Civil Engineering Reference
In-Depth Information
different objective functions that include different cost items. The objective of the mathematical models
presented previously can be summarized as the following categories:
(i) Minimization of cost-tolerance function (Balakrishnan, 1993)
Min
C
()
S.T. tolerance stackup constraints
machining accuracy constraints
(ii) Minimization of cost-tolerance function and rework cost (Lee et al., 1993)
Min
C
()
Cr
S.T.
tolerance stackup constraints
machining accuracy constraints
is the rework cost.
(iii) Minimization of machining, material and rework costs (Malek & Asadathorn, 1994)
where
Cr
Min
C
()
M
1
p
()
R
2
p
()
S.T.
tolerance stackup constraints
machining accuracy constraints
where
R
and
R
are the rework cost for under-sized and over-sized parts,
p
and
p
are the
1
2
1
2
is the material cost.
(iv) Minimization of cost-tolerance function and quality loss (Cheng & Maghsoodloo, 1995)
probability of reworking,
M
2
()
Min
C
Ek
i
y
i
{
(
m
i
)
}
S.T.
tolerance stackup constraints
machining accuracy constraints
where
E
denotes expected quality loss,
k
is constant,
i
y
is a measurement of quality characteristic,
i
m
is the target of
y
i
i
(v) Minimization of scrap cost (Wei, 1997)
()
Min
C
r
{}
S.T.
tolerance stackup constraints
machining accuracy constraints
where
r
denotes the scrap rate of operation.
i
2.5
Computer-Aided Cost-Tolerance Optimization
Computer technology has been widely applied to tolerance design during the last two decades. Along with
the concept of computer-aided design and computer-aided manufacturing, the tasks of tolerance design
are combined with the CAD/CAM system. Farmer [25] has developed an interactive tolerance design
module on a CAD system. Juster [26] has established experimental software named GEOTOL, which
