An expre
ssion for the
stre
ss-
strength reli
ability <
sp
an id="mml
si9" cl
ass="m
athml
src"><
a title="View the M
athML
source" cl
ass="m
athImg" d
at
a-m
athURL="/
science?_ob=M
athURL&_method=retrieve&_eid=1-
s2.0-S1110256X16000213&_m
athId=
si9.gif&_u
ser=111111111&_pii=S1110256X16000213&_rdoc=1&_i
ssn=1110256X&md5=32f87
e1ad8999599
a8d0bb31b602cfde">
ass="imgL
azyJSB inlineIm
age" height="16" width="131"
alt="View the M
athML
source" title="View the M
athML
source"
src="/
sd/grey_pxl.gif" d
at
a-inlimgeid="1-
s2.0-S1110256X16000213-
si9.gif">
script>style="vertical-align:bottom" width="131" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S1110256X16000213-si9.gif">script>
a><
sp
an cl
ass="m
athCont
ainer hidden"><
sp
an cl
ass="m
athCode">
ath altimg="si9.gif" overflow="scroll">R=P(sub>X1sub><space width="0.16em">space>sub>X2sub>)ath>
sp
an>
sp
an>
sp
an> i
s obt
ained when the vector (
X<
sub>1
sub>,
X<
sub>2
sub>) follow
s a gener
al biv
ari
ate di
stribution. Such di
stribution include
s biv
ari
ate compound Weibull, biv
ari
ate compound Gompertz, biv
ari
ate compound P
areto,
among other
s. In the p
ar
ametric c
ase, the m
aximum likelihood e
stim
ate
s of the p
ar
ameter
s and reli
ability function
R are obt
ained. In the non-p
ar
ametric c
ase, point
and interv
al e
stim
ate
s of
R are developed u
sing Govind
ar
ajulu'
s asymptotic di
stribution-free method when
X<
sub>1
sub>
and
X<
sub>2
sub>
are dependent. An ex
ample i
s given when the popul
ation di
stribution i
s biv
ari
ate compound Weibull. Simul
ation i
s performed, b
ased on different
sample
size
s to
study the perform
ance of e
stim
ate
s.