Page 2 - SUBHARADEV SEN AND AHMED

SEN AND AFIFY

distribution with probability density function (pdf) and cumulative
distribution function (cdf) as

,0 ; , 0 (1)

, 0 , (2)

respectively. On a note, Lai and Mukherjee ([3], 1986) have
investigated some of the interesting properties of the density in (1) for
0 < p < 1 in reliability context.

For studying characteristics of multi-component system reliability, it
is rational to assume positive or negative interdependence for the life
lengths of the components. This interdependence might be caused due
to mechanical sticking of configurations, functional dependence on
common source of energy, incidental or environmental stresses, etc.
Although several works have been done in studying coherent
dependent systems for infinite life lengths of components under
different configurations [see, for example, Eryilmaz ([1], 2011),
Mukherjee and Sasmal ([5], 1977), Navarro et al. ([6], 2007), Navarro
and Rychlik ([7], 2007), Thomas ([9], 1986)], no or little is yet
known about dependent systems with finite range lifetimes for even
two components.
The objective of the present investigation is to study the life behavior
of a two-component system under bivariate finite range (BVFR)
distribution assumption. In this article we introduce a bivariate
version of the finite range distribution given in (1) and thereby study
the detailed characteristics of a system life distribution in terms of
failure rate and reliability. The rest of the article is organized as
follows.

In section 2, BVFR is developed following the method of Farlie-
Gumbel-Morgenstern (FGM) copula and some basic properties useful
for the context are studied. Section 3 deals with distributions of
system lives and some basic distributional properties. Mean failure
times of dependent systems are compared, through numerical
considerations, with those of independent systems in subsection 3.1.
System reliabilities are studied in section 4 along with numerical
tabulations. Section 5 deals with the failure rate functions of the

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