Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices

Abstract

In this paper, we consider stochastic comparisons of parallel systems with proportional reversed hazard rate (PRHR) distributed components equipped with starting devices. By considering parallel systems with two components that PRHR and starting devices, we prove the hazard rate and reversed hazard rate orders. These results are then generalized for such parallel systems with n components in terms of usual stochastic order. The establish results are illustrated with some examples.

Keywords

• parallel systems
• hazard rate order
• reversed hazard rate order
• usual stochastic order
• proportional reversed hazard rate distribution
• starting devices