International Journal of Scientific & Engineering Research, Volume 3, Issue 10, October-2012 1
ISSN 2229-5518
IJSER © 2012
http://www.ijser.org
FUZZY PROGRAMMING APPROACH FOR A COMPROMISE ALLOCATION
OF REPAIRABLE COMPONENTS
Irfan Ali* and S. Suhaib Hasan
ABSTRACT
The present paper, considered the allocation problem of repairable components for a parallel-series system as a multi-objective optimization problem for
two different models. In the first model, the reliability of subsystems are considered as different objectives. While in the second model, the cost and time
spent on repairing the components are considered as two different objectives. Selective maintenance operation is used to select the repairable
components and a fuzzy programming algorithm is used to obtain compromise allocation of repairable components for the two models under some given
constraints. A numerical example is also given to illustrate the procedure.
Key Words: Reliability, Fuzzy Programming, Compromise allocation, Selective Maintenance, Multi-objective programming.
.
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1. INTRODUCTION
In every industry, systems are used in the production of
goods. If such systems deteriorate or fail, then effect can
be wide spread. System deterioration is often reflected in
higher production cost, time lower product quality and
quantity. The system maintenance decision is taken on
the basis of the state condition of the system (i.e. whether
the system is good or bad). The aim is to present a model
of reliability improvement maintenance policies that
minimizes the total cost and time spent on maintaining a
system. For this purpose, we consider a system which is
a series arrangement of m subsystems and performing a
sequence of identical production runs.
Suppose that after completion of a particular production
run, each component in the system is either functioning
or failed. Ideally all the failed components in the
subsystems are repaired and then replaced back prior to
the beginning of the next production run. However, due
to constraints on time and cost, it may not be possible to
repair all the failed components in the system. In such
situation, a method is needed to decide which failed
components should be repaired and replaced back prior
to the next production run and the rest be left in a failed
condition. This process is referred to as selective
maintenance (See Rice et al. 1998). In the selective
maintenance the number of components available for
the next production run in the
th
i subsystem will be
i i i
d a n ) ( , m i ..., , 2 , 1 (1)
The reliability of the given system is defined as
R =
m
i
d a n
i
i i i
r
1
) 1 ( 1 (2)
The repair time constraint for the system is given as
0
1
) exp( T d d t
m
i
i i i i
(3)
where
i
t is the time required to repair a component in
th i subsystem and ) exp(
i i
a is the additional time
spent due to the interconnection between parallel
components (Wang et al. (2009)).
The repair cost constraint for the system is defined as
0
1
) exp( C d d c
m
i
i i i i
(4)
where ) exp(
i i
a is the additional cost spent due to the
interconnection between parallel components (Wang et
al. (2009)).
However, in the event when the reliability of each
subsystems are of equally serious concern. Let us
consider, for instance, the following multi-objective
problem (see Ali et al. (2011c)):
) ( integers and ,..., 2 , 1 , 0
) ( ) exp (
) ( ) exp (
to subject
) ( , , ,
0
1
0
1
2 1
iv m i a d
iii C d d c
ii T d d t
i R R R Maximize
i i
m
i
i i i i
m
i
i i i i
m
(5)