Reliability Functions of Bivariate Distributions in Modeling Marked Point Processes

Abstract

The purpose of this article is to study the bivariate distributions, proposed by Hassan and Lii^{[ 19 ]}, in modeling marked point processes, from the reliability point of view. The reliability functions, viz. the survival function, the failure rate, and the mean residual life function, are derived and their monotonicity is discussed for the marginals as well as the conditional models. The monotonicity of the failure rate, in the case of series system, is also investigated. Finally, Clayton's association measure is obtained in terms of the hazard gradient and its value, in the case of our model, is derived.

Keywords:

• Association measure
• Failure rate
• Hazard components
• Mean residual life function
• Monotonicity
• Series system

Mathematics Subject Classification:

• Primary 62E, 62N
• Secondary 60E

ACKNOWLEDGMENT

The author is thankful to the referee for some useful suggestions that enhanced the presentation.