CHAPTER 4 MAINTENANCE OPTIMIZATION USING GENETIC ALGORITHM

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1 44 CHAPTER 4 MAINTENANCE OPTIMIZATION USING GENETIC ALGORITHM 4.1 INTRODUCTION Engineering systems, nowadays, are becoming more and more complex due to the application of automation, miniaturization, embedded technology, presence of software-hardware interfaces, and its interdisciplinary nature. Concern for environment, cost of failures and associated down times and safety of operations are also important considerations. An unexpected failure of equipment results in large financial losses in process industries. In this chapter, the application of Genetic Algorithm (GA) for the maintenance optimization of a Raw-Mill System of a cement industry is presented. Genetic Algorithms have been widely used for solving optimization problems in the area of scheduling and sequencing (Sridhar and Rajendran 1996, Chaudhry and Luo 2005), reliability optimization (Coit and Smith 1996) and performance optimization in complex industrial systems (Robert and Shahabudeen 2004). Genetic Algorithm has been used to decide whether opportunistic maintenance is cost effective or not for complex systems (Saranga 2004). Morcousa and Lounis (2005) have implemented GA for the determination of maintenance alternatives for a network of infrastructure facilities. Optimal maintenance alternatives are those solutions that minimize the life-cycle cost of an infrastructure network while fulfilling the reliability and functionality requirements over a given planning horizon.

2 45 The maintenance resource optimization has been carried out using GA for a manufacturing plant (Castro and Cavalca 2006). The availability of an engineering system assembled in a series configuration, with redundancy of units and corrective maintenance resources as optimization parameters is maximized using GA. A Genetic Algorithm based optimal preventive maintenance planning for a nuclear plant has been determined by Lapa et al. (2006). Researchers have reported that a meta-heuristic, such as the Genetic Algorithm is more suitable for maintenance scheduling problems, even though it does not guarantee a global optimal solution (Prins 2004, Tam et al. 2007). However, there appears to be a lack of Genetic Algorithm applications for reliability based maintenance optimization study in process industries. 4.2 GENETIC ALGORITHM The Genetic Algorithm is a stochastic search technique based on the mechanism of natural selection and natural genetics (Goldberg 1999, Gen and Cheng 2000, Deb 2003). It works with a population of solutions and attempts to guide the search towards improvement, using a survival of the fittest principle. The search procedure uses random choice as a tool to guide a highly exploitative search through the coding of a parameter space. The Genetic Algorithm differs from a conventional search procedure in the following ways: Genetic Algorithm searches from a population of points and not a single point. Genetic Algorithm uses an objective function information and not derivatives or other auxiliary knowledge. Genetic Algorithm uses probabilistic transition rules and not deterministic rules.

3 46 Genetic Algorithm, in contrast to conventional search techniques, starts with an initial set of random solutions called a population. Each individual in the population is called a chromosome, representing a solution to the problem. A chromosome is a string consisting of decision variable informations, either binary or real bits. The elements in the chromosome are called genes. The chromosomes evolve successive iterations called generations. During each generation, the chromosomes are evaluated, using some measures of fitness (Fogel and Ghozeil 1996). 4.3 GENETIC ALGORITHM OPERATORS new generation: Genetic Algorithm employs the following operators for creating the a) Selection b) Crossover c) Mutation Selection Selection is one of the main operators in GA, and relates directly to the Darwinian concept of the survival of the fittest. The main objective of the selection operators is to emphasize better solutions. This is achieved in two of the main steps of the GA: Selection of the new population: A new population of candidate solutions is selected at the end of each generation to serve as the population of the next generation. The new population can be selected from only the offspring, or from both the parents and the offspring. The selection operator

4 47 should ensure that good individuals do survive to the next generations. Reproduction: Offspring are created through the application of crossover and /or mutation operators. In terms of crossover, superior individuals should have more opportunities to reproduce, to ensure that the offspring contain the genetic material of the best individuals. In the case of mutation, the selection mechanisms should focus on the weak individuals. The hope is that the mutation of weak individuals will result in introducing better traits to weak individuals, thereby increasing their chances of survival. Many selection operators have been developed. Reproduction is the process in which individual chromosomes are copied according to their fitness values; i.e., the chromosomes with a higher value have a higher probability of contributing one or more offspring to the next generation. The fitness value is the final arbiter of the chromosome s life or death. Reproduction is the process of producing offspring from the selected parents by applying crossover and/or mutation operators Selective pressure Selection operators are characterized by their selective pressure, also referred to as the takeover time, which relates to the time it requires to produce a uniform population. Selective pressure is defined as the speed at which the best solution will occupy the entire population by repeated application of the selection operator alone (Goldberg and Deb 1991). An operator with a high selective pressure decreases the diversity in the population more rapidly than operators with a low selective pressure, which

5 48 may lead to premature convergence to suboptimal solutions. A high selective pressure limits the exploration abilities of the population Random selection Random selection is the simplest selection operator, where each individual has the same probability of (1/population size) being selected. No fitness information is used, which means that the best and the worst individuals have exactly the same probability of surviving to the next generation. Random selection has the lowest selective pressure among the selection operators Proportional selection Proportional selection biases selection towards the fittest individuals. A probability distribution proportional to the fitness is created, and individuals are selected by sampling the distribution given in equation (4.1). φ ( x ( t) ) = s i n s l= 1 f γ ( x ( t) ) f γ i ( x ( t) ) l (4.1) where n s is the total number of individuals in the population, and ϕ s (x i ) is the probability that x i will be selected; f γ (x i ) is the scaled fitness of x i, to produce a positive floating-point value. Two popular sampling methods used in proportional selection are roulette wheel sampling and stochastic universal sampling. Roulette wheel selection is an example of proportional selection, operator where by the

6 49 fitness values are normalized (e.g. by dividing each fitness by the maximum fitness value). The probability distribution can then be seen as a roulette wheel, where the size of each slice is proportional to the normalized selection probability of an individual. Selection can be likened to the spinning of a roulette wheel and recording which slice ends up at the top; the corresponding individual is then selected. Because selection is directly proportional to fitness, it is possible that strong individuals may dominate in producing offspring, thereby limiting the diversity of the new population. In other words, proportional selection has a high selective pressure Tournament selection Tournament selection selects a group of n ts individuals randomly from the population, where n ts < n s (n s is the total number of individuals in the population). The performance of the selected n ts individuals is compared and the best individual from this group is selected and returned by the operator. For crossover with two parents, tournament selection is done twice, once for the selection of each parent. Provided that the tournament size, n ts, is not too large, tournament selection prevents the best individual from dominating, thus having a lower selection pressure. On the other hand, if n ts is too small, the chances that bad individuals are selected increase. Even though tournament selection uses the fitness information to select the best individual of a tournament, random selection of the individuals that make up the tournament reduces the selective pressure compared to proportional selection. However, the selective pressure is directly related to n ts. If n ts = n s, the best individual will always be selected, resulting in a very high selective pressure. On the other hand, if n ts = 1, random selection is obtained.

7 Rank-based selection Rank-based selection uses the rank ordering of the fitness values to determine the probability of selection, and not the absolute fitness values. Selection is therefore independent of the actual fitness values, with the advantage that the best individual will not dominate in the selection process. Non-deterministic linear sampling selects an individual, x i, such that i ~ U(0, U (0, n s 1)), where the individuals are sorted in the decreasing order of fitness value. It is also assumed that the rank of the best individual is 0, and that of the worst individual is (n s 1) Stochastic universal selection Stochastic universal sampling (Baker, 1987) provides zero bias and minimum spread. The individuals are mapped to contiguous segments of a line, such that each individual's segment is equal in size to its fitness exactly as in roulette-wheel selection. Here equally spaced pointers are placed over the line as many as there are individuals to be selected. Consider N-Pointer the number of individuals to be selected, then the distance between the pointers are 1/N-Pointer and the position of the first pointer is given by a randomly generated number in the range [0, 1/N-Pointer]. Stochastic universal sampling ensures a selection of off spring which is closer to what is deserved than roulette wheel selection Rank-based roulette wheel selection In the modified roulette wheel selection algorithm where each individual is assigned a fitness value equal to its rank in the population, the highest rank has the highest probability of being selected. The probability of selection is calculated based on equation (4.2).

8 51 Probability ( P) = i N 2. Ranki.( N + 1) pop pop (4.2) The roulette wheel probabilistically selects individuals based on their fitness values F i. A real-valued interval, S, is determined as either the sum of the individual s expected selection probabilities S=ΣP i, where P i = F i / ΣF i or the sum of the raw fitness values S=ΣF i over all the individuals in the current population. Individuals are then mapped one-to-one into contiguous intervals in the range [0, S]. The size of each individual interval corresponds to the fitness value of the associated individual. The circumference of the roulette wheel is the sum of all the fitness values of the individuals. The fittest individual occupies the largest interval, whereas the least fit have correspondingly smaller intervals within the roulette wheel. To select an individual, a random number is generated in the interval [0, S] and the individual whose segment spans the random number is selected. This process is repeated until the desired number of individuals has been selected Crossover In crossover operation, members of the regenerated chromosomes are mated at random. In the first step, a pair of chromosomes from the regenerated pool is selected at random. Then the crossover site x is determined by generating a random number between 1 and (l-1), where l is the length of the chromosome. Then two new chromosomes are formed by swapping all the genes between (x+1) and l inclusively. Crossover is applied with a certain probability, p c. Several crossover operators have been developed to compute the mask:

9 52 One-point crossover: Holland (1975) suggested that segments of genes and not single gene be swapped between the parents to create their offspring. A one-point crossover operator was developed, that randomly selects a crossover point, and the bit strings after that point are swapped between the two parents. Uniform crossover: The n x -dimensional mask is created randomly (Ackley 1987). Here, p x is the bit-swapping probability. If p x = 0.5, then each bit has an equal chance to be swapped. Two-point crossover: In this case two bit positions are randomly selected, and the bit strings between these points are swapped. This operator can be generalized to an n-point crossover (Engelbrecht 2007) Mutation The mutation operator arbitrarily alters one or more components of the selected structure, thus increasing the diversity of the population. Each position of each solution vector in the population undergoes a random change with a probability equal to the mutation rate. The aim of mutation is to introduce new genetic material into an existing individual; that is, to add diversity to the genetic characteristics of the population. Mutation is used in support of crossover to ensure that the full range of allele is accessible for each gene. Mutation is applied with a certain probability, p m, to each gene of the offspring, to produce the mutated offspring, x i (t).

10 GENETIC ALGORITHM METHODOLOGY Genetic algorithms are stochastic search techniques based on the mechanism of natural selection and natural genetics. The genetic algorithm, in contrast to the conventional search technique, starts with an initial set of random solutions called a population. The Schematic diagram for the GA procedure is shown in Figure 4.1. Generate initial population (Represent decision variables) Selection of chromosomes Crossover (with p c ) (To produce off springs) Mutation (with p m ) Termination reached? No Yes Report best solution Figure 4.1 Schematic diagram of the Genetic Algorithm 4.5 RMS MAINTENANCE OPTIMIZATION GA APPROACH In this study an attempt is made to explore the use of Genetic Algorithm to determine the near-optimal preventive maintenance policy for a Raw-Mill System of cement industry. The Genetic Algorithm proposed to solve the maintenance optimization problem is described below:

11 Chromosome Structure In a Genetic Algorithm, it is necessary to code the parameters so as to perform the genetic operation. The length of the chromosome depends upon the number of subsystems considered in the study and the number of various levels of maintenance required on these subsystems to achieve the minimum total maintenance cost. The chromosome design considered for the maintenance optimization problem with m number of subsystems is shown in Table 4.1. Table 4.1 The generalized GA chromosome design Chromosome bits 01-m (Binary) (m+1) - (3m) Choice (Maintenance or replacement) B ij and MR ij stages (i.e s ij and a ij ) From Table 4.1, it is observed that the number of first m bits in the chromosome represents the decision on the choice of maintenance or replacement to be carried out in each subsystem during the PM action. The segment of chromosome from m+1 to 3m represents the decision on the stages of improvement in MTBF and MTTR of the subsystem. A sample chromosome structure for the maintenance optimization problem with seven subsystems is shown in Table 4.2.

12 55 Table 4.2 GA chromosome design for Raw-Mill System Chromosome bits Choice (Maintenance or replacement) s ij (8 th,10 th,12 th, 14 th,16 th,18 th,20 th bits) a ij (9 th,11 th,13 th, 15 th,17 th,19 th, 21 st bits) The sample chromosome is: The chromosome design considered for the maintenance optimization problem has twenty one digits which forms the real code that represents the operating status of the subsystems in the raw-mill system. The first seven digits of the code (binary code) are used to represent the choice of simple maintenance or preventive replacement, and the remaining pairs of digits (real code) represent the improvement in the MTBF and MTTR from the current operational level Decoding of a chromosome The chromosome which represents the solution of the maintenance optimization problem is decoded for the given solution chromosome as follows in Table 4.3: The chromosome is:

13 56 The above chromosome which represents the solution of the maintenance optimization problem is decoded as the Booster Fan subsystem would undergo maintenance action and the increase in MTBF is of 5% and no change in MTTR; the CRA subsystem undergo the maintenance choice and the increase in MTBF is of 10% and the decrease in MTTR with 5%; the AMS subsystem would undergo replacement and no change in both MTBF and MTTR; SFE subsystem has to be replaced and 10% increase in MTBF and no change in MTTR; the Separator subsystem would undergo with maintenance choice and 5% increase in MTBF and 15% decrease in MTTR; the IC rotor subsystem would undergo maintenance action and increase in MTBF with 10%, no change in MTTR; RMG subsystem would undergo maintenance choice and 15% increase in MTBF, 5% decrease in MTTR. (Table 4.3) Table 4.3 Decoding of the chromosome for Raw-Mill System Subsystem Booster Fan CRA AMS SFE drive Separator system IC rotor system RMG system Choice M M R R M M M MTBF (% increase) MTTR (% decrease) Initial Population The population size of the GA should be large enough to adequately cover the solution space, without incurring excessive computational effort. The population size considered in this study is fixed by

14 57 means of the Taguchi orthogonal experiments. An initial population is randomly generated Fitness Evaluation The objective of the maintenance optimization problem is to minimize the total discounted maintenance cost. The GA mimics the survival-of-the-fittest principle of nature to make a search process. Therefore, the GA is naturally suitable for solving maximization problems. For maximization problems the fitness function f(x) can be considered to be the same as the objective function or f(x) =Z. For the minimization problem, the fitness function is an equivalent maximization problem, chosen such that the optimum point remains unchanged. Therefore, the following fitness function f is used in this study. 1 f = (1 + Z) (4.3) where Z is the objective function value. As the maintenance optimization model is subject to reliability constraint, a penalty function has to be included in the objective function. The penalized fitness function is calculated using the Equation (4.4). F(x) = 1/(1+Z+g) (4.4) where g is the penalty assigned for not satisfying the constraint. In this study a penalty value of is considered.

15 NOTATIONS AND TERMINOLOGY The following are the notations and terminology used in the proposed Genetic Algorithm. pop_size Population size n_gen Number of generations p c p m C L Rn ch ij Z b Probability of crossover Probability of mutation Chromosome length Random number Chromosome vector of generation i and population j Best objective function value 4.7 PROPOSED GENETIC ALGORITHM Figure 4.2. The mechanism adopted for the selection process is given in Generate ch ij with C L of pop_size Compute F(x) and Rank ch ij Selection of parents based on the rank for reproduction Figure 4.2 Flow chart of the Selection process The chromosomes (ch ij ) are generated with a length of C L for the required population size (pop_size) in a random order. The fitness values of the chromosomes are computed using the simulation process and ranked, based on the fitness values. The reproduction process is carried out based on the assigned ranks. The logic flow chart of the crossover operation is illustrated in Figure 4.3.

16 59 Select two ch ij Generate Rn U[0,1] Is Rn > p c No Yes Find the crossover location in ch ij Do crossover to produce off springs Figure 4.3 Logic flowchart of Crossover operation Two parents are chosen from the selection pool and the chance for the crossover operation is checked using random number generated against the crossover probability (p c ). If the check is passed then the crossover site will be determined through random generation in the range of (1, C L ). The information bits are swapped between the two chromosomes from the crossover site. The mutation process is shown in Figure 4.4. Select a ch ij Generate Rn U[0,1] Is Rn > p m No Yes Find the mutation site in ch ij Do mutation to produce off spring Figure 4.4 Logic flowchart of Mutation operation The aim of mutation is to add diversity to the genetic characteristics of the population. A chromosome is selected and the chance of mutation is

17 60 verified against the probability of mutation (p m ). The mutation site is determined in the selected chromosome. If the site is within the first seven digits, then 0 will be flipped to 1 and vice versa. Otherwise, a new gene will be generated in the range [0, 3] other than the number present in the position. A single point mutation is incorporated. Elitism is adopted to eliminate the chance of any undesired loss of information during the mutation stage. Report the best objective function value (Z b ) and the corresponding chromosome, ch. 4.8 SIMULATION MODEL TO COMPUTE OBJECTIVE FUNCTION VALUE The objective function value Z is calculated using the simulation of the Raw-Mill System of the cement industry for a period of three years, since planned the major overhauling of the system is carried out in every three years Monte Carlo Simulation The Monte Carlo method is a method for analyzing uncertainty propagation, where the goal is to determine how random variation, lack of knowledge, or error affects the sensitivity, performance, or reliability of the system that is being modeled (Averill and Kelton 2000, Banks et al. 2004). Monte Carlo simulation is categorized as a sampling method, because the inputs are randomly generated from the chosen probability distributions to simulate the process of sampling from an actual population. Monte Carlo simulation methods do not require any transformations of the random variables to an uncorrelated standard normal space like FORM methods. A Monte Carlo simulation draws samples directly from the probability distributions of the random variables, and generates the probability space of

18 61 the output variables through integration. A Monte Carlo simulation requires a large number of performance evaluations in order to properly estimate the resulting probability distributions of the system performance (Law and Kelton, 2004). The result is that the Monte Carlo simulation is often too computationally expensive to be used with detailed performance models. In this maintenance optimization problem under study, the Monte Carlo simulation procedure is used to determine the total discounted maintenance cost of failure during the planning horizon. Here, repair times are assumed to follow exponential distribution. The failure characteristics of the subsystems follow the two parameter Weibull distribution, with the shape parameter (β i ) for the subsystem i and the scale parameter (η i ) for the subsystem i. The following assumptions are made in the simulation model: One repair crew is available. Corrective Maintenance is performed, if the subsystem is down; Preventive Maintenance, if it is operable till the time specified for PM interval. The time between the failures of the subsystems follow the two parameter Weibull distribution. Repair time follows exponential distribution. Once a repair action begins on a subsystem, it is completed without interruption. Subsystem failure causes system failure and the failed subsystem undergoes unscheduled repair immediately.

19 62 The replacement of the subsystem makes the subsystem as good as new. The simulation is carried out for a planning horizon of three years as the planned system shutdown is three years. Fixed Preventive Maintenance interval of six months is considered. shown in Figure 4.5. The Flow chart of the Raw-Mill System (RMS) simulation is 4.9 GA PARAMETER SETTING USING ORTHOGONAL EXPERIMENTS GA parameter values are determined using orthogonal experiments. Initially, the population size, the number of generations, crossover probability and mutation probability are assigned the values 50, 40, 0.8 and 0.05 respectively. A set of values for each parameter with a certain percentage deviation from these values, is then considered. Based on the quality of solutions obtained during the pilot runs conducted on the GA, a lower limit and an upper limit value for each parameter are selected. The GA parameters and the levels considered in this study are given in Table 4.4. Table 4.4 GA parameters and level settings GA parameter Level 1 Level 2 Level 3 No. of Generations (A) Population size (B) Probability of Crossover (C) Probability of mutation (D)

20 63 Start Initialize Age, failure cost and PM inteval (P=0) Set Downtime = 0 Simulation clock = 0 Generate Weibull failure times P = P + 1 a failure occurs (min. time of breakdown of subsystem): Update the simulation clock and age Generate exponential repair times Delay for the repair work (i.e., exponential service time) Update the clock, downtime and Compute the effective age of the repaired subsystem Calculate the failure cost No Is Clock time < end of the PM period? Yes Optimal PM strategy determination using proposed heuristics Is clock time reaches end of Simulation time? No Yes Report Total Cost, Maintenance strategy Stop Figure 4.5 Flow Chart of the RMS simulation

21 64 An L 9 orthogonal array (OA) is used in the design of experiments (Robert and Shahabudeen 2004, Ross 2005). The objective function values Z, obtained during the experiments are presented in Table 4.5. Table 4.5 GA Orthogonal Experiment settings and Objective function values Experiment No. Parameter Setting Objective function value, Z (Rs. x 10 5 ) A B C D Replication1 Replication H 0 : H 1 : No significant difference in the objective function value Z due to changes in the GA parameter values. Significant difference in the objective function value Z due to changes in the GA parameter values. The ANOVA of L 9 for the GA parameters is given in Table 4.8. From Table 4.6 it is clear that a change in the GA parameters, namely, the number of generations, crossover rate and mutation rate does not affect the objective function value Z (respective F cal < F table ).

22 65 Table 4.6 ANOVA of L 9 OA for GA Parameters Source Sum of squares ( x 10 5 ) Degrees of freedom (γ) Mean sum of squares ( x 10 5 ) F cal F table at α =0.05, γ 1 =2 & γ 2 =9 A B C D Error Total The values identified for the GA parameters from ANOVA are: No. of generations : 40 Population size : 40 Probability of crossover : 0.7 Probability of mutation : RMS MAINTENANCE OPTIMIZATION - GA RESULTS The GA is used to solve the combinatorial maintenance optimization problem. GA has been coded in C++ programming language and executed on a Pentium Core 2 Duo 3.3 GHz personal computer. The optimal maintenance policy is determined using the GA with a nominal computational time. The optimal maintenance policy for the fixed interval preventive maintenance of the raw-mill system of a cement industry, which minimizes the total discounted cost that satisfies a subsystem target reliability of 0.98, obtained from the proposed Genetic algorithm, is presented in Table 4.7.

23 Table 4.7 Optimal Maintenance Policy using GA PM interval Booster Fan CR assembly ASM System SFE drive system Separator system IC-rotor system RM gear system MTBF MTTR MTBF MTTR MTBF MTTR MTBF MTTR MTBF MTTR MTBF MTTR MTBF MTTR 1 M R R M R R R M R M R M M R M R M R R M R R M M R M M M R R 0 0 R R M R R M- Simple maintenance; R-Preventive replacement 66

24 67 It is observed from Table 4.7 that more number of imperfect maintenance activities need to be carried out than the replacement of the subsystem during each time period. This is due to the improvements in the MTBF of the subsystem. The reduction in the MTTR reduces the downtime of the subsystem, and increases the availability. Figure 4.6 depicts the effect of the subsystem reliability on the discounted maintenance cost using the genetic algorithm. Figure 4.6 Effect of Reliability on the Maintenance cost using the GA It is observed from Figure 4.6 that the discounted preventive maintenance cost during first and third planning interval is higher for the PM policy without the subsystem reliability targets. In general the cost incurred for the maintenance activity with the reliability target for the subsystem is higher. More number of preventive replacements actions have been carried out to achieve the target reliability, increases the total maintenance cost.

25 MAINTENANCE POLICY PLANNING The convergence graph of the proposed Genetic Algorithm employed in the maintenance optimization problem under study is shown in Figure 4.7. Figure 4.7 GA - Convergence Graph From Figure 4.7, it is clear that the objective function value is obtained at the 24 th generation, after which there is no improvement in the quality of the solution OPTIMAL PREVENTIVE MAINTENANCE TIME INTERVAL For the various Preventive Maintenance time interval, the total discounted maintenance cost of Raw-Mill System of the cement industry using Genetic Algorithm is shown in Table 4.8.

26 69 The total discounted maintenance costs of Raw-Mill System obtained for different PM time intervals are given in Table 4.8. Table 4.8 Effect of PM Interval on Total discounted Maintenance Cost PM interval (months) Total discounted maintenance cost (using GA) Rs. x The effect of preventive maintenance interval on the total discounted maintenance cost is shown in Figure 4.8.

27 70 Figure 4.8 Effect of PM Interval on Total discounted Maintenance Cost From Figure 4.8, it is found that the total discounted maintenance cost of Raw-Mill System decreases as the interval increases, beyond a certain point of time (i.e. six months), the total discounted maintenance cost increases. In other words, the less often to perform a preventive maintenance action, the higher the corrective costs will be. Obviously, the longer let a subsystem operate, its failure rate increases to a point that it is more likely to fail, thus requiring more corrective actions. The opposite is true for the total scheduled maintenance costs. The longer you wait to perform a scheduled maintenance (i.e. Preventive Maintenance), the less the costs; while if you do preventive maintenance too often, the higher the costs. There is an optimum point that minimizes the costs. In other words, one must strike a balance between the costs associated with a failure while maximizing the time between preventive maintenance actions. Therefore, the optimal maintenance policy of the real life Raw-Mill system should have PM time interval of six months in order to achieve the cost effectiveness.

28 SUMMARY The planning and scheduling of maintenance activities is often crucial for the cost-effectiveness of many large industrial organizations. However, the costs associated with maintenance can be significant: there are not only costs involved with the maintenance itself, also the costs of production losses during the maintenance activity have to be taken into account. The formulated non-linear combinatorial maintenance optimization model has been validated with the real life Raw-Mill System of the cement industry. Genetic Algorithm has been applied to solve the maintenance optimization problem under study. The new off springs are generated using Rank Order selection, single point crossover and single point mutation. In order to prevent the loss of good solution, elitism mechanism has been incorporated. Genetic Algorithm is found to be suitable for solving this type of maintenance optimization problem.