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APPLIED PROBABILITY METHODS IN ENGINEERING
OEM 2009
March 15, 2008
INCLASS ASSIGNMENT  SOLUTIONS
Slide 10
•
If the design life is 1 year, the minimum required reliability is apparently
r
(1)
=
exp
!
0.048
( )
"
0.953.
•
If the minimum required reliability is 90%, the design life is the solution to
exp(
!
0.04
t
!
0.008
t
2
)
=
0.90
!
0.04
t
!
0.008
t
2
=
ln(0.90)
0.008
t
2
+
0.04
t
+
ln(0.90)
=
0
i.e., the design life is
t
=
!
0.04
+
0.04
2
!
4
"
0.008
"
ln(0.90)
2
"
0.008
#
1.91 years.
(Note that the other solution to the quadratic equation is negative and therefore
meaningless.)
Slide 48
The system reliability function is given by
r
(
t
)
=
r
1
(
t
)
!
1
"
1
"
r
2
(
t
)
!
r
3
(
t
)
( )
!
1
"
r
4
(
t
)
( )
!
1
"
r
5
(
t
)
!
r
6
(
t
)
( )
{ }
.
Slide 49
The system reliability function is given by
r
(
t
)
=
r
1
(
t
)
!
1
"
1
"
r
2
(
t
)
!
r
3
(
t
)
+
r
#
3
(
t
"
s
)
f
3
(
s
)
ds
0
t
$
%
’
(
)
*
+
,


.
/
0
0
!
1
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This note was uploaded on 05/12/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.
 Spring '07
 JosephGeunes

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