Proceedings of the 2008 Winter Simulation Conference
S. J. Mason, R. R. Hill, L. Moench, O. Rose, eds.
OPTIMIZING INSPECTION STRATEGIES FOR MULTI-STAGE MANUFACTURING PROCESSES
USING SIMULATION OPTIMIZATION
Vahid Sarhangian Hamidreza Eskandari Mostafa K. Ardakani
Abolfazl Vaghefi
Dept. of Industrial Engineering School of Industrial Engineering Dept. of Civil Engineering
Iran University of Science & Technology Tarbiat Modares University The Catholic University of America
Tehran, 16844, IRAN Tehran, IRAN Washington, D.C. 20064, U.S.A.
ABSTRACT
This paper deals with the problem of determining the op-
timal inspection strategy for a multi-stage production
process using simulation optimization. An optimal inspec-
tion strategy is the one that results in the lowest total in-
spection cost, while still assuring a required output qual-
ity. Because of the complexity of the problem, simulation
is used to model the multi-stage process subject to inspec-
tion and to calculate the resulting inspection costs. Simu-
lation optimization is then used to find the optimal inspec-
tion strategy. The performance of the proposed method is
presented through the use of a numerical example.
1 INTRODUCTION
Manufacturing systems are generally consisted of several
stages, in which, raw materials pass through various op-
erations and eventually transform into finished products.
Each processing stage will produce a proportion of items
that fail to meet the necessary requirements. A prelimi-
nary idea to maintain the quality level is providing an in-
spection station after the last stage. This is generally re-
ferred to as outgoing inspection. However, with outgoing
inspection, all efforts and costs invested in producing de-
fective items during previous stages are wasted. It is more
reasonable to place inspection stations after every major
manufacturing process to insure that a specific quality
level is being maintained.
Efficient economic inspection strategies minimize the
total inspection cost while ensuring the required output
quality. In other words, a tight inspection results in higher
product quality, but will also lead to higher costs of in-
spection, scrap and rework. An optimum inspection plan
balances these effects.
After each manufacturing stage, a full or sampling in-
spection can be performed. In full (100%) inspection, all
of the items in a lot are inspected and defective items are
replaced or reworked. However, in sampling inspection, a
sample is picked and inspected from the lot and based on
the defective items observed in the sample, the lot can be
rejected or accepted. Accepted lots are released to the
next stage and rejected lots are submitted for full inspec-
tion. Good units replace all of the defectives found during
the sampling or 100% inspection. Thus, in a multi-stage
manufacturing system, the inspection strategy addresses
the number and location of inspection stations and inspec-
tion parameters (sample size, acceptance number) for
each inspection station.
Most multi-stage inspection models have focused on
100% inspection or screening, where defects occur inde-
pendently and costs are proportional to the number of de-
fects detected at each stage. Lindsay and Bishop (1964)
showed that if the cost functions for inspection and re-
working are assumed linear and the fraction of defective
units for each stage is assumed to be fixed, then the 100%
inspection will be more efficient than sampling. The simi-
lar results were found by White (1969) in the case where
the rejected items are repaired and replaced with good
items. Raz (1986) reviewed the previous researches on
multi-stage inspection allocation and found out that when
the inspection costs are concave, then the optimal level at
each stage is probably either 100% or 0%. On the other
hand, Montgomery (2005) presented several situations in
which sampling is most likely to be useful. For example,
when the cost of 100% inspection is high and/or inspec-
tions typically need destructive testing, sampling is pre-
ferred. Heredia-Langner et al. (2002) presented a highly
constrained multi-stage inspection problem where all
stages must receive partial rectifying inspection and they
solved their problem by using a real-valued Genetic Algo-
rithm. Volsem et. al (2007) used simulation to model the
multi-stage inspection problem and found the optimal in-
spection strategy by an Evolutionary Algorithm. Their
method is able to determine which type of inspection (0%,
100% or sampling) should be performed in each stage and
the rigor of the inspections. However, in their research
sampling parameters are considered fixed.
Wu et al. (2001) pointed out in real cases; many un-
avoidable factors (such as the wear of tools and the fluc-
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Proceedings of the 2008 Winter Simulation Conference
S. J. Mason, R. R. Hill, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds.