Orderings and Ageing of Reliability Systems with Dependent Components Under Archimedian Copulas

Abstract

In this paper, we have considered systems with dependent components having a joint distribution modeled by an Archimedean copula and with component lifetimes following accelerated failure time and modified proportional hazards distributions. We have then established characterization results specifically for series, fail-safe, 2-out-of n and parallel systems through comparisons with average systems in terms of mean residual life, hazard rate and reversed hazard rate orders. We have also discussed various stochastic orderings and ageing results for the residual lives of parallel and series systems. The results established here are quite general, and several examples have been used to illustrate all the results and their reliability implications.

Keywords

• stochastic orders
• ageing faster in hazard rate
• ageing faster in reversed hazard rate
• series systems
• parallel systems
• fail-safe systems