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Industrial Case Study

A model for optimal armature maintenance in electric haultruck wheel motors: a case study

Benjamin Lhorentea, Diederik Lugtigheidb,*, Peter F. Knightsc, Alejandro Santanad

aKomatsu Chile, Av. Americo Vespucio 0631, Quilicura, Santiago, Chileb

Condition-Based Maintenance Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto,

5 Kings College Road, Toronto, Ont., Canada M5S3G8cCanadian Chair of Mining and Associate Professor, Pontificia Universidad Catolica de Chile, Centro de Mineria,

Av. Vicuna MacKenna 4860, Santiago, ChiledReliability and Development of Komatsu Chile, Av. Americo Vespucio 0631, Quilicura, Santiago, Chile

Received 25 September 2003; accepted 24 October 2003

Abstract

The objective of the work presented in this paper is the determination of an optimal age-based maintenance strategy for wheel motor

armatures of a fleet of Komatsu haul trucks in a mining application in Chile. For such purpose, four years of maintenance data of these

components were analyzed to estimate their failure distribution and a model was created to simulate the maintenance process and its

restrictions. The model incorporates the impact of successive corrective (on-failure) and preventive maintenance on necessary new

component investments. The analysis of the failure data showed a significant difference in failure distribution of new armatures versus

armatures that had already undergone one or several preventive maintenance actions. Finally, the model was applied to calculate estimatedcosts per unit time for different preventive maintenance intervals. From the resulting relationship an optimal preventive maintenance interval

was determined and the operational and economical consequences and effects with respect to the actual strategy were quantified. The

application of the model resulted in the optimal preventive maintenance interval of 14,500 operational hours. Considering the failure

distribution of the armatures, this optimal strategy is very close to a run-to-failure scenario.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Weibull analysis; Armatures; Electric motors; Repairable system; Maintenance optimization

1. Background

In 1996, Komatsu Chile (KC) put into operation a fleet ofhaul trucks in a mining application in Chile. KC delivered

these machines under a repair and maintenance contract,

taking full responsibility of all repair and maintenance work

at guaranteed availability and maintenance costs.

The haul truck is an electric drive DC truck. This means

that propulsion is delivered to the rear wheels by means of

two parallel electric DC wheel motors. The wheel motors

receive rectified electric power from the main alternator

working in conjunction with a diesel engine. The wheel

motors are mounted on the trucks axle box and provide

the function of axle, transmission and wheel motor at the

same time. The wheel motors main components are the

wheel hub, ring gear structure, planetary gears, sun gear andarmature, seeFig. 1.

The armature is the rotor of the electric motor and

can be removed from it independently. It primarily

consists of bearings, commutator, brushes, spools and

poles. The armature commutator consists of copper bars

and mica plates. The mica plates physically separate and

isolate the copper bars and provide a radial pressure to

ensure the commutators stability. The mica bars have

less altitude than the copper bars and are located below

the commutators superficial area to prevent interaction

with the sliding brushes on the area. The copper bars

have a wedge shape form and together form a cylinder.

Each bar has a riser for connection to the armaturesspools.

0951-8320/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ress.2003.10.016

Reliability Engineering and System Safety 84 (2004) 209218www.elsevier.com/locate/ress

* Corresponding author. Tel.: 1-416-946-5528; fax:1-416-946-5462.

E-mail addresses: [email protected] (D. Lugtigheid),[email protected] (B. Lhorente), [email protected] (P.F. Knights),

[email protected] (A. Santana).
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According to a recent study on the trucks at the same

mining operation, the wheel motors together with its

armatures are the most critical system of the machine. It

can be classified acute and cronic (Knights [1] and

Turina [2]), meaning a high failure frequency and a high

mean time to repair. At the same time the armature is

considered to be critical because of its high maintenance

costs.

Due to the high criticality of the armatures in terms of

reliability, availability and costs, a study was performed to

define how the components operational parameters as well

as its costs could be improved. This was done through thedevelopment and application of an optimal preventive

maintenance (PM) model to determine the PM strategy that

minimizes costs per unit time. As well, the impact of this

strategy on the haul trucks operational parameters was

evaluated. The findings of this study are presented in this

paper.

2. Problem formulation

The current PM strategy is to carry out PMs at intervals

of 9,000 operational hours. If an armature failure occurs

beforehand, a corrective maintenance (CM) is carried out.Although PMs and CMs are different types of events, the

armature reconditioning activities to be undertaken are the

same. The occurrence of armature failures is directly related

to the PM interval. Longer PM intervals will cause more

failures to occur, and vice versa. The objective of this study

is to determine the optimal trade-off between CM and PM

that minimizes the operating costs per unit time of the

armature.

A key activity of the reconditioning process is commu-

tator resurfacing. This activity consists of equalizing the

commutators surface by removing a thin layer of material

from the external surface of the copper bars and mica plates.

A new commutator has a diameter of 16.5 00 and the limit forproper operation is 15.500. In case of a CM, on average 0.2500

of material is removed and, in case of a PM, only 0.1500. This

means that the total useful life is limited by the amount of

material that is removed1 and whenever an armature reaches

the diameter limit of 15.500, the PM or CM activity cannot

restore the proper functioning of the component and a new

armature must be purchased. The repair costs for recondi-

tioning are the same for both a PM or a CM. Besides the

diameter restriction, the armature has a maximum total

useful life of 40,000 h. This means that after 40,000

accumulated operating hours, independently of its diameter,

the armature must be replaced by a new one. The costs of a

new armature are approximately 13 times the cost of

reconditioning and we shall refer to the purchase of a new

armature as a result of any of these two restrictions as

renewal.

The optimization horizon is 40,000 hours. This meansthat if a new armature is needed within this period, KC must

incur full cost. On the contrary, no costs for KC are incurred.

The objective is to define an optimal age-based PM

strategy over a period of 40,000 h. In practical terms, this

means defining a PM interval resulting in the least cost per

unit time.

3. The general PM model

For every component under an age-based PM policy

there exist two types of maintenance actions: preventive

(PM) and corrective (CM). The mean time to failure (atwhich a CM must be carried out) and the PM interval

together with their probabilities of occurrence are

interrelated. Longer PM intervals result in greater mean

times to failure. But at the same time the probability of

occurrence of a failure at higher PM intervals is higher.

These relationships can be used to define the optimal

PM interval that minimizes the costs per unit time.

Defining:

Cp PM Costs (US$)

Cf CM Costs (US$)

Tp PM interval (operating hours)FTp Probability of a failure occurring before reaching

the PM interval TpRTp Survival probability equal to 12 FTp

Thus, within the age-based PM policy two different

cycles can be distinguished: the component survivesTpand

a PM is carried out incurring a cost Cp or the component

fails beforehand and a CM must be carried out incurring

a costCf:For this model the expected costs per unit time in

Fig. 1. Wheel motor components.

1 It is important to mention that the amount of material removed from the

commutators surface per PM or CM is less than the givenvalues. However,

while in operation, the commutator looses material as well and the givenvalues are average values of the differences in diameter between two

consecutive maintenance actions.

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function ofTp can be written as (Jardine[3]),

CTp CpRTp CfFTp

TpRTp MTpFTp; 1

where MTp represents the mean time to failure of an

armature subject to corrective maintenance with a PMinterval ofTp and,

FTp Tp

0ftdt 2

MTp

Tp0

tftdt

FTp; 3

whereft is the probability density function (p.d.f.) of the

times to failure.

Whenever the p.d.f. of the times to failure of the

component is known, the costs per unit time can be

minimized overTp;resulting in the optimal PM interval Tp

p :

4. Data treatment and analysis

From the model presented above it can be seen that the

definition of the p.d.f. is critical to the process of

determining Tpp : The p.d.f. describes the components

failure characteristics. Before using the components

maintenance history to estimate its p.d.f., the data should

be thoroughly analyzed.

The nature of the reconditioning process is to restore the

proper functioning of the component and reduce its risk of

failure. Although the probability of failure should be

reduced by a CM or PM, it is unlikely that its behavior

will be identical to that of a new component (so called good-

as-new or GAN). It is more likely that its failure rate is

higher than that of a new component, but less than just

before the maintenance action was carried out (so called

better-than-old-but-worse-than-new or BOWN). The same

reasoning holds for armatures undergoing a second, third,

etc. maintenance.

It has been shown that an armatures physical state

changes with each maintenance through a reconditioningprocess. This might affect the armatures p.d.f. For this

reason, the failure data was separated into three groups:

new armatures (before the first PM or CM, group 1), after

the first but before the second PM or CM (group 2), and

after the second PM or CM (group 3). At the same time a

separation was made between right-hand and left-hand

side armatures. This was done to verify whether or not the

failure characteristics of armatures are different in these

cases. The amount of data in each data set is shown in

Table 1.

The data in each set consisted of failures and suspen-

sions. The latter correspond to PMs (reconditioning before

failure has occurred). These data were gathered fromAugust 1996 until March 2001.

4.1. Data distribution and independence

The first check undertaken was to examine whether or

not the data in each data set were independent and

identically distributed. If this were not the case, an

Table 1

Amount of data in data sets

Group Left-hand armature Right-hand armature

1 64 63

2 40 37

3 41 35

Total 145 135

Fig. 2. Trend plots for left-hand side (left) and right-hand side (right).

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erroneous estimation of the p.d.f.s would result. A serial

correlation test was applied to test for independency of the

data. This test consists of ranking the failure times (not

suspensions) according to their date of occurrence, making

pairs Xi;Xi21 of each two subsequent failure times for

i 2n where n is the amount of observed failures and

plotting them. If the position of the data points is randomly

distributed among the graph, the data can be considered

independent (Vagenas et. al. [4]). All subsets showed this

behavior, so it was assumed that the data in each of the six

datasets were independent.

To verify whether the data in the different data sets were

identically distributed, trend plots were used. These are

obtained by plotting the accumulated times to failure against

accumulated failure number (ordered according to date of

occurrence). In the case that the graph shows a unique lineartrend, the failure data of the subset can be considered

identically distributed.In thecase that thegraphshowstwo or

more linear segments, it can be concluded that at a certain

moment in time thefailure distributionof thesubset changed.

This can occur due to changes in maintenance procedures or

in operational parameters such as, haul routes, climatic

conditions or other external factors. In this study, whenever

this was detected, only data belonging to the most recent

distribution was considered. This was done because the

objective of this study is to determine the best strategy under

actual circumstances. In Fig. 2 the trend plots for left

and right-hand armatures before the first maintenance are

shown.

4.2. Histograms

The next step in the data analysis process was to

analyze how failure frequencies relate to accumulated

operating hours and month of occurrence for each of the

different data sets. This was done to get a clearerunderstanding of the variation of failure frequencies with

respect to the position of the armature, accumulated

operating hours and calendar time. The following

observations were made.

Fig. 3. Failure frequencies versus time (all groups).


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The failure frequencies versus time and operating

hours are very similar for left and right hand armatures.

This was confirmed by a statistical hypothesis test.

See Fig. 3.

The failure data of group 1 showed higher failure

frequencies at higher operating hours. However, groups

2 and 3 showed more failures concentrated at lower

operating hours. Failure frequencies are highest during first quarters.

First quarters contain 39% of the total failures and the

second, third and fourth 23, 18 and 20%, respectively.

The first quarter of each year coincides with the

occurrence of adverse climatic conditions in the region

where the mine is located. This particular climatic

event is associated with heavy rain and electric storms,

which affects the operating parameters of the armature

and causes additional failures (see Fig. 4).

4.3. Causes of failure

The 280 data of the six data sets consisted of 156 failures

(CMs) and 124 suspensions (PMs). Table 2 shows the

causes of failure of the 156 failures.

The dominant failure mode is flashovers and for a

considerable amount of failures (32) no cause was identified.

4.4. Distribution fitting

For the determination of the p d.f. in this study, the

Weibull distribution was chosen, due to its flexibility in

representing components with constant, increasing and

decreasing failure rates. This property is particularly useful

when dealing with different failure distributions among thedata sets of groups 1, 2 and 3, as was the case in this study.

The p.d.f. of the three parameter Weibull distribution is,

ft b

h

t2 t0

h

b21

e2

t2t0h

; for t. t0: 4

Where b is the shape parameter, h is the scale factor or

characteristic life and to is the failure-free time. The data

in this study consisted of times to failure (CMs) as well as

PMs (suspended or censored data). For this reason the

data were adjusted according to mean and median ranks

before the actual fitting process (OConnor [5]). The

fitting process was carried out in Excel, using linearregression. The results of the fitting process are shown in

Tables 35.

From these tables it may be concluded that:

For new armatures (group 1), the shape parameter varies

between 0.8 and 0.9 and is less than 1 which indicates

infant mortality. For armatures that have undergone one or more

maintenance (groups 2 and 3), the shape parameter varies

between 1.0 (constant failure rate) and 1.3, indicating

near-randomness of the failure data. Some wear is evident

and the characteristic life is much smaller than group 1. In all data sets the shape parameter increases with every

maintenance. This validates the conclusions drawn from

the histograms, that with every maintenance action

the mean life of the component diminishes and failure

rates increase.

Fig. 4. Failure frequency versus time (all groups).

Table 2

Causes of failure

Cause Amount

Flashover 118

Ground fault/short circuit 7Unknown 32

Table 3

Left-hand armature Weibull parameters

Parameter Group 1 Group 2 Group 3 Total

b 0.809 1.247 1.235 1.043

h 36,286 6,382 5,264 12,304

t0 0 0 0 0

Table 4

Right-hand armature Weibull parameters


b 0.897 1.012 1.215 1.119

h 11,014 7,538 5,149 6,914t0 0 0 0 0


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The shape parameters of left and right hand armatures are

very similar, validating the conclusions drawn from thehistograms.

With the exception of the characteristic life difference for

the group 1 right-hand and left-hand armatures, it was

concluded that there was little difference between the failure

parameters for right and lefthand armatures. In theinterests of

developing a uniform maintenance policy, it was decided to

use the Weibull parameters for each group without dis-

criminatingbetween right and left-hand failures(see Table 5).

5. Model application

In order to apply the general optimal PM model to define

the optimal PM interval Tpp ; some adjustments have to be

made, and in order to do so the following variables are

defined:

MnTp Mean time to a CM before the nth maintenancegiven PM at Tp.

FnTp Accumulated failure probability before the nth

maintenance given PM at Tp.

RnTp Survival probability before the nth maintenance

given PM at Tp:

VC The length of the optimization horizon (operating

hours)

CA Cost of a new armature (US$).

As in the general PM model, there exist two different

cycles. The armature can be preventively maintained at time

Tp at a preventive maintenance cost Cp with a survival

probability of RnTp; or can fail at time MnTp with acorrective maintenance cost Cf and a failure probability

FnTp: The successive occurrence of these cycles formmaintenance sequences, Si; with each sequence giving an

armature life ofVi operating hours prior to renewal. These

can be represented by means of a maintenance probability

tree, as shown inFig. 5.

The tree must be interpreted as follows. We start with a

new armature (left node). Two scenarios might happen: the

armature fails with probability F1Tp or survives until

the PM interval Tp with probability R1Tp: In both cases,

the armature must be reconditioned incurring a cost ofCfor

Cp; after which the armature is put back into operation.

Now, the same scenarios might happen once again, but withrespective probabilitiesF2Tpand R2Tp;as the armatures

have been reconditioned one time and now its failure

characteristics are described by the p.d.f. of group 2.The i 1k different sequences represent all possible

successive maintenance (PM or CM) events between t 0

and t VC. However, besides preventive and corrective

maintenance, armature renewals take place and these must

be incorporated in the maintenance tree. Within a cycle,2

renewals, PMs and CMs are mutually exclusive events. This

means that whenever a cycle has been completed within any

sequence i (this can be at time Tp or MnTp), instead of aPM or CM costCporCf;a renewal costCAis incurred when

at least one of the following conditions is met:

The useful life of the armature has reached the

maximum,VM If rij represents the amount of material to be removed

from the commutator surface in maintenance j since

the last renewal of the armature of sequence i; then if

rij , 12Pni21

j1 rij;;i;j a renewal must take place.

Therefore, sequences may vary in length in terms of the

number of cycles of which they consist, however,

accumulated sequence operating hours cannot exceed thelength of the optimization horizon,VC. The cycle number of

a sequence is denoted byj, which can have values between 1

andni(whereiis the sequence number) and it resets itself to

1 whenever a renewal takes place. Additionally the

following variables are defined.

Ci Accumulated maintenance costs of sequencei:

Pi Probability of sequencei:

ai; bi; ci Integer variables indicating amount of PMs (before

the first, second and after third maintenance)

occurring in sequencei:

Fig. 5. The maintenance probability tree.

Table 5

Total armature Weibull parameters


b 0.866 1.163 1.276 1.082

h 24,918 6,785 5,147 6,914

t0 0 0 0 0

2 A cycle refers to the time between two successive event (these can be

PMs, CMs or renewals).


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di; ei;fi Integer variables indicating amount of CMs

(before the first, second and after third mainten-

ance) occurring in sequence i:

CTp Expected total costs of tree with PM interval ofTp:

CMTp Expected maintenance cost of tree with PM

interval ofTp:

CRTp Expected renewal cost of tree with PMintervalofTp:

In this way, the following set of equations represent the

final model:

Pi R1TpaiR2Tp

biR3Tpci F1Tp

di F2Tpei F3Tp

fi 5

Vi ai bi ciTp diM1Tp eiM2Tp fiM3Tp 6

Ci ai bi ciCp di ei fiCf 7

The expected maintenance and renewal costs are:

CMTp

Xk

i1CiPiX

k

i1ViPi

8

CRTp CAXk

i1

ViPi

9

Thus the total expected costs for a PM interval ofTp is:

CTp CMTp CRTp 10

The values of CTp are different for every Tp due to

differences between maintenance trees in terms of sequence

probabilities, amount of maintenance and renewals. How-

ever, the tree configuration (number of cycles per sequence)

also changes in discrete steps according toTp:In the case of

the armature maintenance problem, it was decided to

construct maintenance trees for 250 , Tp , 17; 000; with

steps of 250 h. This was based upon the fact that the

maximum observed lifetime between two successive

maintenance actions was 17,000 h. Within this PM time-span, 16 different maintenance tree configurations could be

constructed (seeTable 6).

6. Results

The results were simulated using a Microsoft Excele

spreadsheet, and are presented inFig. 6.

InFig. 6it can be seen that the expected total useful life

of the armatures increase with higherTpintervals, however,

this increase gradually diminishes. The reason for this is that

at low Tp intervals the armatures total useful life is

restricted by its diameter restriction. At higher values ofTpthe maximum useful life restriction VM becomes

dominant. As well it can be seen that, for all values ofTp;

the expected renewal cost per unit time is much higher than

the expected maintenance cost per unit time. This is to be

expected, as the cost of renewal is 13 times the costs ofpreventive and corrective maintenance. The maintenance

costs decrease continuously as Tp increases. The renewal

costs decrease in general terms but its evolution is discrete,

with local gradually increasing slopes and abrupt falls. This

is caused by the 16 different maintenance trees and the fact

that only an integer amount of armatures is purchased within

the optimization horizon VC:

The maintenance costs per unit time curve does not

present an optimal value. It decreases continuously with

time. At the same time the renewal costs per unit time

decrease as well, however, it does step-wise. The minimal

costs per unit time are found at Tpp

14; 500 hours with a

value of C*3 US$ per hour. Beyond Tpp the expected total

costs per unit time are constant at a value of 1.022 times this

minimum.

7. Sensitivity

To check how sensitive the optimal PM interval Tpp was,

a sensitivity analysis was conducted for the shape parameter

band the corrective maintenance costs Cf; which are the two

most critical variables of the model in terms of sensitivity.

Table 6

Different maintenance probability trees

Tree no. RangeTp Tree no. Range Tp

1 250 # Tp , 6; 750 9 11; 750 # Tp , 12; 000

2 6; 750 # Tp , 8; 000 10 12; 000 # Tp , 13; 500

3 8; 000 # Tp , 9; 000 11 13; 500 # Tp , 14; 500

4 9; 000 # Tp , 9; 250 12 14; 500 # Tp , 14; 750

5 9; 250 # Tp , 10; 000 13 14; 750 # Tp , 15; 250

6 10; 000 # Tp , 10; 500 14 15; 250 # Tp , 15; 500

7 10; 500 # Tp , 10; 750 15 15; 500 # Tp , 16; 7508 10; 750 # Tp , 11; 750 16 16; 750 # Tp , 17; 000

Fig. 6. Results.

3 Value suppressed for comercial reasons.


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Besides, in this studyCfwas chosen equal to Cpas the costs

of preventive and corrective reconditioning are equal for

Komatsu Chile (KC). However, for the mining company

using the trucks in their production process, these costs

would not be the same. For them, corrective maintenance is

more costly than preventive maintenance as these incur an

opportunity cost related to the unscheduled productionlosses. The sensitivity analysis would make clear whether

the optimal PM interval for KC is an optimal policy for the

mining company at the same time. For the shape parameter,

b;95% confidence intervals were defined (seeTable 7).

The optimal PM interval and expected costs per unit time

were calculated and the results are shown in Table 8.

From these results it can be seen that with higher values

ofbthe optimal PM interval decreases. However, since C*

is small, the differences in costs per hour are minimal. In

order to verify the sensitivity of Cf; the same calculations

were made for values of Cf times 1/3, 3, 5 and 10. The

results are shown inTable 9.

The optimal PM interval for lower values ofCfremainsthe same as the original, 14,500 h. With triple values ofCfthe optimal solution is 15,500 h. This solution is optimal for

values of Cf until five times the original value. In the

extreme case of 10 times the original value, the optimal PM

interval is 17,000 h. In general terms the model is not very

sensitive to changes inCf:Any optimal solution for KC will

be very close to optimal for the mining company as well. So

it may be concluded that:

13; 500 # Tpp # 16; 750; when b takes its 95% confi-

dence extreme values.

14; 500 # Tpp # 17; 000; when Cf takes values of 1/3

to 10 times its original value.

To analyze the models results in more detail, four

scenarios were defined and their results compared:

Base case:Tp 9; 000 h, which is the actual PM interval

of KC.

Original case:Tp 10; 000 h, which was the original PM

interval KC used in the beginning of the contract.

Optimal case:Tp 14; 500 h, which is the optimal value

according to this study.

Extreme case: Tp 17; 000 h, which is the maximum

value Tp might take as no armatures have lasted more

than 17,000 h in between maintenance actions.

A summary of these cases is presented inTable 10.

8. Operational consequences

For the four cases, the expected amount CMs and PMs

during the useful life of an armature are the following, see

Table 11:

Taking into account the fleet size and its utilization,

these numbers could be translated into amount of PMsand CMs per year, using the following relationships

(Wong et. al. [6]).

n Amount of components in the fleet.

s Amount of total maintenance (PM and CM) per

year.

tul Total useful l ife of an armature in terms of operating hours

sp Amount of PMs per year.sf Amount of CMs per year.

u Utilization in terms of operating hours per

armature per year.

Table 7

Confidence interval for b

Group 1 Group 2 Group 3

bcalc 0.866 1.163 1.276

bmax 1.065 1.384 1.582

bmin 0.704 0.977 1.029

Table 8

Sensitivity ofb

bmin bcalc bmax

Tp

p 16,500 14,500 13,500CTpp=C

p 0.993 1.000 1.022

Table 9

Sensitivity ofCf

Cf

1

3 Cf3 Cf5 Cf10

Tpp 14,500 15,500 15,500 17,000

CTpp=Cp 0.873 1.194 1.381 2.657

Table 10

Comparison of cases

Base case Original case Optimal case Extreme case

Tp 9,000 10,000 14,500 17,000

CTpp=Cp 1.261 1.253 1.000 1.022

Table 11

Amount of maintenance during armatures useful life


PMs 2 2 1 1

CMs 4 4 4 4

Total 6 6 5 5


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AP Expected amount of PMs during useful life of an

armature.

AF Expected amount of CMs during useful life of an

armature.

The expected amount of total maintenance per year can

be expressed as:

s sp sf 11

where;

sp nuAP

tul 12

sf nuAF

tul

In the case of KC, there are 78 armatures and the average

operating hours per year are 6,100. Applying the above

equations results inTable 12.

The total amount of maintenance per year decreaseswith increasing Tp. This holds for CMs and PMs. The

base case with Tp 9; 000 h is the worst scenario in terms

of amount of maintenance per year and the extreme case

with Tp 17; 000 h the best. Using the same methodology

and incorporating the fact that it takes approximately 12 h

to change-out an armature in case of a PM or CM,

Table 13 represents the impact of each of the four

scenarios on fleet availability.

The total downtime in terms of unavailability is worst

for the base case with a total unavailability due to

armature maintenance of 13.0%. The original case

improves 0.7% with respect to the base case, the optimal

case 2.3% and the extreme case 3.0%. Although in termsamount of maintenance and availability the extreme case

has the best results, in terms of costs this is not the case.

The annual savings with respect to the base case for the

three cases are:

Original case: US$ 5,800

Optimal case: US$ 163,900

Extreme case: US$ 153,400

This means that changing the actual PM interval to the

interval of any of the three alternative cases results in annual

savings between US$ 5,800 to 163,900. Within the three

alternatives the optimal case is best.

9. Conclusions and recommendations

New armatures experience infant mortality. On the

contrary, once maintained the armatures p.d.f. changes

dramatically, showing random failure behavior withshort expected life between successive maintenance

actions. The position of the armature on the truck (left

or right hand side) does not significantly influence its

failure characteristics. The dominant failure mode is

flashovers, which occur more frequently during first

quarters. This increase in failure frequency is believed

due to the particular climatic situation during those

months.

The optimal PM interval Tpp is equal to 14,500 h. This

optimum moves between 13,500 and 16,750 h when varying

the shape parameter bwithin its 95% confidence interval. At

the same time, Tp

p moves between 14,500 and 17,000 h

when changing the cost of corrective maintenance Cfbetween its extreme values.

Three feasible maintenance policies can be rec-

ommended:

The first one is maintaining the armature preventively

every 14,500 h. This is the best policy in terms of costs

and is the optimal solution to the maintenance problem.

Total savings with respect to the actual replacement

policy are US$ 163,000 annually and, in terms of fleet

availability, 2.33%.

The second one is maintaining the armature every

17,000 h. Taking into consideration that no armature sofar has lasted more than 17,000 h, this policy is

equivalent to a run to failure (on-condition) policy. The

savings with respect to the actual policy are US$

153,400 annually. This is US$ 10,600 less than would

have been saved by implementing the optimal policy.

However, the run to failure policy results in higher

fleet availability. The savings in terms of availability

with respect to the actual policy are 3.0, 0.7% more

than the optimal case.

The third alternative would be to implement a run-to-

failure policy for new armatures and a PM interval for

armatures of group 2 and 3. This, however, is more

complex to administrate from a practical point ofview.

Table 13

Impact on fleet availability

Base

case (%)

Original

case (%)

Optimal

case (%)

Extreme

case (%)

Unavailability 13.0 12.3 10.7 10.0

Differencew.r.t. base case

0.0 0.7 2.3 3.0

Table 12

Expected maintenance per year


PMs 25 21 12 10

CMs 70 69 66 63

Total 95 90 78 73


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Acknowledgements

The authors would like to thank the contributions and

support of Enrique Affeld, Operations Manager of Komatsu

Chile.

References

[1] Knights PF. Rethinking Pareto analysis: maintenance applications of

logarithmic scatterplots. J Quality Maintenance Engng 2001;4:

25263.

[2] Turina C. Estudio comparativo de las intervenciones imprevistas en

flotas de camions electricas operando en distintas faenas mineras de

Chile, Final year thesis, Faculty of Engineering, Catholic University of

Chile, Santiago; 2002.[3] Jardine AKS, Maintenance replacement and reliability, Toronto,

Ontario: Pitman Publishing; 1973.

[4] Vagenas NR, Runciman N, Clement S. A methodology for mainten-

ance analysis of mining equipment. Int J Surface Mining, Reclamation

Environ 1997;11:3340.

[5] OConnor PDT. Practical reliability engineering, third edition revised,

student edition. New York: Wiley; 1995.

[6] Wong J, Chung D, Ngai B, Banjevic D, Jardine AKS. Evaluation of

spare parts requirements using statistical and probability analysis

techniques. International Conference of Maintenance Societies, 33,

Melbourne, Australia; 1996.


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