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.
Highlights
Comparison of important characteristics of lifetimes of technical systems is of interest in many problems
We consider only stochastic comparisons of parallel systems with proportional reversed hazard rate (PRHR) distributed components equipped with starting devices
We establish the hazard rate, reversed hazard rate and usual stochastic orders of parallel systems with PRHR distributed components equipped with starting devices
Summary
Comparison of important characteristics of lifetimes of technical systems is of interest in many problems. It is of natural interest to evaluate the influence of heterogeneity among the components and the random shocks on the lifetimes of parallel and series systems, and this reliability problem forms the main basis for the present work. We consider only stochastic comparisons of parallel systems with proportional reversed hazard rate (PRHR) distributed components equipped with starting devices. We establish the hazard rate, reversed hazard rate and usual stochastic orders of parallel systems with PRHR distributed components equipped with starting devices. Mathematics 2021, 9, 856 comparisons of parallel systems are established for different probabilities of starters in terms of reversed hazard rate order.
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