Stochastic comparisons of parallel systems with starting devices

Abstract

In this paper, we consider stochastic comparisons of parallel systems with location-scale distributed components equipped with starting devices. We specifically establish the hazard rate order of parallel systems with two location-scale distributed components equipped with starting devices when the starting devices have different probabilities but with the same location-scale distributed component. Next, we present the usual stochastic order of parallel systems with n location-scale distributed components equipped with starting devices. We also provide some numerical examples to illustrate all the comparison results established here.

Keywords:

• Parallel Systems
• hazard rate order
• usual stochastic order
• location-scale distribution

Acknowledgements

The authors express their sincere thanks to the Editor and the anonymous reviewers for their useful comments and suggestions on an earlier version of this manuscript, which led to this improved version. Ghobad Barmalzan thanks University of Zabol for supporting the work with grant number $\mathit{UOZ}-GR-3384.$