Study on Rolling Stock Maintenance Strategy and Spares Parts Management

Yung-Hsiang Cheng1, Ann Shawing Yang

2 , Hou-Lei Tsao

3

1 National Kaohsiung First University of Science and Technology, Kaohsiung City, Taiwan,

2 Shu-Te University, Kaohsiung County, Taiwan,

3 National Kaohsiung Fist University of

Science and Technology, Kaohsiung City, Taiwan

Abstract

The purpose of this paper was to present a method for rolling stocks maintenance strategy

selection that allows for the consideration of important interactions among decisions levels and

criteria. The methodology adopts Analytic Network Process (ANP) for this evaluation to decide the

possible ratio between preventive maintenance and corrective maintenance that can induce

possible spares parts quantities and replacement interval of component of rolling stock. The

empirical result indicates preventive maintenance should be much more emphasized than

corrective maintenance. Safety is the most crucial factor for rolling stock maintenance strategy

selection.

Key words: rolling stock maintenance, maintenance strategy, spares part

Introduction

The maintenance of rolling stock can be categorized in two types: failure based maintenance

(corrective maintenance) and life based maintenance (preventive Maintenance). The time interval

at which the preventive maintenance could be scheduled is dependent on both the life distribution

of the components and the total cost involved in the maintenance activity. However, the corrective

maintenance cannot be avoided when a random failure of a component occurs. The total cost of the

maintenance depends on p ercentages in performing preventive maintenance and corrective

maintenance.

In addition, contrary to maintenance strategy selection in manufacturing industries, the

performance of rolling stocks maintenance will have great influence on passengers safety and

comfort on board. Consequently, various combination strategies between preventive maintenance

and corrective maintenance will affect railway system safety, passenger comfort and total operation

cost. Railway system operator is therefore required to have a complete overall thought to build

rolling stock maintenance strategy to achieve optimal system operation performance. How to build

a complete and sustainable maintenance strategy will have immense influence on system

operators railway companies, system safety supervisor government and system users

passengers.

Therefore, this study first examines rolling stock maintenance strategy through multiple criteria

decision-making by expert choice. The stock of spare parts is strongly dependent on maintenance

strategy. In the second step, spare parts quantities and replacement intervals estimation were

conducted based on the maintenance strategy chosen by experts in the first step.

The selection of suitable maintenance strategy is very complicated, because the operator needs to

consider the non-metric variables (safety, passenger comfort) and metric variables (maintenance

cost, inventory cost, shortage cost) simultaneously to decide final strategy. Therefore, this study

adopts ANP method that could consider jointly non-metric and metric variables all together.

This study will provide an expert decision method to consider various strategic combinations of

rolling stock preventive maintenance and corrective maintenance and then decide the spares parts

and replacement interval. This fruit of this study could serve as a reference for railway system

operator in adjusting maintenance strategies.

Literature review

There were plentiful studies on manufacturing system maintenance and replacement problems

(McCall (1963), Barlow, and Proshan (1965, 1975), Pierskalla and Voelker(1976), Osaki and

Nakagawa (1976), Sherif and Smith (1981), Jardine and Buzacott (1985), Valdez-Flores and

Feldman (1989), Cho and Parlar (1991), Jensen (1995), Dekker (1996), Pham and Wang (1996),

Van Der Duyn Schouten (1996),and Dekker et al. (1997)). Thousands of maintenance and

replacement models have been created. Most previous researches on maintenance model are

formulated by total cost consideration (Ruhul Sarker, amanul Haque, 2000, Won Young Yun, Luis

Ferreira, 2003)

In comparison with manufacturing system maintenance, the studies on rolling stock maintenance

were relative rare. Dipark Chaudhuri and P.V. Suresh (1995) developed an algorithm for

determining the best type of maintenance, period length and replacement policy using fuzzy set

theory. But this study did not consider the safety for model formulation which is the crucial factor in

the rolling stock maintenance.

In spare parts consideration, Chelbi and Ait-Kadi (2001) proposed a jointly optimal periodic

replacement and spare parts provisioning strategy, the performance of this strategy was evaluated

in terms of total average cost per time unit over an infinite horizon. Yun and Ferreira (2003)

described the development of a simulation model to assess the inventory requirements of

alternative rail sleeper replacement strategies. The main aim of the model is to determine the

optimal replacement strategy, given replacement costs and resultant train operating cost benefits.

The replacement cost consists of the fixed cost and variable cost proportional to the number of units

replaced. A finite horizon is considered and total expected cost is a criterion for comparing the

proposed policies. But they all have no accurate mentioning about the spare parts that the quantity

must prepare in the unit time, but about this part in Almeida (2001) in the research has considered

this point. Almeida (2001) presented multi-criteria decision models for two maintenance problems:

repair contract selection and spares provisioning. In the repair contract problem the model

incorporates consequences modeled through a multi-attribute utility function. The consequences

consist of contract cost and system performance, represented by the system interruption time. Two

criteria (risk and cost) are combined through a multi-attribute utility function in the spares

provisioning decision model.

Chaudhri and Suresh (1995), Cassady et al. (1998), and Nakagawa (1989) conducted their

researches on principles of maintenance cost minimization to seek best replacement cycle. They

considered maintenance costs including preventive maintenance costs and facility damage

maintenance costs.Huang et al. (1995) and Sarker and Haque (2000) suggested system damage

rates will increase with amortization. When damage maintenance costs are superior of preventive

maintenance costs, a suitable preventive maintenance period will minimize total maintenance costs.

This study follows related literatures assumption to apply Weibull distribution on rolling stock

component amortization to obtain a more realistic result.

According to the literatures reviewed, most researches regarding maintenance s trategy and

replacement policy concentrated on model development which formulated by total cost

consideration. The rolling stock maintenance model formulation should avoid merely consider the

cost-oriented model. Thus, in this present study we incorporate the safety as the crucial factor and

adopt expert decision model (Analytic Network Process, ANP) method to select the appropriate

maintenance strategy of rolling stock.

Research Design and Methodology

This study applies expert decision methodology to obtain the appropriate maintenance strategy

followed by related spare parts inventory estimation to reach rolling stocks component

replacement interval. Expert questionnaires are conducted in two phases. Phase 1 interviews

maintenance staffs on site to establish questionnaire framework for Phase 2. Phase 2 interviews

maintenance managers and applies ANP method to obtain the appropriate rolling stock

maintenance strategy and to decide he weight for the evaluation factors. In addition, multiple utility

function assumptions are applied to obtain spare parts estimation values to comprehend preventive

and corrective maintenance ratio. Finally, the Weibull distribution is applied to assume component

life cycle to obtain optimal replacement interval and cost differences between preventive and

corrective maintenances. Figure 1.1 presents analysis procedure.

Figure 1 Research analysis procedure

Chang (2002) applied AHP methodology to conduct investigation analysis. A drawback of AHP is

the assumption of independent condition that is in contrast of actual situation. Therefore, many

latest researches apply ANP methodology. The ANP methodology is applied in areas including

priority ranking, substitution production, most suited selection, decision demand, resource

allocation, maximization, performance evaluation, forecasts and risk evaluation. Lee and Kim

(2000) suggested an improved Information system (IS) project selection methodology which reflect

interdependencies among evaluation criteria and candidate projects using analytic network

process (ANP) within a zero-one goal programming (ZOGP) model. But the ANP not only uses in

the appraisal aspect, also may apply in the management domain. Wolfslehner et al. (2005)

compared two different multi-criteria analysis approaches: the analytic hierarchy process (AHP)

with a hierarchical structure and the analytic network process (ANP) with a network structure.

Comparisons are made for evaluating sustainable management strategies at forest

management-unit level by using a C&I approach based on the Pan-European guidelines for

sustainable forest management (SFM). But this research also because will consider to in the

maintenance criterion, some many criteria are to be dependent, therefore will use the ANP to take

Best maintenance strategy obtained

through ANP technique by expert decision

Spare part quantity and replacement interval

estimation through Weibull distribution

The ratio between preventive maintenance

and corrective maintenance is decided

this research the appraisal method.

3.1 The analytic network process

Hierarchical models (for example, Analytic Hierarchy Process, AHP), premising independent

elements, face certain limitations when the complexity of decision problems increases and

interactions among criteria and sub-criteria are not implicitly covered. Different approaches have

been proposed to consider interaction and dependence among elements. ( Bernhard Wolfslehner,

Harald Vacik, Manfred J. Lexer, 2005)

ANP model building requires the definition of elements and their assignment to clusters, and a

definition of their relationships (i.e., the connections between them indicating the flow of influence

between the elements). ANP is founded on ratio scale measurement and pair-wise comparisons of

elements to derive priorities of selected alternatives. In addition, relations among criteria and

sub-criteria are included in evaluations, allowing dependencies both within a cluster (inner

dependence) and between clusters (outer dependence) (Saaty, 2001). Pair-wise comparison has

two goals, one for weighting the clusters (i.e., criteria) and the other for estimating the direction and

importance of influences between elements, numerically pictured as ratio scales in a so-called

supermatrix.

Mathematically, an ANP model is implemented following a three-step supermatrix calculation

(Saaty, 2001). In the first step, the unweighted supermatrix is created directly from all local priorities

derived from pairwise comparisons among elements influencing each other. The elements within

each cluster are compared with respect to influencing elements outside the cluster.

This also yields an eigenvector of influence of all clusters on each cluster (Saaty, 1999). In the

second step, the weighted supermatrix is calculated by multiplying the values of the unweighted

supermatrix with their affiliated cluster weights. By normalizing the weighted supermatrix, it is made

column stochastic. In the third and final step, the limit super matrix is processed by raising the entire

super matrix to powers until convergence in terms of a limes.( Bernhard Wolfslehner, Harald Vacik,

Manfred J. Lexer, 2005)

3.2 Spare parts maintenance model

This study follows Almeida (2001) spare parts maintenance model with few adjustments. A

multi-criteria decision model U(c,) allows the quantification of spare provisioning for a single item

taking into account the total spare cost (C) and the risk of item non-supply ( ). That is

MaxqU( ,C) (1)

Item reliability is assumed to follow an exponential probability distribution with a mean failure rate

. The system maintainability is also assumed to follow an exponential probability distribution with a known mean time to repair (MTTR).

Total spare cost C depends on the unit cost C1 and the number of spare q

C = qC1 (2)

The probability of the provisioning shortage , when the number of failures x > q is assumed to

follow a Poisson distribution, given the assumption of exponential distribution for reliability. Thus

= Pr{ x > q } = 1 Pr{ x q }

=

=

q

j

jMTTR

j

MTTRe

0 !

)(1

(3)

where =

=

q

oj

j

j

MTTR

!

)(

As before, first one-dimensional utility functions are obtained for U() and U(C), and then a

multiattribute utility function U( ,C) is obtained. This multiattribute utility function is assumed to be

additive

U( ,C) = K1U( ) + K2U(C) (4)

Substituting (2) and (3) into (4)

)(]1()(( 1,1 qCUKeUKCUMTTR

+= (5)

If (5) is applied to (1), the optimum solution can de obtained.

3.3 Replacement interval estimation

3.3.1 Weibull distribution

This study relies on Weibull distribution for parts amortization assumption through parameter

changes of Weibull distribution. Developed frequency intensity function is characterized in multiple

variations and suitable for upward or downward product failure description. It is widely applied in

reliability life analysis and consists of 2-parameter Weibull distribution with a frequency intensity

function expressed as:

])())2(1)(

xxF = , where 0x 0> 0>

Frequency intensity function is:

f(x)=

(x

)1expp-(

x )

p , where 0x 0 0 A3-parameter distribution cumulative intensity function is:

])())2(1)(

=x

xF , where x 0> 0> 0

In addition, x represents random variable of Weilbull distribution. On reliability life analysis, units are

measured in time; represents scale parameter represents shape parameter. The different between 3-parameter and 2-parameter Weibull distribution is location parameter represented by . Weilbull distribution frequency intensity function is mainly affected by scale parameter and shape

parameter.

3.3.2 Weibull parameter estimation

Montanari (1997) conducted his study through the application of graphical analysis to estimate

shape parameter and scale parameter. Weibull Probability Paper is a relatively easy and frequently

applied graphical analysis. Its advantages are simple and rapid. Weibull Probability Papers

principle is to conduct linear transformation of failure function of Weibull distribution into a 1st

degree linear function with life data indicated. This linear functions slope is shape parameter

estimated value. The distance of linear parameter could estimate value of scale parameter. If spare

parts lack utilization time or pre-heating time, location parameter is set at 0. Linear transformation

of Weibull failure function is as follows:

We set natural logarithm in this equation and obtained the following

)())(1**(x

xF = ,

)())(1**(x

xF =

We set natural logarithm again:

)**())](1**(**(

xxF = **** = x

Make ))](1**(**( xFY =

xX **=

Rewrite above function into a straight function, we have:

**= XY

Fothergill (1990) suggested the application of cumulative frequency graphic analysis when

Monte-Carlo simulation method evaluation possesses 2-parameter Weibull distribution. We take Pi

as the estimation value for F(x)

)(

)(1

x

exF

=

e+0

++0

+

=

n

iPi

where, Pi represents the ith observed cumulative frequency value of n numbers of samples.

Therefore, this study applies F(x) for value estimation followed by frequency graphic analysis

expressed as Y = lnp-ln(1-F(x))p, X = ln x t o obtain shape and scale parameters of Weibull

distribution. Spare parts replacement interval forecasting is conducted by following Huang et al.

(1995).

Empirical result analysis

4.1 Appropriate maintenance strategy selection

This study applies expert questionnaire survey to select an appropriate rolling maintenance

strategy. Accordingly, this study needs to find most suited evaluation factors affecting maintenance

strategy selection. Theses evaluation factors selected will be an evaluation framework of ANP

questionnaire. There are three different maintenance strategy were provided according to various

combination between preventive maintenance and corrective maintenance.

Figure 4.1 Questionnaire investigation process

4.2 Questionnaire design and investigation

This study adopts a two-phases questionnaire design. First phase questionnaire is designed by

following Shu (1999) who has considered some specific factors affecting maintenance strategy

selection. Interviews are conducted on site with the maintenance staffs working for various railway

Previous literature review to comprehend rolling stock maintenance strategy evaluation factors and design 1st

questionnaire

Executive factor analysis through 1st phase questionnaire and develop 2

nd

phase ANP questionnaire

Apply ANP technique to analyze 2nd phase questionnaire results to select an appropriate maintenance strategy and to find weight for the evaluation factors

and sub-factors

operators including conventional railway system, mass rapid transit system, and high-speed rail

system. This study applies factor analysis technique to conduct data reduction and summarization

and extract important evaluation factors to select the most suitable rolling stock maintenance

strategy.

4.2.1 Factor analysis result

This study adopts the KMO test and Bartlett test to examine the appropriateness of 13 sub-factors

on rolling stock maintenance for factor analysis. Table 4.1 shows a KMO value greater than 0.7 and

a Bartlett test value at 635.797. This indicates the appropriateness of factor analysis application in

rolling stock maintenance related issues. Rolling stock maintenance factor analysis result evidence

total explainable variance at 71.143% and extract three factors.

Table 4.1 KMO and Bartletts Test

Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .799

Approx. Chi-Square 635.797

Df 78

Bartletts Test of

Sphericity

Sig. .000

As for the reliability analysis result, this study conducts a Cronbachs value to examine rolling

stock maintenance questionnaire reliability to assure all measured factors are highly consistency.

Table shows all Cronbachs individual are above 0.7. Table 4.2 presents factor analysis result.

It is suggested to reduce the sub-factors considered in applying ANP technique. Therefore, this

study groups highly correlated sub-factors into one factor through correlation analysis. Empirical

Results show correlation between rolling stock shut-down time and maintenance time reduction is

at 0.626. Therefore, we group these two sub-factors into one factor and rename as maintenance

cost and shut-down time reduction. Correlation between worker and staff safety and passenger

safety is at 0.643. Therefore, we group these two sub-factors into one factor and rename as worker

and passenger safety assurance. Correlation amongst maintenance cost reduction, staff efficiency

improvement, and staff work assignment are at 0.643 and 0.673 respectively. Correlation between

staff efficiency and work assignment improvement reach as high as 0.780. Therefore, we group

these three sub-factors into one factor and rename as staff work efficiency increases. Correlation

between sudden incident occurrence reduction and railway failure rate improvement is at 0.704.

Therefore, we group these two sub-factors into one factor and rename as rolling stock failure rate

reduction.

Table 4.2 Empirical result of factor analysis to extract evaluation factors affecting selection the

suitable maintenance strategy

Factor Sub-factor

Factor loading

Eigenvalue % of Variance

Cumulative variance

%

Cronbachs

Maintain high quality maintenance

0.615

Maintain appropriate available spare parts

0.735

Staff work efficiency improvement

0.643

Staff work assignment and preparation improvement

0.668

Reduce the impact in case of emergency

0.696

Quality and

Efficiency

Railway car out-of-service rate improvement

0.814

6.357

48.898

48.898

0.889

Maintain rolling stock in good condition

0.436

Reduce rolling stock shut-down time

0.812

Reduce maintenance time

0.894

Cost and Reliability

Reduce maintenance cost

0.721

1.814

13.957

62.855

0.820

Assure staff and personnel safety

0.874

Assure railway system safety

0.832

Safety

Assure passenger safety

0.693

1.077

8.288

71.143

0.810

4.2.2 ANP questionnaire design and empirical result

The 2nd

phase questionnaire design is based on factor analysis result of 1st phase questionnaire.

The 2nd

phase questionnaire is constructed on three main evaluation factors with eight sub-factors

and three selection alternatives. This study refers to Taipei Mass Rapid Transit System on

preventive maintenance and corrective maintenance percentages for selection possible

alternatives.

The following presents eight reorganized sub-factors categorized into three main factors.

(1) Factor 1: Cost and quality

This factor includes four sub-factors such as high quality maintenance, staff work efficiency

increase, appropriate usable spare parts maintenance and rolling stock failure rate reduction

(,) Factor 2: rolling stock availability

This factor includes two sub-factors such as facility maintenance in good condition and

maintenance cost and shut down time reduction

(+) Factor 3: safety

This factor includes two sub-factors such as worker and passenger safety assurance and

railway car safety assurance.

We took the model 321 metro rolling stock current collecting shoe as a component for analysis.

Because it is crucial for MRTs daily operation. In addition, three alternatives are proposed:

Alternative A : the ratio between PM and CM is 7:3

Alternative B : the ratio between PM and CM is 1:1

Alternative C : the ratio between PM and CM is 3:7

Table 4.3 Evaluation factors and sub factors as the basis for ANP method questionnaire

Factor Sub-factor

High quality maintenance

Increase staff work efficiency

Maintain appropriate usable

spare parts

Quality and Efficiency

Reduce rolling stock failure rate

Maintain rolling stock in good

condition

Cost and Reliability

Reduce maintenance cost and

shut-down time

Assure worker and passenger

safety

Safety

Assure rolling stock safety

Table 4.4 maintenance strategy expectation index

Evaluation factors maintenance strategy weights kjiCT

S

Cj Weight(Rj) 1T

W ,T

W +T

W jCT

S1

jCT

S,

jCT

S+

C1 0.176 0.619 0.244 0.137 0.109 0.043 0.024

C2 0.092 0.521 0.281 0.198 0.048 0.026 0.018

C3 0.294 0.615 0.239 0.146 0.181 0.070 0.043

C4 0.234 0.641 0.230 0.129 0.150 0.054 0.030

C5 0.052 0.615 0.227 0.158 0.032 0.012 0.008

C6 0.048 0.508 0.293 0.199 0.024 0.014 0.010

C7 0.042 0.576 0.268 0.156 0.024 0.011 0.007

C8 0.062 0.629 0.219 0.152 0.039 0.014 0.009

Maintenance strategy expectation index DIi 0.607 0.244 0.149

For evaluation results, Figure 4.2 shows Cost and Reliability, Safety and Quality and Efficiency with

weight values of 0.268, 0.528, and 0.204 respectively. This result fully explains safety as first

priority in railway rolling stock maintenance considerations. Figure 4.2 further shows maintenance

strategy A (0.607) is significantly superior of other two maintenance strategies after calculation of

maintenance strategy expectation index in table 4.2. Therefore, best maintenance strategy A is

preventive maintenance and corrective maintenance with percentages at 7:3 followed by

preventive and corrective maintenance strategy weight percentages at 1:1 (alternative B, weight

value 0.244). Finally, preventive and corrective maintenance strategy weight percentage at

3:7(alternative C, weight value 0.149). This result explains a majority of maintenance work is

focused on preventive maintenance for rolling stock maintenance. It is dangerous to cease railway

system operation for the reason of component failure of rolling stock. It seems that a

preventive-oriented maintenance strategy could probably assure rolling stock safety. In addition,

this study applies questionnaire analysis result of ANP for estimating spare parts of component and

replacement interval.

Figure 4.2 ANP analysis framework and weight value of factors and sub-factors

Rolli

ng s

tock m

ain

tenance s

trate

gy

Cost and Reliability

(0.268)

Maintain rolling stock in good condition (0.176)

Reduced maintenance cost and shut-down time

( 0.092)

Assure rolling stock safety (0.234)

Assure workers and the passengers safety (0.294)

High quality maintenance (0.052)

Increase staff work efficiency (0.048)

Maintain appropriate usable spare parts (0.042)

Reduce rolling stock failure rate (0.062)

Safety

(0.528)

Quality and Efficiency

(0.204)

PM CM=7 3

( 0.607)

PM CM=1 1

(0.244)

PM CM=3 7

(0.149)

4.3 Spare Parts Estimation

Through ANP methodology, railway rolling stocks preventive maintenance and corrective

maintenance ratio is obtained 7 3 and applied to this ratio to estimate needed spare parts quantities

for of Taipei MRTs rolling stock model 321 current collecting shoe. The multiple utility function is

applied to estimate maximum efficiency of spare parts.

Supply shortage possibility

Assumed reliability follows a Poisson distribution. Random 50 current collecting shoes data

provided by Taipei Mass Rapid Transit obtains MTTR at 12.78 months. Therefore, supply shortages

possibility is:

= P r{ x > q } = 1 Pr{ x q }

=

=

q

j

jMTTR

j

MTTRe

0 !

)(1

where is unknown, and !

)(x

exf

x= in a Poisson distribution. Therefore, this study applies

as estimation value for MTTR . It is set MTTR at 12.78 months, we obtain at 0.939 failures/year. With known value, we can obtain supply shortage possibility of individual spare parts quantities. When q = 5, obtained value is 0.00062.

4.3.1 Multiple utility function

Multiple utility function is applied to obtain maximum utility value after the calculation of value.

The multiple utility function is expressed as follows:

U( ,C) = K1U( ) + K2U

= )(]1( 1,1 qCUKeUKMTTR

+

where )))2()( 1 AU =

)))2()( ,CACU =

In current collecting shoe cost estimation, due to various purchase volumes of Taipei Mass Rapid

Transit, current collecting shoe costs vary in the range between NT$2000 and NT$4000. This study

assumes current collecting shoe cost as U.S$10.

A1 and A 2 are variables. This study assumes A1 =16 and A2 =0.002 to obtain maximum utility value.

Because the most suitable strategy derived from ANP result in the first step is to take the ratio

between PM and CM = 7 : 3. We take K1 = 0.7 and K2 = 0.3 to obtain effective value of individual

spare parts. When q=5, the utility value is 0.964

4.3.2 Optimal spare parts estimation

According to the result derived form the multiple utility function, we obtained that when q=5, the

utility value is maximum. Therefore, 5 spare parts need to be prepared. This study follows Almeida

(2001) and assumes a one-to-one facility and spare part composition. Therefore, this study

assumes model 321 of Taipei Mass Rapid Transit adopts the one-to-one car and current collecting

shoe with one rolling stock containing 6 cars. That is, each rolling stock must be equipped with 30

spare parts, 36 rolling stock require 1080 spare parts per year, and 90 spare parts per month on

average.

4.4 Optimal replacement interval

This study examines optimal replacement interval as reference for Taipei Mass Rapid Transit

(MRT) conducting maintenances. Statistical data are obtained from 50 random maintenance record

of past maintenance history of Taipei Mass Rapid Transit. Results found average replacement time

at 12.779 months. This study follows Huang et al. (1995) in assuming preventive and corrective

maintenance cost ratios at 1:15. The cost of corrective maintenance is 15 times more than

preventive maintenance.

4.4.1 Parameter estimation

Random replacement data shows ))](1**(**( xFY = and xX **= and obtains 1 st Weibull

distribution failure function linear equation expressed as Y = 7.50X-19.6. Through this linear

equation, obtained Weibull distribution shape parameter and scale parameter are 7.50 and 13.644 respectively. Huang et al. (1995) apply values of these two parameters to obtain optimal

replacement interval.

4.4.2 Replacement interval calculation

This study follows Huangs et al. (1995) mathematical model = x1+0x0 sTT to obtain MRT 321 type rolling stocks collecting current shoes optimal replacement interval with x0T as optimal

replacement time. The value is estimated from 50 random replacement data. Replacement time xsT is obtained by following Huang et al. (1995) through the value and ratio between corrective and preventive maintenance costs. This study adopts value of 7.50 and ratio between corrective and preventive costs at 15 1. Through estimation graph proposed by Huang et

al. (1995), estimated replacement time xsT is between 5.0 and 6.0. Therefore, optimal

replacement interval is between 6.822 and 8.1864 months.

Conclusion and Suggestion

The purpose of this paper was to present a method for rolling stocks maintenance strategy

selection that allows for the consideration of important interactions among decisions levels and

criteria. The methodology adopts ANP for this evaluation. Consequently, we use the empirical

result derived from ANP to decide the possible ratio between preventive maintenance and

corrective maintenance that can induce the possible spares parts quantities and replacement

interval of component of rolling stock.

The empirical result based on ANP method on maintenance strategy of rolling stock indicates

preventive maintenance should be much more emphasized than corrective maintenance. This

result is consistent with the studies of maintenance strategy on industrial equipments

(Nakagawa,1989, Huang et al. 1995, Chelbi and Ait-Kadi,2001)

According to the empirical result derived from ANP method, safety is the most crucial factor for

rolling stock maintenance strategy selection. Safety here considers not only passenger safety but

also maintenance mechanic agent safety. The second important factor is to keep high availability of

rolling stock for operation to avoid trains idling in the maintenance site. Maintenance cost and

quality is the third factor affecting rolling stock maintenance strategy choice by the experts. This

result exists essential difference between industrial facility and equipment maintenance and rolling

stock maintenance.

This study chooses Taipei MRTs rolling stock component: model 321 current collecting shoes as

an analytical component to estimate spare parts quantities and optimal replacement interval. The

empirical result indicates each rolling stock must be equipped with 30 spare parts. The optimal

replacement interval is between 6.822 and 8.1864 months. The developed method presented in

this study could be useful for railway operator to select its appropriate rolling stock maintenance

strategy and to decide components spare parts quantities and optimal replacement interval.

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