Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices
1
Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada
2
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
▼
Show Figures
Figure 1
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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 StyleBalakrishnan, 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
Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
