Stochastic order relations among parallel systems from Weibull distributions

TL;DR

This paper investigates stochastic order relations among parallel systems with Weibull distributions, extending previous exponential-based results to Weibull cases and exploring multiple-outlier models.

Contribution

It introduces new stochastic order results for Weibull-distributed parallel systems, generalizing prior exponential distribution findings and analyzing multiple-outlier models.

Findings

Extended stochastic order relations from exponential to Weibull distributions.

Derived results for multiple-outlier Weibull models.

Compared system magnitudes based on majorization of scale parameters.

Abstract

In this article, we focus on stochastic orders to compare the magnitudes of two parallel systems from Weibull distributions when one set of scale parameters majorizes the other. The new results obtained here extend some of those proved by Dykstra et al. (1997) and Joo and Mi (2010) from exponential to Weibull distributions. Also, we present some results for parallel systems from multiple-outlier Weibull models.