1
Reliability Problem
Consider a prototype reliability problem where
n
components in series define the
reliability of a system.
It is possible to install multiple units of a given component which
results in a corresponding increase in that component's reliability.
The problem then is to
determine how many units of each of the n components should be installed so as to
maximize the total system reliability subject to a budget constraint.
Component
reliability is given by a matrix of reliability's as a function of the number of units of each
component (limited to
m
).
In addition, we have a cost matrix which has arguments of
the component and number of units assigned by component.
The problem is to maximize the reliability subject to a budget constraint.
The
mathematical formulation of this problem is:
max
R
=
r
[
i
,
x
i
]
i
=
1
n
∏
subject to
c
i
=
1
n
∑
[
i
,
x
i
]
≤
t
x
i
∈
{1 ,
"
,
m
}, for
i
∈
{1,
"
,
n
},
where
r
[
i,j
] and
c
[
i,j
] are the reliability and the cost, respectively, of
j
units of component
i
and
t
is the total budget available to allocate among the
n
components.
The bracket
notation is used here since we are defining these data via matrices as opposed to general
functions.
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 Spring '07
 Klutke
 Hilbert space, component

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