Optimization Od Ship Machinery Maintenence

8/11/2019 Optimization Od Ship Machinery Maintenence

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International Journal of Reliability, Quality and Safety EngineeringVol. 19, No. 3 (2012) 1250014 ( 16 pages)c World Scientic Publishing Company

DOI: 10.1142/S0218539312500143

OPTIMIZATION OF MAINTENANCE SCHEDULINGOF SHIP BORNE MACHINERY FOR IMPROVED

RELIABILITY AND REDUCED COST

AJIT KUMAR VERMA , , A. SRIVIDYA ,COMMANDER ANIL RANA and SANJAY K. KHATTRI

Stord/Haugesund University College, Haugesund, Norway Indian Institute of Technology, Bombay, India [email protected]

Received 20 April 2012Revised 19 May 2012

Published 12 September 2012

Ships have a wide variety of machinery available onboard that is crucial for hersustenance at sea for prolonged durations. The machinery can be grouped into vari-ous plants, such as propulsion plant, air conditioning plants, power generation plants,etc., each having its own specic function. The plants in turn are composed of varioussystems which further comprise various types of machinery. There are redundancies builtin at the plant level, as well as at the system and at machinery level, so as to improvethe reliability of the ship as a whole. Planning of maintenance schedule, specically fortasks which can only be undertaken in an ashore repair yard is a daunting task for themaintenance managers. The paper presents a NSGA-II (nondominated sorting geneticalgorithm) based multi-objective optimization approach to arrive at an optimum main-tenance plan for the vast variety of machinery in order to improve the average reliabilityof ships operations at sea at minimum cost. The paper presents the advantages thatcan accrue from introducing short maintenance periods for a select group of machinery,within the constraints of mandatory operational time, over the method of following a

common maintenance interval for all the machinery. The problem function in hand isnonlinear, multi-modal and multi-objective in nature. The search spaces for the prob-lem is noncontinuous and the (multiple) variables, such as time interval for maintenance,serial number of equipment, number of minor maintenance actions, etc., are uncoded realparameters.

Keywords : Multi-objective optimization; TBPM (time-based preventive maintenance);CBPM (condition-based preventive maintenance); NSGA-II.

1. Introduction

Machinery present onboard warships are organizationally similar to that presentin a large industrial set up, however, there is one very important difference; theships need to depend on ashore-based repair facilities for a large portion of hermaintenance requirements. Though some minor maintenance can always be carriedout by her crew at sea itself, majority of maintenance on her machinery needs to

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be carried out ashore for which the ship has to return to harbor thereby incurringhuge opportunity costs. Moreover, untimely failure of her machinery at sea can jeopardize her entire mission and therefore reliability of her machinery for mission

accomplishment is of utmost importance. In view of the above factors, it is impor-tant that the maintenance schedule for a ships machinery is prepared with extremecare and caution so as to balance her reliability needs and maintenance costs. Theproblem for maintenance scheduling for ships machinery is compounded by thepresence of a vast variety of equipment organized into various systems and plantseach with its own set of redundancies. It is therefore important that the problemin hand is solved keeping the organizational set up of the ships machinery in thebackdrop.

A large amount of literature is available dealing with the problems of mainte-

nance optimization, however not many of them have covered maintenance schedul-ing of vast number of machinery available on a single platform, such as a warship.From Barlow and Hunter 1 in 1960, till date, there have been many models and casestudies on optimization of PM intervals. References 15 are few such examples.Authors such as Dekker, 6,7 Scarf 8 and Horenbeek et al. 9 have collectively surveyedmore than 300 works on the subject. It has been brought out by them that most of the research work on the subject has been carried out at an individual componentor equipment level. Studies are often used only to demonstrate the applicability of a developed model, rather than nding an optimal solution to a specic problemof interest to a practitioner. Another limitation perceived in literature is that mostof the models focus on only one optimization criterion, making multi-objectiveoptimization models an unexplored are of maintenance optimization. As far asmaintenance planning/scheduling for ship borne machinery is concerned, Perakisand Inozu 10 had developed reliability-based models to optimize the winter layupreplacement practices for major components of one and two diesel engines for Greatlake vessels (cargo ships). Although single objective optimization is attractive fromthe modeling point of view, this approach does not capture all important aspectsof a real life situation.

2. Peculiarities of the Ship Borne Machinery

There are three main peculiarities of the ship borne machinery vis- a-vis an industrialplant or any other large machinery installation.

First, as far as the maintenance requirements of the ship borne machinery areconcerned, they can be divided into two major groups: one that requires supportfrom the repair facilities-based ashore and the other that do not require such support

and can be easily carried out by the staff present onboard the ship. How it effectsthe maintenance planning of the ship machinery is that the maintenance that needto be carried out in harbor calls for the ship to be down (in terms of operationalavailability) and this comes at a huge opportunity cost. All the maintenance actionsthat can be undertaken at sea by the ships staff do not call for the ship to be put

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away from her operational zone. At best the ship can remain nonavailable for theduration of the maintenance time. In view of the above reasons, the maintenanceactions that need support from shore-based facilities are considered to be more

critical than those that can be undertaken by the ships staff. Due to this differencein the requirement of shore-based facilities for carrying out maintenance, the twogroups of maintenance actions need to be treated separately and may be optimizedseparately.

Second, the equipment where the condition-based PM is followed and wherethe maintenance actions can be carried by the ships staff, the maintenance can bescheduled as and when the condition of the equipment demands. However, for equip-ment under CBPM where the maintenance actions need to be carried out ashore,the maintenance manager needs to decide, during the ships every visit to harbor,

whether the maintenance actions can be carried during her stay or deferred tillnext visit. This decision can be based on the condition of the equipment monitoredduring her current visit to harbor.

Lastly, by virtue of all the machinery borne on the same platform, that is, theship itself, it is intuitively clear that the optimal time for maintenance in harborwould be the one in which, all the machinery need to be attended to at the sametime. It would seem to be sub-optimal to bring the ship to harbor again and againfor carrying out maintenance that falls (TBPM) due on different equipment atdifferent times. It is for this reason that the maintenance managers plan what iscalled the rets of the ships. These rets are planned in advance and it is the timewhen the ship is known to be unavailable for any mission requirement. The ret isgenerally the time when most of the equipments are put down time for maintenance.However, whether these onetime planning of all maintenance jobs are optimal ornot and what is the basis of planning these rets needs some investigation and thisis the topic of this paper.

The problem in hand for deciding maintenance intervals of a large numberof ship machinery is nonlinear, multi-modal and multi-objective in nature. Thesearch spaces for such problems are noncontinuous and the problem (multiple) vari-ables are uncoded real parameters. One of the most suitable methods to deal withthese problems is the evolutionary algorithms, such as the NSGA-II (see Refs. 11and 12).

3. Maintenance Scheduling of Ships Machinery

As has been brought out earlier, a ship consists of a variety of plants each with adifferent function. There might be redundancies available in the plants that improve

the reliability of the plant. These plants in turn will consist of many equipments.There could be some equipment which follow a time-based preventive maintenance,TBPM and there would be others that follow a CBPM. However, by virtue of being present on the same platform, as that of a ship, we will have to nd out whatis the most optimal time interval T for carrying out maintenance on all these

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TR TOps TA TOps TA TOps

TR Refit time. Major ship equipments are under repair. Ship is down.TOps Operational time. The ship is operationalTA A short maintenance period when a few select equipment are under maintenance.The ship is down.

TR TOps TOpsTR

Fig. 1. Operation and maintenance cycle of a ship.

equipment. Such a time period for maintenance on the ship equipment is calledRet in naval parlance.

The search for such an optimal time schedule seems to be a simple optimizationproblem, but it is not. The reason, as will be shown with an example, are theadvantages that accrue from following a staggered, but grouped time schedules forsome, but not all the equipment. Figure 1 above would provide a much neededclarication.

In Fig. 1 above T R is the scheduled ret of the ship, wherein the majority orall of the equipment will be brought under maintenance. The T Ops is the operationaltime for the ship where she fullls all her mission commitments. In the rst cycleof the gure, the maintenance managers nd out the optimal time for ret T R . Theobjectives are cost rate and average reliability during the operational time of theship. This is the general trend amongst the maintenance managers. What has beenobserved in the research work is that, if the operational time of a ship is given tobe say not less than T Ops (a constraint) then by bringing up a small select group of equipment under maintenance both the above stated objectives can be improved.Such short maintenance intervals may be called short maintenance period (MP)and these can be scheduled in between the ret periods of the ship. Though inFig. 1 it appears that the bottom cycle has a shorter operational time T Ops thismay not be the case.

The strategy shown in Fig. 1 however requires solution of a multi-objectiveoptimization problem with multiple variables. The variables for the optimizationproblem can be listed down as follows:

Selection of equipment that need to be maintained during MP (maintenanceperiod). Scheduling of the maintenance period T mp after completion of a ret. Total number of MPs (maintenance periods required between the ret period). Scheduling of ret period T rp after completion of the previous ret.

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Among the other variables are the MP and/or the ret duration, however, theseare values that are generally given and can be considered to be constraints of themulti-objective problem being discussed.

3.1. Example

The above approach to the problem can be demonstrated taking an example of aship system. We consider a group of three main plants of a ship comprising 13 equip-ments. The power generation plant has a redundancy. The life distribution and itsassumed parameters are listed in Table 1. The search is for an optimal maintenanceplan for the entire ship such that the ship is available for operations at least fora minimum period of T Ops at the maximum average reliability AvgRelb and

at the minimum maintenance cost rate Costrate. Maintenance actions coveredare only replacement of the equipment, except for the turbines, which based on thelevel of deterioration, undergo replacement of its worn down components.

Table 1. Parameters of distribution of the 13 equipment example.

S. Equipment/ Distribution Scale Shape Cost Manpower MaintenanceNo. component parameter parameter required time

1 Plant 1 Ancillary system

Weibull 150 1.109 1200 3 2

2 Plant 1 Distributionsystem

Weibull 465 1.3 4000 2 2

3 Plant 1 Turbine Gamma 0.089 0.97 550 3 14 Plant 1

Ancillary systemWeibull 150 1.109 1200 3 2

5 Plant 1 Distributionsystem

Weibull 465 1.3 4000 2 2

6 Plant 1 Turbine Gamma 0.089 0.97 550 3 17 Propulsion

plant ASDsystem

Weibull 907 2.9 19,000 2 2.5

8 Propulsionplant Turbine

Gamma 0.075 0.52 5500 4 2.5

9 Propulsionplant Ancillary system

Weibull 95 1.1 650 3 3

10 Propulsionplant Shaftline system

Weibull 200 1.43 1100 2 2

11 AC plant compressor

Weibull 340 2.109 1200 4 1

12 AC plant Ventilationsystem

Weibull 139 1.02 1100 4 2.5

13 AC plant Cooling pump

Gamma 0.045 0.82 1200 2 1

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Fast Attack Craft Machinery

Power Generation Plant AC plantPropulsion plant

Plant 2Plant 1

Ancillarysystem-

TBPM

Distributionsystem-TBPM

Turbine-CBPM

Ancillarysystem-

TBPM

Distributionsystem-TBPM

Turbine-CBPM

ASDsystem-TBPM

Turbine-CBPM

Ancillarysystem-TBPM

Shaft linesystem-TBPM

Compressor-TBPM

Ventilationsystem -TBPM

Cooling ppCBPM

1

2

3

4

5

6

7

8

9

10

11

12

13

Fig. 2. Schematic list Group of three plants of an attack craft.

Initially we consider the case without any MP (or short maintenance periods).In this case the search is for a common time where all the equipment would bemaintained together. The problem equation can be written as:

OBJECTIVESminT [Costrate( T )]max

T [AverageRe lb(T )]

s.t.

costrate( T ) = Exp cost of failure ( T ) + C P M Re lb(T )

T

0 Re lb(t )dt, (1)

AverageRe lb(T ) = T

0 Re lb(t )dtT

, (2)

where

Re lb(T ) =i = n

i =1

R i (T ) 1 1 j = n

j =1

R j (T ) 1 k = n

k =1

R k (T ) , (3)

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Exp cost of failure ( T ) =n

j =1 T

0f j (x )

n

i = j

R i (x ) 1 R k (x )

(Cost j + N Rj T Rj Cost R+ C Oprn ( T Rj + T RH + T LD ))dx, (4)

where j and k are equipment belonging to the plants which have a hot redundancywith each other and

N Ri = number of people required for maintenance of equipment i,T Ri = Time required for maintenance of equipment i,

T RH = Time required for ship to reach harbor,T LD = Logistics delay time,agei = age of equipment i measured from completion of previous ret

since all equipment ,Cost i = i equipment cost,C Opm = cost of opportunity,Cost R = Cost of repair action per time per repair crew,

f i ( ) = pdf of lifetime for equipment i,F i ( ) = cdf of lifetime for equipment i,R i ( ) = reliability of equipment i,

CPM =

n

j =1(Cost j + N Rj T Rj CostR ).

Given an assumption of cost of opportunity of Rs 250,000/- and a cost of repairof Rs 3500/- per man per day and the cost of equipment and manpower as shownin Table 1, we get the plots as shown in Fig. 3. The range of multiple objectiveslay to the left of the optimal point T = 30 days. At this point the cost rate is0.5478*105 and the average reliability during the operational duration is 0.7610.

Any time to the left of T = 30 is also an acceptable point since the averagereliability remains higher than 0.7610 but at a higher cost rate. At any time to the

Fig. 3. Plot of Cost rate and Average reliability.

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right of T = 30 days we approach a zone of lower average reliability at a highercost rate and hence all time points to the right of T = 30 are clearly sub-optimal.

We now consider the case when we can introduce some minor/short MPs or

maintenance periods in between the ret schedules. The problem equation can nowbe written as given in the next section.

3.2. Example of multi-objective optimization of maintenance interval scheduling

We now allow some MP in between the ret periods and nd out what are theeffects on the multiple objectives of average reliability and maintenance cost rate.The acceptance of minor maintenance intervals in between the ret period gives

rise to multiple variables such as selection of equipment to be included in theminor maintenance period, time interval for carrying out such minor maintenance,time interval for scheduling the ret of the ship and number of maintenance periodallowed to be carried out before the ret is carried out. The multi-objective problemfor the present case can be written as follows:

OBJECTIVESminM [][Costrate( M [n t , n amp , E [], T ])]max M [][AverageRe lb(M [n t , n amp , E [], T ])],

s.t.

(5)

costrate( T ) =

Exp cost of failure ( M [n t , n amp , E [], T ])+ PM cos t (M [n t , n amp , E [], T ])

nn amp=1

(T Ops + n t ) (n amp )(T Ops + n t ) (n amp 1) Re lb(t)dt +

T T Ramp(T Ops + n t ) (n ) Re lb(t)dt

,

(6)

AverageRe lb(M [n t , n amp , E [], T ]) =nn amp=1

(T Ops + nt

) . (n amp )(T Ops + n t ) (n amp 1) Re lb(t)dt[T Ops + n t ] n

+ T T Ramp

(T Ops + n t ) (n ) Re lb(t)dt

(T T Ramp ) [(T Ops + n t ) (n )], (7)

where

Re lb(x ) =

i = N

i =1

R i (age i + x)R i (age i )

1

1

j = N

j =1

R j (age j + x)R j (age j )

1 k = N

k =1

R k (age k + x)R k (age k ) age i =0 i E []

, (8)

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where j and k are equipments belonging to the plants which have a hot redundancywith each other

PMcost( M [n t , n amp , E [], T ])

=n

n amp =1

N

j =1

[Cost j + N Rj T Rj CostR ] Re lb((T Ops + n t ) n amp )j E []

+N

i =1

[Cost i + N Ri T Ri Cost R ] Re lb((T T Ramp (T Ops + n t ) n ),

(9)Exp cost of failure ( M [n t , n amp , E [], T ])

=n

n amp =1

N

j =1 (T Ops + n t ) (n amp )

(T Ops + n t ) (n amp 1)

f j (age j + x)R j (age j )

N

i = j


1 R k (age k + x)

R k (age k ) age i =0 i E [] [Cost j + N Rj T Rj Cost R + C Oprn (T Rj + T RH + T LD )]dx

+N

j =1 T

(T Ops + n t ) n

f j (age j + x)R j (age j )

N

i = j


1 R k (age k + x)

R k (age k ) age i =0 i E [] [Cost j + N Rj T Rj Cost R + C Oprn ( T Rj + T RH + T LD )]dx, (10)

whereM[] = set of selected variables that affect the cost rate and average reliability

of the ship,T Ops = minimum operational time the ship needs to be operational after a

ret or maintenance period,n t = time after T Ops when the MP is scheduled,

n amp = number of MPs that are scheduled before the ret of ship falls due,E [] = set of equipments selected to undergo maintenance during MP,

T = time (after the previous ret) when the ships ret falls due,

T Ramp = cumulative maintenance time for equipment chosen for maintenanceduring MP,N Ri = number of people required for maintenance of equipment i,T Ri = time required for maintenance of equipment i,

T RH = time required for ship to reach harbor,

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T LD = logistics delay time,agei = age of equipment i measured from completion of previous ret.

Since all equipment E [] are maintained at every MP, age for such

equipment = 0 after every MP,Cost i = i equipment cost; C Opm = cost of opportunity,

Cost R = cost of repair action per time per repair crew,f i ( ) = pdf of lifetime for equipment i,F i ( ) = cdf of lifetime for equipment i,R i ( ) = reliability of equipment i.

4. Use of NSGA II Elitist Genetic Algorithm Program

The above noncontinuous, discrete, multi-objective, multi-variable optimizationproblem can be approached using the elitist NSGAII program as explained earlier.A chromosome for the GA population is shown in Fig. 4 below. The chromosomecontains all the multi-variables required for evaluating the health (or magnitude of its objectives).

The rst 13 slots of the chromosome are for the equipment which in this caseare a total of 13. The slots can contain either a 1 or a 0 showing whether thatspecic equipment is selected to undergo replacement/repair during the MP or notrespectively. The 14th slot shows the number of MP (short maintenance period)

selected by the chromosome. A 0 in this position would mean that there are noMPs for equipment and therefore the number 0 or 1 in any of the rst 13 slotswould then be irrelevant.

The 15th slot shows the time after the mandatory T Ops period when the MP isbeing scheduled. Since time is continuous, this slot may have innite choices. Wetherefore choose a small time interval t the multiples of which in integers canbe shown in this 15th slot. A 0 in this slot would therefore mean that the MPhas been scheduled right after completion of the mandatory T Ops period. It hasbeen brought out before that the T Ops period is the minimum time the ship should

E E E na n t T

13 Slots for 13 equipment

This slot decides the number of MPs

Time after T Ops when the MP is scheduled

Time when the refit is scheduled. The time iscounted from the end of the previous refit

Fig. 4. A chromosome used for solving the NSGAII-based MOOP.

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remain operational after maintenance to meet her operational commitments. The16th slot shows the time when the ret is scheduled. The time shown here is countedfrom the elapse of the previous ret period.

5. Assumptions and Result

We make the following assumptions for the example under discussion:

Maintenance actions considered are only replacement of equipment. All maintenance actions require assistance of repair crew present ashore. All maintenance actions are considered sequential in nature. In actual practice

simultaneous repair actions can be undertaken resulting in reduced downtimedue to maintenance actions.

Time required for maintenance is considered deterministic in nature. The failure of all the equipments is statistically independent in nature. The equipment which is being monitored for wear or deterioration follows a non-

stationary gamma wear process. All other equipments follow a Weibull processfor failure.

The equipments which have been selected for maintenance during MP remainxed for every MP. In practice, we may consider to choose the equipment thatcan be maintained during every MP. The chromosome for solving the GA problemin this case would be three-dimensional in nature.

The crossover probability for the example selected above is 0.8 and the mutationprobability is 0.01. A random population of 40 chromosomes brings out interestingresults after just four generations, as shown below through 2 out of the total 40solutions.

Soln 1 = [1 0 1 1 0 1 0 1 1 1 1 0 1 2 0 145];

Cost rate = 0.4647*10 5; Average reliability= 0.6738.

Soln 2 = [1 0 1 0 0 1 1 1 0 1 1 1 1 3 6 225];Cost rate = 0.3993*10 5; Average reliability= 0.6275.

The above two solutions bring out two such nondominated solutions. The rstsolution shows that if nine equipments are selected to undergo 2 MPs exactly aftercompletion of T Ops of 30 days and the ret is scheduled after every 145 days thecost rate drops to 0.4647*10 5 down from 0.5478*10 5 (that happens when no MP isselected). The average reliability of course drops from 0.7610 to 0.6738.

The second solution also brings out another nondominated solution. When nine

equipments are selected to undergo 3 MPs, 12 days after T Ops of 30 days (or afterevery 42 days) and if the ret is scheduled after every 225 days, the cost rate dropsfurther to 0.3993*10 5 but the average reliability also drops to 0.6275.

When the T Ops becomes 20 days we see improvement in both the objectives(Fig. 5). This shows that it is not optimal to put down all the equipments together

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Fig. 5. Set of optimal solutions obtained from NSGA II program.

for maintenance during a ret without keeping any short maintenance periodMP in between the ret periods. The number of MPs and the scheduling of theMPs play a vital part in improving the cost rate and average reliability of the shipduring the operation phase in between the ret periods. The NSGA II programroutines for the example were written in Matlab 7. The objective values and theelite solutions are placed in Tables 2 and 3 below.

Table 2. Objective values for a population of 40 after 20 generations.

Solution no. 1 2 3 4 5 6 7 8 9 10

Cost rate 0.4815 0.2592 0.2861 0.2585 0.2449 0.1967 0.2426 0.4815 0.1418 0.22241-Avg

Reliab 0.1785 0.2257 0.1943 0.2418 0.2587 0.4259 0.2643 0.1785 0.5476 0.3083

Solution no. 11 12 13 14 15 16 17 18 19 20Cost rate 0.1927 0.4239 0.2426 0.2585 0.1967 0.2283 0.4815 0.1927 0.1418 0.19671-Avg

Reliab 0.4426 0.1789 0.2643 0.2418 0.4259 0.2932 0.1785 0.4426 0.5476 0.4259

Solution no. 21 22 23 24 25 26 27 28 29 30Cost rate 0.2449 0.1913 0.1967 0.1927 0.2794 0.4815 0.1927 0.2886 0.1913 0.27381-Avg

Reliab 0.2587 0.4864 0.4259 0.4426 0.205 0.1785 0.4426 0.194 0.4864 0.2051Solution no. 31 32 33 34 35 36 37 38 39 40Cost rate 0.2224 0.2738 0.1458 0.1999 0.2283 0.201 0.2149 0.2338 0.1988 0.48151-Avg

Reliab 0.3083 0.2051 0.4872 0.3977 0.2932 0.3968 0.3252 0.2723 0.4112 0.1785

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Table 3. 40 solutions of the MOOP obtained through NSGAII.

Soln no. 1 [1 1 0 1 1 1 0 1 1 1 0 0 1 2 1 101]Soln no. 2 [1 1 0 0 0 0 1 0 0 1 0 0 1 5 1 183]

Soln no. 3 [0 1 0 1 1 1 1 1 0 1 0 0 1 5 1 209]Soln no. 4 [0 1 1 1 1 1 1 0 0 1 0 0 1 5 2 211]Soln no. 5 [0 1 1 1 0 1 1 0 0 1 0 0 1 5 2 209]Soln no. 6 [0 1 0 0 0 0 0 1 0 0 1 0 1 5 13 312]Soln no. 7 [1 1 1 1 0 1 0 0 0 1 0 0 1 5 2 209]Soln no. 8 [1 1 0 1 1 1 0 1 1 1 0 0 1 2 1 101]Soln no. 9 [0 0 0 0 0 0 1 0 0 0 1 0 1 5 11 312]Soln no. 10 [0 1 1 0 0 0 1 0 0 1 0 0 1 5 2 211]Soln no. 11 [0 0 0 0 0 0 0 1 0 0 1 0 1 5 13 312]Soln no. 12 [1 1 0 1 0 1 0 1 1 1 0 0 1 5 1 209]Soln no. 13 [1 1 1 1 0 1 0 0 0 1 0 0 1 5 2 209]Soln no. 14 [0 1 1 1 1 1 1 0 0 1 0 0 1 5 2 211]Soln no. 15 [0 1 0 0 0 0 0 1 0 0 1 0 1 5 13 312]Soln no. 16 [0 1 1 1 0 1 0 0 0 1 0 0 1 5 2 209]Soln no. 17 [1 1 0 1 1 1 0 1 1 1 0 0 1 2 1 101]Soln no. 18 [0 0 0 0 0 0 0 1 0 0 1 0 1 5 13 312]Soln no. 19 [0 0 0 0 0 0 1 0 0 0 1 0 1 5 11 312]Soln no. 20 [0 1 0 0 0 0 0 1 0 0 1 0 1 5 13 312]Soln no. 21 [0 1 1 1 0 1 1 0 0 1 0 0 1 5 2 209]

Soln no. 22 [0 1 0 1 1 1 0 0 0 1 0 0 1 5 9 312]Soln no. 23 [0 1 0 0 0 0 0 1 0 0 1 0 1 5 13 312]Soln no. 24 [0 0 0 0 0 0 0 1 0 0 1 0 1 5 13 312]Soln no. 25 [0 1 1 1 0 1 1 1 0 1 1 0 1 5 2 218]Soln no. 26 [1 1 0 1 1 1 0 1 1 1 0 0 1 2 1 101]Soln no. 27 [0 0 0 0 0 0 0 1 0 0 1 0 1 5 13 312]Soln no. 28 [1 1 0 1 0 1 1 1 0 1 0 0 1 5 1 209]Soln no. 29 [0 1 0 1 1 1 0 0 0 1 0 0 1 5 9 312]Soln no. 30 [1 1 1 1 0 1 0 1 0 1 0 0 1 5 2 209]Soln no. 31 [0 1 1 0 0 0 1 0 0 1 0 0 1 5 2 211]Soln no. 32 [1 1 1 1 0 1 0 1 0 1 0 0 1 5 2 209]Soln no. 33 [0 0 0 0 0 0 1 0 0 0 1 0 1 5 11 275]Soln no. 34 [0 0 0 0 0 1 0 1 0 0 1 0 1 5 13 286]Soln no. 35 [0 1 1 1 0 1 0 0 0 1 0 0 1 5 2 209]Soln no. 36 [0 0 0 0 0 1 0 1 0 0 1 0 1 5 13 284]Soln no. 37 [0 1 1 0 0 1 0 0 0 1 0 0 1 5 2 209]Soln no. 38 [0 1 1 0 1 0 1 0 0 1 0 0 1 5 2 209]Soln no. 39 [0 1 0 0 0 1 0 1 0 0 1 0 1 5 13 312]Soln no. 40 [1 1 0 1 1 1 0 1 1 1 0 0 1 2 1 101]

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6. Conclusion

The paper has presented a NSGA II-based MOOP approach for maintenancescheduling of a vast number of ship borne machinery that need the support of a repair yard present ashore. The objectives of the problem were to maximize theaverage reliability of the ship during her operational phase and to minimize thecost rate, which included the maintenance costs. Using the failure information of various equipment and depending upon how they are organized into plants and sys-tems each with its own redundancies, it has been shown through an example that itis benecial to introduce short MPs for a select group of equipment in between theret periods of the ships instead of following a common maintenance interval for allher machinery. Multiple variables such as the choice of equipment, the number of MPs required to be scheduled, time interval for scheduling the MPs and the timeinterval for scheduling the ret of the ship can be all chosen in accordance withthe solutions arrived at by the solution of the MOOP using NSGA II an elitistgenetic algorithm method.

References

1. R. Barlow and L. Hunter, Optimum preventive maintenance policies, Oper. Res. 8(1960) 90100.

2. H. Mine and H. Kawai, Preventive replacement of a 1 unit system with a wear outstate, IEEE Trans. Reliab. R-23 (1) (1974).

3. T. Nakagawa, Optimum preventive maintenance policies for repairable systems, IEEE Trans. Reliab. R-26 (1977).

4. K. S. Park, Optimal continuous wear limit replacement under periodic inspections,IEEE Trans. Reliab. 37 (1) (1988) 97102.

5. I. B. Gertsbakh, Models of Preventive Maintenance (North Holland Publishing Com-pany, 1977).

6. R. Dekker, Applications of maintenance optimization models: A review and analysis,Reliab. Eng. Syst. Saf. 51 (3) (1996) 22940.

7. R. Dekker, On the use of operations research models for maintenance decision making,Microelectron. Reliab. 35 (910) (1995) 13211331.

8. P. A. Scarf, On the application of mathematical models in maintenance, Eur. J. Oper.Res. 99 493506.

9. V. A. Horenbeek, L. Pintelon and P. Muchiri, Maintenance optimization models andcriteria, in Proc. 1st Int. Congress on e-Maintenance , Lulea, Sweden, 2224 June2010, pp. 513.

10. A. N. Perakis and B. Inozu, Optimal maintenance repair and replacement of GreatLakes marine diesel, Eur. J. Oper. Res. 55 (1991) 165182.

11. D. E. Goldberg, Genetic Algorithm for search, Optimization and Machine Learning (Addison-Wesley, Reading, MA, 1989).

12. K. Deb, Multi-Objective Optimization using Evolutionary Algorithms (John Wiley &

Sons, Ltd, 2002).

About the Authors

Ajit Kumar Verma is a Professor in Engineering, Haugesund/Stord University Col-lege, Haugesund, Norway and has been a Professor (since Feb 2001) with the

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Department of Electrical Engineering (currently) at IIT Bombay (India) with aresearch focus in Reliability Engineering and Quality Management. He was theDirector of the International Institute of Information Technology Pune, on lien from

IIT Bombay, from August 2009September 2010. He is also a Guest Professor atLulea University of Technology, Sweden. He has supervised/co-supervised 31 PhDsand 92 Masters theses in the area of Software Reliability, Reliable Computing,Power Systems Reliability (PSR), Reliability Centered Maintenance (RCM) andProbabilistic Safety/Risk Assessment (PSA). He has jointly edited books on Reli-ability Engineering & Quality Management and Quality, Reliability & InformationTechnology, and is also an author of books titled Fuzzy Reliability EngineeringConcepts and Applications (Narosa), Reliability and Safety Engineering (Springer)and Dependability of Networked Computer Based Systems (Springer). He has over

225 publications in various journals (over 100 papers) and conferences. He has beenthe Editor-in-Chief of OPSEARCH published by Springer (January 2008January2011) as well as the Founder Editor-in-Chief of International Journal of SystemsAssurance Engineering and Management (IJSAEM) published by Springer and theEditor-in-Chief of SRESA Newsletter and Journal of Life Cycle Reliability andSafety Engineering. He is a recipient of Leadership in Reliability Engineering Educa-tion & Research award by Society of Reliability Engineering, Quality & OperationsManagement.

Professor A. Srividya is a guest Professor at Stord/Haugesund University Col-lege, Haugesund, Norway on lien from IIT Bombay since July end 2012. She hassupervised/co-supervised 28 PhDs and 50 Masters theses in the area of Struc-tural Reliability, Reliability Based Optimisation, Simulation Studies for ReliabilityEstimation, Quality Benchmarking Studies for Service Industries, Quality Systemsand Accelerated Life Testing. She has jointly edited books on Reliability Engi-neering and Quality Management, Quality, Reliability and Information Technol-ogy, and is also author of books titled Fuzzy Reliability Engineering-Concepts and

Applications (Narosa), Reliability and Safety Engineering (Springer), Dependabil-ity of Networked Computer Based Systems (Springer) and Optimal Maintenanceof Large Engineering Systems (NarosaIn press). She has over 196 publications invarious international and national journals and conferences. She is a recipient of Leadership in Reliability Engineering Education & Research award by Society of Reliability Engineering, Quality & Operations Management.

Anil Rana, Commander, Indian Navy, has been working in the maintenance man-agement eld for the past 20 years. He is presently on the verge of completing hisPhD in the eld of reliability engineering from the prestigious Indian Institute of Technology, Mumbai with maintenance management as his key research eld. Asan officer of the Engineering Branch of the Indian Navy, he has had a hand onexperience on maintenance of a wide variety of ship borne equipment and this is

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reected in the papers he has published on the subject in national and international journals.

Sanjay K. Khattri received his PhD from the University of Bergen in 2006. He iscurrently working as an Associate Professor at the Stord/Haugesund UniversityCollege. His research interests include, but not restricted to, scientic computing,numerical analysis and optimization.

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Optimization Od Ship Machinery Maintenence

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