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Article

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

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Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada
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Department of Statistics, University of Zabol, Zabol 98615-538, Sistan and Baluchestan, Iran
3
Department of Mathematics, University of Zabol, Zabol 98615-538, Sistan and Baluchestan, Iran
*
Author to whom correspondence should be addressed.
Academic Editor: Jean-Charles Pinoli
Mathematics 2021, 9(8), 856; https://doi.org/10.3390/math9080856
Received: 4 February 2021 / Revised: 24 March 2021 / Accepted: 8 April 2021 / Published: 14 April 2021
(This article belongs to the Special Issue Reliability and Statistical Learning and Its Applications)
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. View Full-Text
Keywords: parallel systems; hazard rate order; reversed hazard rate order; usual stochastic order; proportional reversed hazard rate distribution; starting devices parallel systems; hazard rate order; reversed hazard rate order; usual stochastic order; proportional reversed hazard rate distribution; starting devices
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MDPI and ACS Style

Balakrishnan, N.; Barmalzan, G.; Kosari, S. Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices. Mathematics 2021, 9, 856. https://doi.org/10.3390/math9080856

AMA Style

Balakrishnan N, Barmalzan G, Kosari S. Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices. Mathematics. 2021; 9(8):856. https://doi.org/10.3390/math9080856

Chicago/Turabian Style

Balakrishnan, Narayanaswamy, Ghobad Barmalzan, and Sajad Kosari. 2021. "Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices" Mathematics 9, no. 8: 856. https://doi.org/10.3390/math9080856

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