential component distributions, enhancing understanding of system reliability.

Findings

Cold and warm standby systems' lifetimes are compared under various parameter assumptions.

Stochastic orders provide a framework for system lifetime comparison.

Extension to non-exponential distributions broadens applicability.

Abstract

We consider two models of two-units repairable systems: cold standby system and warm standby system. We suppose that the lifetimes and repair times of the units are all independent exponentially distributed random variables. Using stochastic orders we compare the lifetimes of systems under different assumptions on the parameters of exponential distributions. We also consider a cold standby system where the lifetimes and repair times of its units are not necessarily exponentially distributed.