On comparison of two parallel systems having Log–Lindley distributed components

Abstract

In this article, we compare two parallel systems of heterogeneous-independent Log–Lindley distributed components using the concept of matrix majorization. The comparisons are carried out with respect to the usual stochastic ordering when each component receives a random shock. It is proved that for two parallel systems with a common shape parameter vector, the majorized matrix of the scale and shock parameters leads to better system reliability. Results related to the comparison of two parallel systems having heterogeneous -dependent Log–Lindley component are also presented in terms of usual stochastic ordering.

Keywords:

• Parallel system
• stochastic order
• Log–Lindley distribution
• random shock
• matrix majorization
• Archimedean copula

AMS 2010 SUBJECT CLASSIFICATIONS:

• 62G30
• 60E15
• 60K10

Acknowledgments

The authors would like to thank the referees for their valuable suggestions, which helped to improve the presentation of this article. On behalf of all authors, the corresponding author states that there is no conflict of interest.