analysis of the effectiveness of shovel-truck mining system.pdf

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Analysis of the effectiveness

of shovel-truck mining systems

S Yuan and R.L. Grayson

Abstract

stochastic model or evaluating the impact

of the reliability and maintainability of shovels and trucks on

the operational effective ness of shovel-truck mining systems

is presented. In the mo del , the Marko v modeling tech nique

is used to analyze the operating status of a sho vel-truck

mining system. Th en , simulation is used to study the produc-

tivity of a shovel-truck system in a particular state. Fina lly,

the relationship between the effectiveness of a shovel-truck

system in terms of productivity and the reliability and main-

tainability of equipment is established. Th is relationship

may be very useful to mine managers in making decisions in

surface mining e . g . , egarding production process control,

equipment replacement, andma intenanceplanning . quan-

titative study is given to demonstrate h ow the reliability and

maintainability of equipment affect the system effectiven ess

and ho w to pinpoint the parameter that has the most signifi-

cant effect on the system effectiveness. The quanrirarivestudy

indicated that in order to improve the system effectiveness

significantly, the reliability and maintainability of the equip -

ment need to be improved simultaneously.

reliability, maintainability and availability were given in a

detailed manner. Case studies were used to study the impacts of

longwall equipment, geological conditions and outby haulage

on system reliability and availability. Topuz and Duan (1991)

applied the reliability concept and Markov modeling to study the

reliability and effectiveness of a continuous mining system.

From an operational point of view, a shovel-truck mining

system in surface mining is more complicated than either a

longwall system or a continuous mining system in under-

ground mining. Even though extensive research work has

been conducted to analyze shovel-truck operations, not much

of the work considers the impact of reliability and maintain-

ability of the shovels and trucks on the productivity of the

system. Therefore, this paper evaluates the effectiveness of

the shovel-truck system in terms of productivity by studying

the relationship between productivity and the reliability and

maintainability of shovels and trucks. The approach and

results may be helpful to mine operators in controlling the

production process, planning equipment maintenance poli-

cies, and for making other possible decisions.

Introduction

Reliability maintainability and system effectiveness

Shovel-truckoperations continue tobe the most popular form

of material handling operations in surface mining since they

often offer many operational advantages. The haulage cost is the

largest component of the operating cost of an open pit mine, in

some cases accounting for about 50 of the operating cost.

From an equipment design point of view, shovel-truckoperating

economics can be improved by increasing the shovel and truck

capacities, or by enhancing equipment reliability and perfor-

mance. From a mining-system design perspective, a good mine

layout, an optimal mining sequence, and utilization of in-pit

crushers with conveyors can also improve operational econom-

ics. A close operational control of shovel-truck operations is

another activity that can result in significant improvements in

system efficiency and productivity. As a matter of fact, exten-

sive studies have been conducted to analyze the effect of various

truck allocation strategies (Kim and Ibarra, 1981; Lizotte and

Bonates, 1987; Luo and Lin, 1988; Tu and Hucka, 1985; White

and Olson, 1986). Another factor that can affect the productivity

of a shovel-truck system is equipment availability. good

maintenance program can increase equipment availability and

so reduce the economic losses associated with unreliability.

Reliability theory has found some applications in mining

engineering. Ramani, Bhattacherjee and Pawlikowski

1

988)

applied the concept of reliability engineering o the evaluation of

longwall system performance. In their paper, definitions of

Reliability is defined as the probability that a piece of

equipment successfully performs its intended function for a

given period of time under specified conditions (Martz and

Waller, 1982). The reliability of a piece of equipment is

usually measured in terms of mean time to failure (MTTF).

which is the expected time during which the equipment will

perform successfully. For a reparable item, mean time to

failure (MTTF) is also known as mean time between failures

(MTBF).

Maintainability is the probability that a system in a failed

state can be restored to its operational state within a specified

time period when maintenance is performed. The maintain-

ability of a piece of equipment is usually measured in terms

of mean time to repair (MTTR), which is the expected time

for the system to be restored.

System effectiveness is defined as the probability that the

system can successfully meet an operational demand within

a given time period when operated under specified conditions

(Martz and Weller, 1982). It can be measured in different

terms such as reliability, availability, or productivity. In this

paper, the system effectiveness is evaluated in terms of

productivity, which means the production of the system in a

time period (for instance, an hour or a shift).

Markov processes

S. Yuan

andR.L.

Grayson

members SME are research associate

A stochastic process is a collection of random variables that

and dean and professorof rniningengineering espectively with the

defined

n the same

probability 'pace

and indexed

by a

Department of Mining Engineering West Virginia University

real ~arameter(He~mannd Sobel, 1982). It is oftendenotedas

Morgantown WV. SME nonrneeting paper 92-324. Manuscript

X(t), t E T

1

where T is a set ofmmben that index the random

Nov. 16 1992. Discussion of this peer-reviewed and approved paper

variables X(t). The index t is often interpreted as time, and X(t)

is invited and must be submitted in duplicate prior to Oct. 31 1995.

is the value or the state of the process at time t.

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A stochastic process {X(t) , E TI is a Markov process or

a Markov chain if, for any positive integer n, time points to 0 and s > 0,

P{X(t+s)= j/X(t) = i ) is independent oft , then the Markov

chain is homogeneous or stationary.

A Markov chain is said to be irreducible if all states

communicate with each other. A state i is said to be positive

recurrent if the probability that, starting in state i, the process

will reenter state i equals one, and the expected time until the

process returns to state i is finite. For an irreducible, positive

recurrent, aperiodic Markov chain, the limiting probability

(Pj),which represents the long-run proportion of time that the

Markov chain is in state j exists.

For a continuous-time Markov chain, the amount of time it

spends in a state before making a transition into a different state

is exponentially distributed. Let v be the rate at which the

process makes a transition when in state

;

let q jbe the rate when

in state i, that the process makes a transition into state

;

and let

pi, be the probability that when in state i, this transition is into

state j. If the process is an irreducible, positive recurrent,

apbriodicMarkov chain, the limiting probability Pj)xists.

From Kolrnogorov's forward equation (Ross, 1989, p. 268):

obtain:

Or, preferably:

This equation shows that the rate at which the process leaves

state j equals the rate at which the process enters state j.

odel development

Operating status of shovel truck systems

In a shovel-truck operating system, equipment is subject to

frequent failure, especially the trucks. Non-availability of the

equipment can cause great production and economic losses. It

has been demonstrated that the times between failures and the

repair times of trucks

are

exponentially distributed. And that

shovel repair times and the times between failures of a shovel

could be represented by exponential distributions as well (Tu

and Hucka, 1985). Therefore, Markov modeling can be used to

analyze the operating status of the system.

The following assumptions are made in the formulation of

the model:

The number of shovels and trucks are M and N respec-

tively.

The time between failures and repair time of a shovel

are exponentially distributed with sh and k h . respec-

tively. Thus:

1

MT F

=

Sh

Ash

where:

MTBFsh s the mean time between failures of a shovel, and

MTTRsh s the mean time to repair a shovel.

Generally, sh and k h are often considered as the failure

rate and the repair rate of a shovel, respectively.

The time between failures and the repair time of each

truck are exponentially distributed with &,and

h

espec-

tively. Similarly,

I

MTTR

=

tr

where:

MTBF,, is the mean time between failures of a truck, and

MTTR, is the mean time to repair a truck.

All the parameters (Ash,kh,

ht

and

hr

are stationary.

That is, they do not change with time. This assumption

may not be true for the entire life cycle of the equipment.

However, it is suitable, at least, for a period of time.

In the assumptions it is assumed that the reliability and

maintainability are identical for each piece of equipment. In

the real world, this is not the situation.

However, if the

average reliability and the average maintainability of a type

of equipment (shovel or truck) are used as the common

reliability and common maintainability for that type of equip-

ment, the assumptions are reasonable for the stochastic

process defined below. That is because the m shovels and n

trucks in a state (m, n) can be any of the M shovels or the N

trucks. These assumptions simplify the model to be devel-

oped next without loss of generality or applicability.

A continuous-time stochastic process can be defined as:

where m and n are the numbers of shovels and trucks

operating or operable in the system, respectively.

From the assumptions it is known that the times between

failures and the repair times of both shovels and trucks are

exponentially distributed. Therefore, the amount of time the

stochastic process spends in a state before making a transition

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pshJ/MAsb

pshlTMAsh

~ . b l / M A s b

N p t r N - a + )C tr N-n)C tr C tr

M,O)

M,n)

.

M,N)

Xtr nXtr a + 1)Xtr NXtr

Fig. 1 tate transition and transition rates

of

the shovel-truck system.

to a different state follows an exponential distribution. Thus,

M k h + (N-n)ktr - nb r ) P(o,n)

this stochastic process is a continuous-time M arkov chain .

Let

v(,,~)

be the rate at which the process makes a

N-n+l)ptrP o,

+

(n+l)htrP(o,+I)

transition w hen in state (m,n), an d let q(,,, ,

) m2,n2)

be the rate

(12)

at which the process m akes a transition into state (m2,n2)

+

hP(l,n)

for n = 1, ..., N-1

when in state (m l n 1). T he state transition and the transition

rates are shown in Fig. 1.

In addition to the mem oryless property , this Markov

( M k h N b r ) P ( ~ , ~ )

ktr

P ( ~ ,-1) hshP( l ,~)

3,

chain ha s the folIowing properties:

All the states of the Markov chain comm unicate. There-

((M-m)kh mhsh N~tr)P(rn,O)

fore, this Markov chain is irreducible.

This is a finite-state Markov chain, and it is aperiodic.

=

( -m+l

)khP(m-l,

0)

(14)

An irreducible, finite-state Markov chain is positive re-

current in the sen se that, starting in any state , the mean time

to return to that state is finite. Thus, this Markov chain is

positive recurrent.

Since this M arkov chain is irreducible, positive recurrent

and aperiodic, the limiting probability that the Markov pro-

cess is in a particular state (m,n) exists. Furthermore, this

limiting probability is independent of the initial state of the

stochastic process. This limiting probability represents the

long-run portion of time that the process will be in state (m,n).

Let

P(,,n)

be the limiting probab ility that the process w iIl be

in state (m,n). From Kolm ogorov's forw ard equation , the

following equation can be obtained:

for k,l) =

(OD),

...,

(M,N)

This gives the following set of equations:

(Mkh Nktr)

P(o,o) hshP(1,o)

+ htrP(0,l)

1 1)

(m+l)hshP(rn+~,) htrP(rn,~)

f o r m = 1, ...,

M-1

M-mIkh

m h h

(N-n)~tr+nhtr)P(rn,n)

= (M-m+l )khP(rn-1 ,n) (m+l)hhP(rn+ln)

+ (N-n+l )~trP(rn,n-l)

+

(n +l )brP(rn,n+~) 15

fo rm

= 1, ...,

M-1; n = 1, . . . , N-1

((M-m)kh

+

m h h Nhtr)P(rn,~)

(M-m+l )khP(rn-1 N)

+

( m + l hhP (rn+l,N ) ~ ~ t r ~ ( r n . ~ - l )

for m = 1, ..., M-1

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low Erlang distributions,and they are identical for each piece

of eaui~ment.

I

17)

The parameters describing the distributions do not

change in the simulation process, that is, the activity times

are stable.

After dumping, a truck will go to a shovel with mini-

mum queueing length.

N-n+l )~trP M,n-1)

n+l

)htrP M,n+l)

l a )

These assumptions are just for this study. If a study is

conducted for a particular mine, the above assumptions are

for

n

=

1 ,

...,

N-1

not necessary and the simulation can be done in accordance

with the actual situations of that mine.

The simulation language SLAM

I

(Simulation Language

Mhsh Nhtr IP M,~)

for Alternative Modeling) (Pritsker, 1986) is used to model

the system. Depicted in Fig. is the SLAM

I

network model

khP M- 1 ,N) PtrP M,N-1)

I)

for routing then entities representing then trucks based on the

assumptions given above. The n entities need to be inserted

The preceding set of equations, along with the following

into the network directly. These entities will continue to

equation:

cycle through the network until the simulation is terminated.

When an entity arrives at the node SELQ, it will select the

MN)

shovel with minimum queueing length for loading. After

P rn.n)

=

20)

completing the loading operation, the entity then undertakes

rn,n)= O,o)

the activities representing hauling, dumping and traveling

can be used to solve for P(,,-,). back, and returns to node SELQ. The global variable XX(1)

keeps the record of the production during the simulation

Unit time productivity

o

the system in specific state

process.

LOAD, HAUL, DUMP, and TRAVEL are at-

tributes of an entity used to specify the Erlang distributions

To determine the unit-time productivity of the system in a

describing loading, hauling, dumping and traveling back

specific state (m,n), we can consider a shovel-truck system

activities. From the production and the simulation time, the

with m shovels and n trucks in the system without break-

unit-time productivity (U(m n)) can be determined.

downs of trucks and/or shovels. For such a system, the basic

activities include loading, hauling, dumping and traveling

Effectiveness

o

the shovel truck system

back. The times for performing these activities can be

described by distributions such as a triangle distribution, a

System effectiveness is a measure of the ability of a

normal distribution, a lognormal distribution, an exponential system to accomplish its objectives. In this paper, the

distribution, an Erlang distribution, or a Weibull distribution, objective is to evaluate the system effectiveness in terms of

depending on the real world situations in the particular mine. productivity, or more specifically, to study the relationship

Theoretically, the system can be described as a cyclic,

between the productivity and the reliability of the equipment

closed queueing network. If the activity times are exponen-

(MTBFshand MTBF,,) and the maintainability of the equip-

tially distributed, the steady state probability can be easily

ment (MTTRshand MTTR,,).

achieved by using the Markovian property. However, in the

For a shovel-truck system with M shovels and N trucks,

real world, the activity times are often not exponentially

the probability the system will be in state (m,n), or the long-

distributed. An Erlang distribution can describe the actual

run portion of time the system will be in state (m,n), is P(,,n).

activity times better than an exponential distribution. If the

The unit-time productivity of the system in state (m,n) is

activity times follow Erlang distributions, the activities can

U(,,.,,. Therefore, the unit-time productivity of the system is:

be treated as if they are camed out in a number of phases

M.N

where the time interval for each phase is exponentially

distributed, and the Markovian property can still be used in

= P rn.n)U rn,n)

rn,n)= O,O)

21

the analysis.

Suppose there

are

no breakdowns of shovels and trucks (i.e.

However, queueing models with Erlang distributed activities

the system is always in state (M,N)), hen the effectivenessof the

suffer from computational difficulties, since the number of states

system is 1. The unit-time productivity of such a system is:

that

describe the system will be huge when the numbers of shovels

and trucks increase. Queueing networks with activity times follow-

S M,N) = U M,N)

22)

ing other distributions are very difficult

to

solve mathematically.

Thus, in general,

the

effectiveness of a shovel-truck system is:

Therefore, a sirnulation technique is used

to study the unit-time productivity of the

system in a particular state (ma)

in

this

study.

The following assumptions are

made in the simulation:

There is enough space at the

dumping points so that there is no

waiting for dumping when a truck

arrives at a dumping point.

Activity times for loading, haul-

ing, dumping and traveling back fol-

Fig. - LAM II network for the system in a state m,n).

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LFT ,,

The relationship between the system effectiveness and

BBT


For a given shovel-truck system, if the activity times are

stable, the system effective ness is a function of the reliability

of equipment (MTBFshand MTBF,,) and the maintain ability

of the equipment (M ITR sh and MTTR,,) .

A quantitative study o system effectiveness

A personal compute r program w as coded to solve the prob-

lem. The main tasks of the program include setting up the

coefficient ma mx and solving the linear system for P ,,n). The

linear system was solved by the Gaussian-elimination method.

The outcom es of simulation (the unit-time productivity of the

system in different states)

are

input to the program an d used to

determine the system effectiveness.

A shovel-truck system with four shov els and 20 trucks is

used for the quantitative example. Figures

3.

4. and 6

illustrate how M ITR sh, MlTR ,,, MTBF sh and MTBF,, will

affect the system effectiveness. These figures are based on

the following conditions:

Figure

3

-The values of MTBF sh, M lTR ,, and MTBF,,

Eb:


ZFB;


are fixed at 90, 5 and 45 hours, respectively.

Figure 4 -The values of MTTR sh, MTBF shand M TBF,,

are fixed at 8 , 9 0 and 45 hours, respectively.

Figure 5 he values of MT TRsh, MTTR,, and MTBF,,

are fixed at 8 , 5 and 45 ho urs, respectively.

Figure 6 -The values of M lT Rs h, MTBFshand MTTRtr

are fixed at 8 ,9 0 and 5 hours, respectively.

From Figs.

3

an d4 , i t can be seen that the system effective-

ness decreases when the mean time to repair the equipment

increases. Figures 5 and 6 indicate that the system effective-

ness increases when the mean time between failures of the

equipment increases.

Figure 7 is based on the data in Table 1. From condition

1 to condition 2 1, MTBF sh and MTBF,, increase, MTTRsh

and MTTR,,decrease, and only one of the param eters changes

each time.

From Fig. 7 and Table

1

note that MlTR ,, and MTBF,,

have a grea ter effect on the system effectiveness thanMTT Rsh

and MTBFsh , espectively. In other words, the reliability and

maintainability of trucks hav e a greater effect on the system

effectivene ss than those of shovels. For example, from

condition

1

to condition 5, M TTR sh, MTB Fsh, M'ITR,, and

MTBF,, increase or decrease by one hour, respective ly, and

the system effectiven ess increases by 0.0057,0.0006 ,0.0129

and 0.0024, respectively. This is partly because MT BFsh s


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SOCIETY FOR MINING. METALLURGY, AND EXPLORATION, INC.

increase of the system effectiveness by 0.0217. Thus, it is

clear that the system effectiveness may not be improved

significantly by only improving the reliability or the main-

tainability of one type of equipment. If both the reliability

and the maintainability of both types of equipment can be

improved simultaneously, the system effectiveness can be

improved significantly.

onclusions

This paper has presented a methodology for analyzing the

system effectiveness of shovel-truck mining systems. By

performing sensitivity analyses, the effect of the reliability

and maintainability of each type of equipment on the system

effectiveness was assessed. The parameter that has the most

onditions

significant effect on the system effectiveness was pinpointed.

The quantitative study suggested that in order to obtain high

Fig 7 he system ef fect i veness under di f ferent

conditions.

system effectiveness, it is necessary to simultaneously im-

prove the reliability and maintainability of the equipment, or

larger than MTBF, and the number of trucks is larger than the

in other words, the quality and efficiency of the maintenance

number of shovels in the system.

program must be improved.

It can also be noted that each time when M-decreases by

The quality and efficiency of the maintenance program

one hour, there is a jump of the system effectiveness. Thus, the

can be enhanced by better planning of equipment mainte-

maintainability of trucks is the most sensitive parameter. Mea-

nance (including better preventive or predictive maintenance

sures should

be

taken to reduce the repair time of trucks.

and better work procedures), by using better trained mechan-

From Fig. it seems that, except for MTTR,,, each of

ics, by better controlling parts inventory, and by utilizing an

the other factors (MTTRsh, MTBFShand MTBF,,) alone

information system to achieve better response time. Basi-

does not have a significant effect on the system effective-

cally, better preventivelpredictive maintenance will increase

ness.

For example, from condition-

5

to condition

9,

the reliability of equipment (MTBFsh and MTBF,,), while

MTTRsh,MTBFSh nd MTBF,, increase or decrease by one

better workforce capability (training level) and response time

hour, and the systemeffectiveness only increases by 0.0061,

will improve the maintainability of equipment

(MTTRsh nd

0.0006 and 0.0020, respectively. However, the combined M ITR,,). Even though some costs will be involved in such

effect of these three parameters (an increase of the system

activities, the increase of system effectiveness will generally

effectiveness of 0.0087) will be non-negligible. Together

result in

a

significant increase of productivity.

with the effect of MTTR,,, the total effect will be an


Table

he

system ef fect i veness under di f ferent conditions

System

Condition MlTR MTBF MlTR MTBF effectiveness

10

80 8 36 0 8093

2 9 80 8 36 0 81 50

3 9 81 8 36 0 8156

4 9 8 7

36 0 8285

5 9

81 7 37 0 8309

6 8

8 7 37 0 8370

7 8 82 7

37 0 8376

8 8 82 6

37 0 8506

9 8 82 6 38 0 8526

10 7

82 6 38 0 8591

7

83 6 38 0 8596

12 7 83 5

38 0 8726

13 7

83 5 39 0 8743

14 6

83 5 39 0 881

15 6

84 5 39 0 881

16 6

84 4 39 0 8947

17 6

84 4 40 0 8960

18 5

84 4 40 0 9032

19 5

85 4 40 0 9037

20 5

85 3 40 0 91 6

21 5

85 3 41 0 91 6

References

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in Operations Research. Volume I, Stochast icProcesses

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and Lin,

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