Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management
Dhaka, Bangladesh, January 9 10, 2010
647
Preventive Maintenance Optimization of Critical Equipments in
Process Plant using Heuristic Algorithms
Mahadevan ML, Poorana Kumar S, and Vinodh R
Department of Mechanical Engineering
Thiagarajar College of Engineering, Madurai, Tamilnadu, India
Paul Robert T
Department of Industrial Engineering
Anna University, Chennai, Tamilnadu, India
Abstract
The rapid growth of industries has complicated the functioning system and has intensified the maintenance process
emphasizing the need for effective maintenance planning. Maintenance planning is complex and inherently
stochastic, indicating the need for heuristic techniques. In this paper, maintenance planning problem for a process
industry is addressed. The problem is formulated to predict which of the two possible actions (viz. imperfect
maintenance or component replacement) is to be carried out for each of the components during the planning period.
The net present cost for the entire design out period is minimized and furthermore, improvement possibilities during
the preventive maintenance action are analyzed in terms of Mean Time Between Failures (MTBF) & Mean Time To
Repair (MTTR). Two search techniques, Simulated Annealing (SA) and Genetic Algorithms (GAs), are used to
solve the problem.
Keywords
Maintenance planning, Simulated Annealing technique, Genetic Algorithms, Simulation.
1. Introduction
Maintenance Management is a key function used by industrial systems that deteriorate and wear with usage and age.
The primary objective of maintenance management is to increase equipment availability and overall effectiveness.
Since the cost of maintenance is very high, modern industry requires not only the theoretical basis to express the
experience of operators, but also the identification of proper techniques to optimize the maintenance action.
Maintenance Scheduling grows importance as the maintenance cost accounts for a significant portion of the total
production cost in capital intensive industries. Scheduling is a crucial component of maintenance management.
Effective use of scheduling is a major factor of workforce productivity.
The maintenance scheduling problem is a combinatorial optimization problem. Many traditional techniques have
proved to be fruitful in maintenance optimization problems. The use of Max to Min and Min to Max heuristics has
been proposed for solving preventive maintenance problems and their performances are compared [1]. The use of
dynamic Lipschitz optimization algorithm has outperformed heuristic techniques for solving the Maintenance
Scheduling Problem for a Family of Machines [2]. However, non traditional modeling techniques have typically
been used in Maintenance planning. Non traditional techniques such as SA and GA overcome many of the
limitations of the traditional optimization techniques and are well suited to solve generator maintenance scheduling
problems [3]. A methodology based on GA and Monte Carlo simulation has been designed to optimize the
preventive maintenance planning by evaluating the expected cost of maintenance and the expected economic loss
[4]. An Ant Colony Optimization approach to solve Thermal Generator Maintenance Scheduling Problem has
pointed out not only the good solutions to be adopted but also the bad solutions to be neglected [5]. A method for
preventive maintenance scheduling optimization of standby systems based on genetic algorithm and probabilistic
safety analysis with an approach to improve the average availability of the system has been proposed [6].
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Hybrid models are known to include the positive aspects of two or more techniques to reach an optimal solution. A
tabu-based GA prevents inbreeding and supplies moderate selection pressure so that the selection efficiency is
improved and the population diversity is maintained [7]. A combined use of SA and GA considering reliability and
operation expense provides a compromising solution for unit maintenance scheduling problems [8]. A hybrid
approach based on combined use of SA and GA is more effective than approach based on GA for complex
multidimensional maintenance scheduling problems [9]. The use of SA in a GA framework for solving generator
maintenance scheduling in power systems has proved to be more effective than approaches based only on GA or SA
[10]. A hybrid algorithm of SA and TS method is found to improve the computation time and the convergence
property [11]. A combination of SA, GA and Tabu Search (TS) method has proved to be effective in solving large
scale long-term thermal generating unit maintenance scheduling problems [12].
2. The Maintenance Model
Raw-mill process is one of the critical processes in a cement industry. In this process, lime ore is pulverized in
different stages and is supplied to the clinkerization process. A schematic diagram of a raw-mill process system for a
cement process industry including the subsystems is shown in figure1. The accurate failure and repair data required
for a realistic system performance study are obtained from the in-house plant records maintained for the companys
own use. The problem considers the choice of two possible actions (viz. imperfect maintenance or component
replacement) for each of the components during the planning period. The study proposes various corrective
maintenance actions on the critical components during the preventive maintenance to maximize the system
performance at minimal costs.
Figure 1: Raw-mill system of the cement industry
In practice, the two corrective maintenance policies namely increase in MTBF and/or decrease in MTTR can be
implemented. The improvements to the MTBF and MTTR at 5%, 10% and 15 % levels in the critical components
are considered for maintenance action. Hence, the objective is to determine the most cost effective maintenance
policy. The identified critical subsystems are: (1) Booster fan (2) Conveyor roller assembly (3) Air slide (4) Silo
feed elevator (5) Separator system (6) Impact crusher - rotor system (7) Raw-mill gear system NWCS bearing and
countershaft.
3. Objective Function
The problem considered is a maintenance scheduling problem for a process industry. There are seven subsystems
connected in series configuration. Maintenance or replacement activity in any of these subsystems results in
cessation of the entire process. In this problem, the combination of maintenance or replacement activities for the
components during the entire design out period is obtained and for each period maintenance and replacement costs,
time to repair, downtime cost, failure cost and standby costs are all included. The historical failure data of the raw-
mill system are well fit into 2-P weibull distribution and the parameters , are estimated.
Total cost:
1
( ( * ))
(1 )
=
+
=
+
n
j jp sd
j
j
C d C
Z
k
1,2,...15 = j (1)
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Where,
1
{ ( ) }
=
= + + + +
m
j ij ij ij ij ij ij ij i j
i
C X M Y R X B MR F 1,2,...7; 1,2,...15 = = i j (2)
( )
ij ij i ij
F = R + TTR*Csd *V(t) (3)
i
-1
ij
i
ij
i i
t
V(t) =
(4)
1(1 )
j
ij i
M M m = + (5)
1(1 )
j
ij i
R R r = + (6)
1
1(1 )
=
= +
s
n
ij n
n
B k P Where s =1,2,3 (7)
1* =
ij
MR k Sc Where s =1 (8)
1 1
(1 )
ijs ijs ijs n
MR MR MR Q
= + + Where s =2,3 (9)
P, Q Improvement percentage in MTBF and MTTR respectively
X
i,j
0 represents no maintenance & 1 represents maintenance for component i at period j
Y
i,j
0 represents no replacement & 1 represents replacement for components i at period j
M
i,j
Maintenance cost for component i at period j
R
i,j
Replacement cost for component i at period j
TTR
i
Time to repair the component i
C
sd
Downtime cost of the system per hour
V(t) Failure rate (Failure/period)
F
i,j
Failure cost per period for component i at period j
B
i
Cost of increasing MTBF of a component i
MR
i
Cost of decreasing MTTR of a component i
d
j
Downtime during the j period in hours
T
i,j
Age of the component at the end of the period j
Maintenance improvement factor (0 1)
i
,
i
Weibull parameters for component i
K Discount factor per period
4. Genetic Algorithm
4.1 Principle
Genetic algorithms are stochastic search techniques based on the mechanism of natural selection and natural
genetics [13]. GAs start with an initial set of random solutions called a population. Each individual in the population
is called a chromosome. A chromosome is a string that is usually but not always a binary bit string. The
chromosomes evolve through successive iterations called generations. During each generation, the chromosomes are
evaluated using some measures of fitness. To create the next generation, crossover and mutation operations are
carried out. Exceptional elements in the new generation are replaced by new chromosomes so as to keep the
population size constant. After several generations, the solution converges into the best optimum value.
4.2 Fitness function
GA is naturally suited to solve maximization problems. Minimization problems are usually converted into
maximization problems using an appropriate conversion. In general, a fitness function F(x) is first derived from the
objective function f(x) and then used in successive genetic operations. The following fitness function is often used
for minimization problem: F(x) =1/(1+f(x))
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4.3 Reproduction
The reproduction operator is applied to emphasize good solutions and to eliminate bad solutions in a population
while keeping the population size constant. There are a wide number of reproduction operators. Rank order selection
is one of the popular methods where the best fitness chromosomes are selected for the mating pool.
4.4 Crossover
Crossover operates on two chromosomes at a time and generates offspring by combining both chromosomes
features. In single point crossover of two chromosomes, a cross over point is selected (Random) in both
chromosomes and the part of the chromosome before or after this point is replaced by the similar part from the other
chromosome. A higher crossover rate (p
c
) allows the exploration of large solution space and reduces the chances of a
false optimum.
4.5 Mutation
Mutation involves flipping a bit in the chromosome. It replaces the genes lost from the population during the
selection process or provides the genes that were absent in the initial population. The mutation rate (p
m
) controls the
rates at which new genes are introduced into the population. Very low mutation rate would neglect many useful
genes and a very high value would result in large number of random perturbations, loss of parent-offspring
resemblance and the algorithm will finally lose the ability to learn from the history of search.
4.6 GA procedure
begin
g =0
initialize P(g)
evaluate P(g) using fitness function
termination_condition =false
while (NOT termination_condition) do
begin
g =g+1; select parents from P(g)
crossover
mutation
evaluate P(g+1) using fitness function
end
end
5. Simulated Annealing Technique
5.1 Principle
The technique simulates the process of cooling of molten metal to achieve the minimum function value in a
minimization problem [14]. Since a system at a low temperature has a small probability of being at a high energy
state, the temperature is lowered from the initially set value to the terminating temperature where the convergence is
achieved. The cooling factor reduces the temperature which in turn confines the search area towards the optimal
solution.
5.2 Temperature
The initial temperature (T) and the number of iterations for a particular temperature determine the effective
performance of this technique. When the T value is large, it takes a number of iterations for convergence while a
small T value does not provide an adequate investigation of the search space before a true optimum solution is
achieved. There is no proper strategy to set the initial temperature value and hence a trial and error approach is to be
adopted. Unlike many traditional algorithms, the SA technique does not simply reject the less probable solutions but
uses the Metropolis Algorithm to determine their acceptability. The algorithm generates a probability value which
when compared with a random number generated from 0 to 1 says whether the solution is to be accepted or not. The
common equation used to find the probability value is P =min[1, exp(-E/kT)].
5.3 SA procedure
begin
initialize (T,x)
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termination_condition =false
while (NOT termination_condition) do
begin
for i =1 to L do
begin
generate y from x
if (f(y) f(x) 0)
then x =y; else if (exp[-(f(y) f(x))/T] >random[0,1]) then x =y
end
lower T
end
end
6. GA Implementation
In this problem, the genotype encodes the possible combinations for all the subsystems. In the following canonical
GA paradigm, a chromosome of 21 bits is considered. Among the first 7 bits (Binary) of the genotype, ones
represent the maintenance activity and zeros represent the replacement activity. Among the next 14 bits (Real), the
first seven bits represent the percentage increase in MTBF and the next seven bits represent the reduction in MTTR
of the corresponding components. Chromosome: (Decision bits) (Improvement bits)
1001011 13202312130201
The process starts with a random selection of 40 chromosomes. A random choice of a pair of chromosomes is made
from these 40 chromosomes, crossover probability (p
c
) is checked and the single point crossover is carried out to
generate the offspring. A random choice of chromosomes is made and is checked with the mutation probability (p
m
).
The mutation location is chosen in random and single point mutation is carried out. Exceptional chromosomes are
replaced by new ones during the evaluation process. This is repeated for 50 generations. F(x) value is calculated for
each chromosome and the best one is selected. The same procedure is repeated for all the periods. Each period yields
one best chromosome. Using these best chromosomes, the total cost and the combination of activities for each
period are calculated.
7. SA implementation
The initial temperature and the number of iterations are fixed as 700 and 20 respectively. A string is generated in
random and is considered as the global optimum value. Two strings are generated in random and compared. If the
fitness of the second string is better than that of the first, then perturbation takes place. Or else, Metropolis algorithm
is used to determine the acceptability of the string. The same procedure is repeated for 20 iterations. The global best
is replaced at the end of each generation. The temperature is then lowered with a cooling factor of 0.04 and the
entire process said above is repeated. A minimum temperature of 30 is set as a termination factor at which the
process terminates. Using the final result, the total cost and the combination of maintenance activities for each
period are decoded.
8. Numerical Analysis
The formulated maintenance model is validated using the following data collected from a cement industry.
Table 1: Input values for the critical components
Critical subsystem M1 (Rs.) R1 (Rs.) Sc(Rs.) TTR
(min)
Booster fan 5000 18000 23000 2.14 22687 90
Conveyor roller assembly 4000 22000 27000 1.83 18647 40
Air slide 6000 15000 20000 1.98 18263 120
Elevator 6000 22000 27000 1.59 18170 150
Separator system 8000 20000 25000 1.45 28459 60
Impact crusher 12000 35000 40000 1.14 32477 200
Raw-mill gearbox 15000 38000 43000 2.29 11788 80
=0.8; C
sd
=Rs.1666/min; k =0.1; m =0.05; r =0.04
The parameters are tuned using sensitivity analysis and are shown below:
GA parameters: No. of generations =50; P
c
=0.8; P
m
=0.05; Population size =40.
SA parameters: Initial temperature=700; Final temperature=30; Cooling factor=0.04; No. of iterations=20
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9. Conclusion
The maintenance optimization in a cement industry has always been a critical issue. This paper effectively utilizes
non-traditional optimization techniques to obtain optimal solution. The obtained results imply that GA and SA have
capably solved the combinatorial maintenance optimization problem. The strategy of maintenance and replacement
activities obtained during the PM action for all machines gives the minimum cost for the entire design out period.
From figure 2, it is seen that GA exhibits a quick convergence to the optimal than SA. A continuation of this work
intends to investigate the impact of component reliability on the decision making process. The work can be extended
to solve the maintenance problem of any process industries.
Table 2: Typical outcome by GA or SA for each period
Maintenance Strategy
M(0.15,0.05), M(0,0.05), M(0.05,0.05), M(0,0.1), R, M(0.1,0.1), M(0,0.1)
Figure 2: Convergence graph GA, SA
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