Page 4 - SUBHARADEV SEN AND AHMED

SEN AND AFIFY

The corresponding cdf of (X, Y) is given by

, 1 , 0 , . (4)

The distribution has identical finite range marginals with
and . Further,

4
, 1,
1 1

and
4 2
, 1,
1
which is independent of θ. Note that for α = 0, ρ(X, Y) = 0, i.e., X and Y are
linearly independent (although may be dependent in non-linear sense). Since
| α | ≤ 1, we have, , for 1.

3. DISTRIBUTION OF SYSTEM LIFE
This section deals with the distributions and related characterizations of the
system lives with respect to two-component configurations of coherent
dependent systems.
As we know, the system life distribution depends on system configuration
and in this present article we have considered series, hot (parallel) redundant
and cold (standby) redundant systems. A two-component series system
survives as long as both the components survive. On the other hand, a
parallel redundant system survives as long as either of the two
simultaneously functioning components survives. In a standby redundant
system the second redundant component starts functioning from the instant
at which the first basic component fails. As mentioned earlier, the
assumption of a BVFR distribution as given in (3) indicates that life
distributions of the two components are identically finite range distributions
given in (1). Let T 1, T 2 and T 3 denote, respectively, the lifetimes of a two-
component series system, a two-component parallel system, and a two-
component standby redundant system.
So, if X and Y denote the lifetimes of components 1 and 2, respectively, then
we have

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