Download Preventive Maintenance Scheduling Based On Given

Proceeding of The 2nd International Conference on Applied Statistics 2016
ISSN : 2579-4361
<MATS2>
Preventive Maintenance Scheduling Based On Given
Budget Fitness Function Using Generational Genetic
Algorithm
Yeny Krista Franty1,a) and Budhi Handoko 2,b)
1,2)
Department of Statistics, Jl. Bandung-Sumedang km 21 Jatinangor 52353
a)[email protected]
b)[email protected]
Abstract. Cost function analysis is an important activity in order to optimize the multi objective function using
genetic algorithms. This is due to the accuracy of the resulting cost of components will be part of the input to the
programming process which will affect preventive maintenance schedule for components of the engine. Multi
objective cost analysis in optimization will be associated with the reliability of the machine that is expected to be
maximized at minimum cost. The cost analysis will also use technical economic parameters namely the failure of
inflation, inflation of maintenance, replacement cost inflation, and the inflation of rate fixed cost.
INTRODUCTION
Cost is one of important factors that cannot be ignored in the optimization process of preventive
maintainance of industrial engine. Optimization is often used as a method for the cost constraints
determination when maintenance or repairment engine components are optimized so that the necessary costs
can be minimized. In a classic preventive maintenance optimization, the total cost function is formed of
various components costs, for example maintenance cost and replacement cost. Inflation term included in the
optimization with cost constraints due to the fact that inflation can affect the cost incurred by the company in
its production activities, including maintenance activities.
Several methods have been used to carry out the scheduling of preventive maintenance with the cost
constraints. One of them were introduced by [1] without taking into account the reliability of the engine or its
components and also inflation. In addition, [2] introduced the Exact Algorithm with cost limit provided by the
company but does not take into account inflation.
Scheduling preventive maintenance approach multiobjective function in [2] using a genetic
algorithm. In addition, to the cost component in the classical approach also includes several technical
parameters of inflation is considered as external factors that may affect the optimization process. Some
inflation is concerned that inflation at the cost of damage (inffailure), the inflation rate for maintenance
(Infm), the inflation rate for the replacement (infr), and the rate of inflation for a fixed fee (infz), also the
interest rate (int).
The total cost function approach Multiobjective function is formed from the elements of cost and
value of inflation is one of the restriction that must be minimized. Another obstacle is the reliability that is
also stressed in the maintenance and reliability of components or engines are expected to be maximum. Thus,
in this paper will discuss the scheduling of preventive maintenance using optimization methods that involve
the total cost function and taking into account inflation and the value of the reliability function.
Based on the background described previously, the identification of problems in this research is how
to schedule preventive maintenance by optimizing multi objective function taking into account the inflation
rate in the total cost function. The goal of this research is to determine the scheduling of preventive
maintenance based fitness function on the total cost function and reliability function. This research has a role
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Proceeding of The 2nd International Conference on Applied Statistics 2016
ISSN : 2579-4361
in scientific development, especially on the reliability analysis is to give recommendations on a method that
is able to guarantee the optimum solution for models with more than one objective function. In addition, in
the application of this method is able to provide the complete recommendation to the manufacturing
companies in order to conduct a more optimal preventive maintenance.
METHOD
If it is assumed that inflation would increase the cost of damage over time at a rate inffailure percent
per period. Then it can be defined the cost of damage to the component-i in period j is as follows:
   

 ' i  X ' i
Fi, j  Fi .i  X i, j
i, j
1  inffailure j


(1)
where i = 1,2,…,N ; j = 1,2,…,T.
Furthermore, if the rate of inflation for maintenance (info), the inflation rate for the replacement
(infr), and the rate of inflation for a fixed fee (infz). In order to obtain the cost of maintenance actions i-th
component in the j-th period, as follows:
j
M i, j  M (1  infm)
(2)
Ri, j  Ri (1  infr )
j
(3)
 

N
j

Z j  Z 1  infz  1   1  mi, j  ri, j 
 i1

(4)
where i = 1,2,…,N ; j = 1,2,…,T; mi,j and ri,j is a binary variable of action of maintenance and replacement of
i-th component in the j-th period. For additional component of the model is the interest rate at this time is
denoted by int.
Taking into account the economic parameters engineering, we can then form objective function to be
minimized total cost. The multi objective optimization model is an optimization that has two functions of
interest that must be done simultaneously optimization is minimizing the total cost function and maximize the
reliability function. The objective function is as follows:
i 
 
j  
 ' i
 X i, j
  N  Fi .i  X i, j
 1  inffailure    



 
T   i 1 
j
Min Total Cost       M (1  infm) j .m  R 1  infr  .r
   1  int 
i
i
,
j
i
i
,
j
 
j 1   
N
j



 Z 1  infz  1   1  mi, j  ri, j 


 i 1



   
 
(5)

where:
X i ,1  0; i  1,...,.N
'
'
X i, j  (1  mi, j 1 )(1  ri, j 1 ) X i, j 1  mi, j 1 ( i . X i, j 1 )
; i  1,..., N j  2,..., T
T
'
X i, j  X i, j  ;
J
;
mi, j  ri, j  1 ;
mi, j , ri, j  0 atau 1 ;
'
X i, j , X i, j  0 ;
;
;
;
i  1,..., N j  1,..., T
i  1,..., N j  1,..., T
i  1,..., N j  1,..., T
i  1,..., N j  1,..., T
;
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Proceeding of The 2nd International Conference on Applied Statistics 2016
ISSN : 2579-4361
Genetic Algorithm (GA) proposed [3] is a search technique used to obtain computing optimization
solutions both exact and approximation. These algorithms are categorized as global search meta heuristic.
Excess GA is able to simultaneously find a region in space solutions that allow finding a solution to a
difficult problem with the solution space that is non-convex, discontinuous, and multimodal.
There are some steps of Genetic Algorithm:
1. Establish encoding of the solution
2. Maintenance and Replacement Preventive Role As "chromosome".
3. A chromosome is an array of size N x T, with N = component, T = period.
4. The array will contain a value of 0.1, or 2 depending on the three types of action.
5. Determine the suitability function (Fitness function)
Fitness = (-Reliability) + (1 / Costmax) x | Total Cost-Given Budget |
6. Perform procedures mutation
Mutation procedure is applied to the solution of the "descent". With the following steps:
1. Generate a random number between 1 s.d. N x T.
2. Then mark "genes" which turned into 1 or 2 if equal to 0, or change it to 0 if it is equal to 1 or 2.
3. Perform the same steps in the same period for the other components.
7. Getting optimization solutions
GA is a generalization of Genetic Algorithms General (GAG) which replace the entire population in
every generation. GAG uses two populations at the stage of "reproduction". According to [4] and [5] form
GAG algorithm is as follow:
1. Determine the initial value of g = 0.
2. Generate initial population P (g)
3. Determine the suitability of members in P (g)
4. Perform iterative algorithm GA if the conditions have not been met
a. Choose a solution of P (g-1) to P (g) based on the value of a match with chances Ps as the
"parent" is selected
b. Create a "seed" of the "old man" was selected from P (g-1) with probability Pc
c. Find a solution with a mutation of P (g-1) with probability Pm
d. Determine the suitability value of new solutions generated
5. Provided optimization solutions
RESULTS
Scheduling preventive maintenance with a generational genetic algorithm will be applied to time to
failure data of a particular sub machine at a pharmaceutical company. The first step is to determine the size of
the initial population of 1000 and the number of generations of 180, because of the number of generations
have been converging both in cost and in reliability so that further analysis can be done.
In analyzing the data using genetic algorithms commonly required parameters consisting of Lambda
= 0.0037 and Beta = 1.8283 which are the Weibull distribution parameters of time between failures of data
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Proceeding of The 2nd International Conference on Applied Statistics 2016
ISSN : 2579-4361
sub-machine, Failure_cost which is cost incurred by the company due to an engine failure = Rp
11,139,000.00, Maintenance Costs (M_cost) = Rp 3,171,000.00, The replacement cost (R_cost) = Rp
4,393,000.00, Alpha = (R-M) / R = 0.2782, Fixed_cost (charges of technicians) = Rp 4,050,000.00. After the
economic parameter values obtained, inflation value also included in the analysis which consists of inflation
of failure cost = 0,01 / 12; inflation of maintenance maintainance cost= 0,015 / 12; inflation of replacement
cost = 0,01 / 12; and inflation due to the fixed costs = 0,01 / 12; and the level of interest rate = 0,03 / 12.
The next step is to complete the equation by using the second fitness function of multi objective
which include the value of inflation on the total cost function and also involves the function of the reliability
of the sub-components. After completing the fitness function 2, the subsequent analysis is complete the
procedure mutations by determining the amount of the component (N) to sub this machine as much as 1 and
the period of time scheduling (T) is 15 months so that the resulting maintenance scheduling preventive and
estimated costs necessary to carry out maintenance and estimation engine reliability when maintenance
actions were done, for more can be seen in Table 1.
Table 1. Preventive Maintainance Schedule
GB (in
thousand
s of
rupiah)
Cost
(actual)
Reliabilit
y
Schedule Preventive Maintainance (Month)
1
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
5
1000
7,354
0.7266
-
-
-
-
R
-
-
-
-
R
-
-
-
-
-
5000
12,176
0.8102
-
-
-
-
R
-
-
-
-
R
-
-
-
-
-
10000
16,316
0.8312
-
-
-
-
R
-
-
-
-
R
-
-
-
-
-
15000
22,604
0.8550
-
-
R
-
-
-
R
-
-
-
R
-
-
-
-
20000
29,481
0.8722
-
R
-
-
R
-
-
R
-
-
R
-
-
-
-
25000
31,766
0.8904
-
R
-
R
-
R
-
R
-
-
R
-
-
-
-
30000
34,965
0.8917
M
M
-
R
-
R
-
-
R
-
-
R
-
-
-
35000
39,898
0.9059
M
M
-
R
-
R
-
R
-
R
-
R
-
-
-
40000
44,293
0.9124
-
R
-
R
-
R
-
R
-
R
-
R
-
R
-
45000
49,489
0.9177
-
R
-
R
-
R
R
R
-
R
-
R
-
R
-
Table 1 shows the schedule Preventive Maintenance based on Given Budget provided by the
company. If the budget is provided by the company amounting to Rp. 10 million, then the reliability of the
machine is expected to reach 83.12% with the schedule of repairs in the 5th and 10th.
As the rule of standard reliability [1] suggests that the reliability of the engine is should be more than
or equal to 90% means that the machine has a chance of 0.9 to be able to work well in a certain period of
time, so as to sub this machine recommended companies performing maintenance / care in the first and
second month and the replacement sub machines for 5 times with the replacement was carried out in the 4th,
6th, 8th, 10th and 12th after the engine was damaged for the last time, and provides a total cost of Rp
35,000,000.00.
CONCLUSION
Based on the analysis conducted conclusion: that the reliability of the machine is able to reach 90%,
the company must provide a budget of 35 million, with the twice maintenance and five replacements.
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Proceeding of The 2nd International Conference on Applied Statistics 2016
ISSN : 2579-4361
ACKNOWLEDGMENTS
We would like to thank to Mr. Yudi Rosandi who gave us valuable advise to our paper, so that we can
made our work better.
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1.
2.
3.
4.
5.
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210