Application of reliability-centered maintenance for ...

J. Cent. South Univ. (2014) 21: 2372−2382 DOI: 10.1007/s11771-014-2190-2

Application of reliability-centered maintenance for productivity improvement of open pit mining equipment: Case study of Sungun Copper Mine Amin Moniri Morad1, Mohammad Pourgol-Mohammad2, Javad Sattarvand1 1. Department of Mining Engineering, Sahand University of Technology, Tabriz 51335-1996, Iran; 2. Department of Mechanical Engineering, Sahand University of Technology, Tabriz 51335-1996, Iran © Central South University Press and Springer-Verlag Berlin Heidelberg 2014 Abstract: Equipment plays an important role in open pit mining industry and its cost competence at efficient operation and maintenance techniques centered on reliability can lead to significant cost reduction. The application of optimal maintenance process was investigated for minimizing the equipment breakdowns and downtimes in Sungun Copper Mine. It results in the improved efficiency and productivity of the equipment and lowered expenses as well as the increased profit margin. The field operating data of 10 trucks are used to estimate the failure and maintenance profile for each component, and modeling and simulation are accomplished by using reliability block diagram method. Trend analysis was then conducted to select proper probabilistic model for maintenance profile. Then reliability of the system was evaluated and importance of each component was computed by weighted importance measure method. This analysis led to identify the items with critical impact on availability of overall equipment in order to prioritize improvement decisions. Later, the availability of trucks was evaluated using Monte Carlo simulation and it is revealed that the uptime of the trucks is around 11000 h at 12000 operation hours. Finally, uncertainty analysis was performed to account for the uncertainty sources in data and models. Key words: operating costs; maintenance; mining dump truck; reliability; availability; uncertainty

1 Introduction Surface mining stands for major way of raw material production in contemporary mining and have been continuously modernized during last decades by introducing ultra large machinery and highly automated equipment. Trucking is the most conventional and classical method of haulage system in mining industry. In this regards, loading and hauling equipments are considered as the most precious assets of an open pit mine which correspond to the vast amount of capital invested. Similar to all kind of machineries, trucks also need to be carefully preserved under a cautious maintenance program which sometimes contributes as 30% to 50% of the whole haulage costs [1]. Accordingly, the current work was aimed to investigate the maintenance related to the mining trucks using reliability-centered maintenance. Reliability and availability are two suitable metrics for quantitative evaluation of system survival analysis. Reliability is defined as the probability of the system mission implementation without occurrence of failure at a specified time period [2]. In class of statistical methods,

analyzing the reliability is based on the observed failure data and proper statistical techniques [3]. Suitable modeling and interpretation of inter-item relationships are the most important activities in the reliability assessment and improvement of the system performance. Evaluation of the reliability is not singly a right indicator for analyzing of a typical system under the recurrent maintenance. Several types of maintenance could be applied on a system including preventive and corrective maintenance in order to restore it to operational mode. Therefore, this analysis plays an important role in dependability evaluation of repairable items. The availability is the probability that a component operates at an intended mission time. Due to the application of both failure and maintenance downtime data, availability is generally used for measuring performance of the repairable items [4]. This work describes the reliability-centered maintenance analysis process of the mining dump trucks in Sungun Copper Mine. The aim of the research is firstly to decrease trucks’ sudden failures and breakdowns as well as to improve the service lifetime and finally to reduce the maintenance costs. The reliability management (e.g. improvement) decreases the

Received date: 2013−09−02; Accepted date: 2013−12−10 Corresponding author: Mohammad Pourgol-Mohammad, PhD; Tel: +98−4113459422; E-mail: [email protected]

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unexpected failures by estimating the failure time and a suitable maintenance program such as preventive maintenance and inspection enhance the service lifetime and reduce the maintenance costs. The availability analysis investigates the effectiveness of the maintenance policy, though, the mine manager can make the preferred decision about the maintenance policy contrarily. In this work, uncertainty analysis is performed due to the uncertain nature of parameters and lack of sufficient data.

2 Literature review A reliability, availability and maintainability (RAM) program is crucial in an effective maintenance management. This program is used because the failures cannot be prevented entirely; however, well planned maintenance minimizes both probability of failure (increases the reliability) and its impact on the equipment (decreases the equipment breakdown) [5]. The RAM method could be very beneficial in the mining industry because of the complication of the mining equipment operation and maintenance [6]. KUMAR et al [7] investigated the reliability of the load-haul-dump (LHD) machines. The main objective of their research was to analyze failure based on complete and censored data. Their investigation demonstrated that the choice of each approach in utilization of either complete or censored data leads to various directional results. BARABADY and KUMAR [5] studied the reliability and availability of a crushing plant, studied the importance measure to identify the critical sub-systems and highlighted the planning for system reliability improvement. UZGÖREN et al [8] analyzed the mechanical failure data of draglines machine. It is considered as a repairable system and then renewal process approach is applied for statistical modeling of the system. HOSEINIE et al [9] also investigated the reliability of the hydraulic system of drum shearer. Accordingly, the maintenance strategy and proper statistical distribution were selected based on failure behavior of the system. Table 1 summarizes the research articles reviewed in conjunction to the reliability evaluation of different mining equipment and demonstrates the failure process models of the equipment restoration rate after a maintenance operation.

3 Methodology and modeling Methodology and analysis process, as illustrated in Fig. 1, describe the procedure of the model identification and selection of the optimal statistical distribution for analysis of the failure and maintenance data. The study started initially by trend analysis of the truck failure

2373 Table 1 Researches summary in area of reliability of mining industry equipment Reference

Year

[7] [10] [11] [12] [13] [14]

1989 1992 1995 1997 2001 2004

[15]

2005

[16] [5] [17] [18] [19]

2005 2008 2009 2009 2009

[8]

2010

[20]

2011

[9]

2011

Kind of mining equipment Load-Haul-Dump Load-Haul-Dump Hydraulic excavator Load-Haul-Dump Hydraulic shovel Electric haul truck Mining system (reliability allocation) Crushing plant Crushing plant Flexible conveyor backhoe Load-Haul-Dump Dragline’s mechanical failure Electrical system of drum shearer Hydraulic system of drum shearer

Failure process model RP NHPP NHPP RP, NHPP RP, NHPP RP RP RP, NHPP RP, NHPP RP NHPP RP RP RP RP

RP stands for renewal process; NHPP stands for non-homogenous Poisson process

times using graphical method. Basically, trend testing is accomplished using either graphical method [21] (i.e., probability plotting [22−23] and time test on plot [24]) or analytical method [25−26] (i.e., Mann test [27], Laplace test [28] and Military Handbook test [18]). Hence, the repairable and non-repairable items of trucks are identified and the probabilistic failure process methods are distinguished for modeling the maintenance operations. Generally, reliability analysis of the repairable systems is estimated by several assumptions including renewal process (RP), homogenous Poisson process(HPP), non-homogenous Poisson process (NHPP) and generalized renewal process (GRP) [29]. In this work, the RP method is used when the state of the system after the maintenance is “as good as new” which means the age of the system restored to zero. In cases that the system converts to “as bad as old” state, which means the age of system remains unchanged after the maintenance, NHPP is the method of choice whereas, HPP model is applied when the failure intensity is constant and the time between failures follows from the exponential distribution. Hence, the GRP model is assumed to generalize all three presented states for mining trucks. Then, the optimal distribution and its parameters need to be obtained via either parametric or non-parametric approaches. Subsequently, reliability of the system and its components should be evaluated. The availability of the trucks is estimated by using maintenance policy data

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Fig. 1 Flowchart of reliability evaluation

and reliability functions. The Markov chain method is also used to evaluate the performance and availability of some repairable systems [29]. This is a direction for system analysis which is not used in this work.

4 Case study Sungun Copper Deposit is the second largest copper mine in Iran. Geological reserve of the deposit is estimated up to 828 million tons with average copper grade of 0.62%. The mine operation is managed in the mine site by employing a fleet of 52 and 20 Komatsu 32 and 100 ton trucks, respectively, 11 Caterpillar 988 loader, 1 Liebherr 17 cubic meter shovels, 8 Komatsu PC800 excavators and 9 drilling rigs. This work is

limited on the maintenance operation analysis of mine trucks only. 4.1 Data collection Collection of failure data was the first phase in this project. The failure data come from different sources like field data, generic data, test and inspection data. Due to availability of the collected field data, the modeling and analysis are mostly performed by utilization of this field data. The database is composed of operation time, age of the trucks, maintenance data recorded for the truck’s components. The maintenance and operational data were collected in time interval of 2010—2011. The equivalent operation times for a month and a year are approximately considered as 500 and 6000 h, respectively.

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A main obstacle in data collection process was the deficiency of adequate data for the appropriate statistical analyses. There are methods to deal with this situation including expert judgment [30], Bayesian updating method [31], and combination of homogenous data method (similar parts of the equipment). Accordingly, it is assumed that the maintenance data are homogenous in this work. Therefore, the combination of homogenous data technique is applied to deal with the scarcity of data. This method is appropriate for the fleet of equipment or the systems with dominant identical components and similar condition [32]. The assumptions are made in a way that the design, hardware, function, operation conditions, procedures, system structure, location and environment are all similar [18]. Moreover, the age of dump trucks was a major factor for justification of the identical conditions of trucks. Since each system has an intrinsic different failure random behavior at its service lifetime, in this work, 10 dump trucks are chosen with the age of approximately 15000 operation hours. This age is in the region of useful lifetime of trucks. In the useful lifetime, the failure mostly occurs under a systematic process whereas the failure behavior for a new system is based on the infant failure and in older systems, the failure occurs in wear out region. 4.2 Modeling of system The system of dump truck is decomposed to its sub-systems and components in order to analyze the system reliability. Figure 2 demonstrates the hierarchical decomposing of dump truck system into the main subsystems and also further decomposition of each sub-system into its components. The failure mode and effect analysis approach were conducted to assess the significant failure modes for each component [33]. The

Fig. 2 Decomposion of dump truck system

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reliability block diagram was developed for the system based on its structure. Due to the design configuration of the truck system, the operations of considered subsystems were required for mission success of the dump truck. Therefore, the weakest link model was found a proper model for this purpose. 4.3 Trend analysis Non-parametric methods are alternatives for analysis of the failure and repair data trend. This analysis provides a curve of the mean cumulative function for mean number of failure at specified time against service lifetime to illustrate the trend of failure data during total period [34]. If the failure data plot results a straight line, it is concluded that there is no trend. Based on this analysis, each unit is composed of a staircase function that demonstrates the cumulative number of failures for a particular event. Finally, regression of the generated points describes the trend procedure. Also, assembly of units generates a set of staircase curve of each unit in the population, so that the mean cumulative number of failures is estimated. The serial correlation test is used for studying the independence of the failure data. Serial correlation plot is based on i-th lifetime failure against (i−1)-th one. If only one cluster of points is generated then no trend is observed. The trend exists if two or more clusters, or a straight line is generated [18]. Probability plot is used for estimating the statistical distribution parameters when the failure data follow IID condition whereas the GRP method is used whenever the failure data demonstrate a trend. The testing trend and serial correlation for braking sub-system shows that the IID condition is obtained as shown Fig. 3 and Fig. 4, respectively.

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Fig. 3 Testing trend for braking component

Fig. 4 Testing serial correlation for braking component

4.4 Estimation of statistical parameters As shown in the process (Fig. 1), reliability analysis of selected distributions requires estimation of statistical parameters. In this work, probabilistic distributions of the components are selected based on repairable and non-repairable situations. The distribution parameters are estimated according to GRP model and ordinarily distributions. 4.4.1 Repairable items The trend test is used for performance analysis of the repairable items to identify the failure behavior. The trend analysis of failure data leads to determination of rate of occurrence. It also determines whether the part has increasing failure intensity (IFI) or decreasing failure intensity (DFI). If the intensity function decreases, the system is improving whereas the increasing intensity function leads to deterioration of the system. According to flowchart process exhibited in Fig. 1, the parameters of failure probabilistic distribution of repairable items are computed using GRP technique. GRP model is selected because of its capability to consider the imperfect

maintenance data in truck items. Therefore, the TBF data are collected as the input parameter of the PLP model to estimate the statistical parameters. Weibull++8 software is used as the computation tool for the calculations in this work. It is assumed here that the maintenance is imperfect in determining system behavior after a maintenance task on the system components. The restoration rate is estimated for the components after a repair task whose value is specified in range of 0 to 1, where restoration value 0 means no improvement in component status after repair and restoration value 1 is perfect repair making unit as good as new. In this approach the assumptions are more realistic in comparison with traditional methods discussed above which they only consider either minimal repair state (NHPP) or perfect repair state. However, a main challenge in the method is to estimate the restoration rate of item after completion of a maintenance task. It leads to the consider ation of the uncertainties of model for assessment of confidence level in estimation process. Accordingly, two types of maintenance is considered for corrective maintenance activities which are called Types I and II. Type I model assumes that the repairs can remove some portion of the damage which has accumulated since the last repair. In other words, the age of the components after the m-th maintenance immediately return to the age of the (m−1) maintenance considering coefficient of maintenance effectiveness. The model Type II assumes that the repairs can remove a portion of all damage that has accumulated since the system was new. The models of Types I and II are used for calculation respectively as follows:

vi  vi 1  qX i

(1)

vi  q(vi 1  X i )

(2)

where vi is the virtual age after i-th maintenance, Xi is the TBFs, q is the parameter of the virtual age (the range is between 0 and 1) and q=1−FR where FR is restoration factor. A general parametric method for solving the GRP model is the power law process. This process is able to model the failure intensity for repairable systems. The occurrence of the first failure follows Weibull distribution method which is defined as

 (t )      t  1

(3)

1

v  1/ 



(4)

where λ(t) is intensity function, λ is PLP parameter, β is Weibull parameter. In this work, the Monte Carlo simulation and MLE

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method are combined for estimation of the PLP statistical parameters. Monte Carlo simulation is utilized here for supplying data set of failure times in order to compute virtual age. This process implemented by generating random variables from conditional PDF for component’s failure time. Random variables sampling is accomplished in conditional CDF plot. It is assumed that the time to first failure fitted on Weibull distribution. Therefore, the conditional PDF and CDF are defined as f (ti ti 1 )   ( X i  vi 1 )  1 exp{[( X i  vi 1 )   vi1 ]} (5) F (ti vi 1 )  1  exp{[( X i  vi 1 )   vi1 ]}

(6)

where f (ti t i 1 ) is the conditional PDF, F (ti vi 1 ) is the conditional CDF, ti is successive failure times i

(ti   X j ),

vi 1 is the virtual age after (i-1)-th

j 1

maintenance. In the next step, the PLP parameters (λ, β and q) are estimated by MLE method. The maximum likelihood estimation function is formulated for the problem in Eq. (7) [35]. To solve the equation, the Newton search method is applied to maximize the MLE function. According to this method, at each iteration, the type of maintenance (Types I and II) is chosen by likelihood value so that the lower LK estimates are selected for this process. 



ln L  n(ln   ln  )  [(T  t n  vn )  vn ]  n

n

i 1

i 1

  [( X i  vi 1 )   vi ]  (   1) ln( X i  vi 1 ) (7) where T=tn, if the observation stops right after the last occurrence; L is MLE function; n is the whole number of occurrences during observation period; T is stop time of the observation; vn is virtual age after n-th maintenance. 4.4.2 Non-repairable items The probability plot is provided to assess the reliability of non-repairable items. The plot is a technique for testing goodness of fit of data to a distribution. As shown in Fig. 1, the RP technique is accomplished when the identical and independent distribution conditions are valid for the dump truck items. Initially, the TBF data are obtained and a suitable statistical distribution is fitted for each failure data set of items. The goodness of fit method is used for choosing optimal distribution. This method studies the problem of determining whether a sample belongs to a hypothesized theoretical distribution. Kolmogorov-Smirnov test [29] is performed as a proper procedure for this method. Results of statistical estimations of each component (repairable and non-repairable items) are given in Table 2.

According to Table 2, while dealing with heavily censored data (CND), the likelihood value was used to select the better fitness of data and right model. The likelihood function of censored data is obtained by Eq. (8). For complete data (CMD), the rank regression on X axis is used. The rank regression method is based on the plotting position of the time to failure data. The ρ value indicates the correlation coefficient of the RRX method. Hence, the selected distribution for each component is validated. In this table, the time to repair is calculated by appropriate distributions and goodness of fit method (K-S test). The restoration factors (RF) for Type I and Type II are considered as 0.30 and 0.70, respectively. The type of maintenance is selected based on the LK value. The parameters of PLP method are estimated via the Monte Carlo simulation. Results of Table 2 endorse the trend test outcomes. Thus, when the failure intensity of the repairable items decreases, the β parameter of the Weibull distribution in PLP model is less than 1.0 and it shows the decrease in failure intensity. For β>1, the increase in failure intensity occurs while β>2 indicates that the components are in wearing region. Results of this table (distributions and quantity of parameters) are used for reliability analysis of the dump truck sub-systems. n

m

i 1

j 1



L   f (Ti ; x1 , x2 ,  , xk )   1  F ( S j ; x1 , x2 ,  , xk )



(8) where f(Ti; x1, x2, …, xk) is PDF, n is the number of failures, Ti is the i-th failure time, xk is statistical parameters, F(Sj; x1, x2, …, xk) is CDF, Sj is the j-th time to suspension of data. 4.5 Reliability analysis The reliability of dump truck system and its sub-systems are temporarily estimated by selection of optimal fitted distribution and by considering their estimated parameters (Table 3). According to Table 3, the transmission is concluded to be the most unreliable sub-system and the Frame and body as the most reliable sub-systems (reliabilities for two sub-systems at 3000 operation hours are 3×10−6 and 0.36, respectively) in comparison to other sub-systems’ reliability. Figure 5 indicates the reliability values of the dump truck system and its sub-systems during 3000 operation hours. 4.6 Importance measure T h e i mp o r ta n c e me a s u r e is a me a n s f o r identification of the most critical items. By ranking of the items based on their reliability importance, prioritizing policy is planned in a way that the weakest items from reliability point of view are improved. Importance measure I Ri (t ) is defined as probability that

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2378 Table 2 Results of statistical analyses for each dump truck component Modeling maintenance Kind of Features FR/% maintenance

TBF estimation LK Optimal ρ/% value fit

TTR estimation Parameters Optimal fit estimation

Component

Trend

Engine body

IFI

GRP

Type I

70

N/A

N/A −81.8

PLP

β=2.87 η=10887

N-2P

M=14.1 S=7.45

Fuel

IID

RP

CMD RRX

N/A

0.326

99.3 −338.2

W-2P

β=1.47 η=3237

L-N-2P

ML=0.99 SL=0.47

Lubrication

IID

RP

CND MLE

N/A

0.0002 N/A −34.8 EXP-1P

M=39661

EXP-2P

M=1.16 G=1.24

Radiator & Cab

IID

RP

CMD RRX

N/A

0.010

98.4 −257

L-N-2P

ML=7.81 SL=0.98

L-N-2P

ML=1.1 SL=0.66

Fan & Pulley

IFI

GRP

Type I

70

N/A

N/A −73.4

PLP

β=2.20 η=12463

L-N-2P

ML=1.63 SL=0.42

Intake & Exhaust

IID

RP

CMD RRX

N/A

2.47

98.6 −252.4

W-2P

β=1.29 η=3411

L-N-2P

ML=1.03 SL =0.56

Clutch

IFI

GRP

Type II

30

N/A

N/A −34.4

PLP

β=1.84 η=22171

EXP-2P

M=4.38 G=0.84

Gear box

DFI

GRP

Type I

30

N/A

N/A −55.5

PLP

β=0.98 η=24384

W-2P

β=1.01 η=15.35

Connections & Bearing

IID

RP

CMD RRX

N/A

1.04

99.5 −351.8

W-2P

β=1.58 η=3139

W-2P

β=1.82 η=4.49

Universal joint

IID

RP

CND MLE

N/A

0.04

N/A −80.3

W-2P

β=1.87 η=9903

N-2P

M=2.35 S=1.08

Differential

DFI

GRP

Type I

70

N/A

N/A −64.8

PLP

β=0.64 η=28483

W-3P

Wheels

IID

RP

CMD RRX

N/A

1.81

98.6 −398.9

W-2P

β=1.70 η=2735

W-2P

Steering

IID

RP

CND MLE

N/A

0.001

N/A −189.6 L-N-2P

ML=8.35 SL=0.77

W-2P

β=1.61 η=0.68

Braking

IID

RP

CMD RRX

N/A

0.78

99.4 −416.6 L-N-2P

ML=7.54 SL=0.78

L-N-2P

ML=1.06 SL=0.52

Hydraulics

IFI

GRP

Type II

30

N/A

N/A −395.5

β=2.41 Η=4949

W-2P

β=1.6 η=2.54

Starter

IID

RP

CND MLE

N/A

0.00001 N/A −23.3 L-N-2P

ML=10.74 SL=1.86

L-N-2P

ML=1.55 SL=0.37

Cables

IID

RP

CND MLE

N/A

0.00002 N/A −43.7 L-N-2P

ML=9.70 SL=1.55

N-2P

M=3.49 S=0.68

Battery

IID

RP

CND MLE

N/A

0.001

N/A

EXP-1P

M=12376

EXP-1P

M=1.26

Lights

IID

RP

CND MLE

N/A

0.37

N/A −223.8 EXP-1P

M=2840

N-2P

M=0.95 S=0.24

Alternator (Dynamo)

IID

RP

CND MLE

N/A

W-2P

β=1.19 η=10903

W-2P

β=0.79 η=1.01

Related electrical items

IID

RP

CND MLE

N/A

0.002

N/A −34.5

N-2P

M=5360 S=2485

EXP-1P

M=2.10

Tiers

IFI

GRP

Type I

70

N/A

N/A −396.6

PLP

β=1.55 η=3862

L-N-2P

ML=0.98 SL=0.34

Shock absorber

IID

RP

CND MLE

N/A

N/A

N/A −142.8 L-N-2P

ML=8.36 SL=0.82

N-2P

M=2.63 S=1.30

Frame and body

IID

RP

CMD RRX

N/A

0.004 −99.2 −38

M=4000

EXP-2P

M =4.57 G=2.37

K-S test/%

−73

0.00001 N/A −61.9

PLP

EXP-1P

Parameters estimation

β=0.58 η=1.06 0 85 β=1.67 η=5.76

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Table 3 Analyzing reliabiltiy of all sub-systems and dump truck system at various times Sub-systems Engine Transmission Hydraulics Electrical time/h

Frame and Body

Tires

Dump truck system

0

1

1

1

1

1

1

1

50

0.888

0.823

0.871

0.919

0.983

0.955

0.549

100

0.788

0.676

0.759

0.845

0.966

0.911

0.301

200

0.621

0.456

0.575

0.713

0.933

0.83

0.09

500

0.301

0.139

0.247

0.429

0.842

0.625

0.0023

1000

0.088

0.018

0.058

0.183

0.71

0.387

5×10−6

0.0001

0.006

0.36

0.051

1.75×10−17

3000

0.0005

3×10

−6

Fig. 5 Reliability values for each sub-system and dump truck system

component i is critical to system failure and is calculated by I Ri (t )  Rs (t ) / Ri (t )

(9)

where Rs is reliability of the system, Ri is reliability of the component i. The analysis reveals that the transmission system is identified as the most critical sub-system. Also, the reliability importance measure reveals that the wheels are the most important among the transmission components. The reliability importance value for the wheel component was calculated as 0.31 at 500 operation hours. This value is a relative importance of an individual item in comparison with total reliability of truck system at a specific time. Importance measures are shown in Fig. 6, for all of the transmission components. 4.7 Availability assessment Availability is a better metric for performance analysis of the maintainable equipment. The availability of the truck system is a function of the sub-systems and component’s reliability and maintenance portfolio. The input data for calculating availability are reliability distribution functions and maintenance policy for a specified time period. Monte Carlo simulation is utilized

Fig. 6 Measuring reliabiltity importance for all of transmision components at 500 operation hours

for modeling the failure behavior under the maintenance activities. The maintenance policies for simulation process include time to repair (for all kinds of maintenances), delay time for fault detection and diagnosis and also logistic delay times which consists of the required time for providing spare parts and delay time before the crews start the tasks. Due to limitation of paper pages, maintenance tasks of wheels is only provided in Table 4. For further details, the reader can refer to Ref. [33]. The mean availability is estimated as 91.8% at 12000 operation hours from simulation. Some of the simulation results are given in Table 5. The value of downtime is shown in Fig. 7, for each component at 12000 operation hours. As it is illustrated, the tires have the highest contribution to the unavailability of the system and shock absorber is found as the most reliable component. 4.8 Uncertainty Uncertainty ranges are derived for the problem for demonstration of the confidence on the obtained results. There are various input and model uncertainty sources in

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2380 Table 4 Maintenance policy for wheels component Corrective maintenance Time Spare part’s duration/h delay/min

W-2P, β=1.67, η=5.76

N-2P, μ=60, δ=30

Preventive maintenance

Crew’s delay & failure diagnosis/min N-2P, μ=50, δ=10

Task

Final drive oil change

Inspection

Time Crew’s Spare part’s Interval/h duration/ delay/min delay/min min

2000

N-2P, μ=30, δ=10

N-2P, μ=10, δ=5

N-2P, μ=15, δ=5

Task

Interval/ Crew’s h delay/min

Final drive oil inspection

250

Wheel’s inspection

100

N-2P, μ=15, δ=5 N-2P, μ=35, δ=10

Table 5 Simulation results for estimating availability features Feature

Value

Feature

Value

Mean availability (All events)/%

91.84

Uptime/h

11021

Point availability (All events) at 12000 hours/%

93.5

Corrective maintenance downtime/h

766

Mean availability (w/o PM & Inspection)/%

93.61

Inspection downtime/h

133

Mean time to first failure/h

95.37

Preventive maintenance downtime/h

80

Fig. 7 Downtime for each component

the calculations and results. It includes approximations, assumptions, sampling errors, selecting probability distribution functions, models for estimation of statistical parameters and simulation process. Methods for estimation of input uncertainty include maximum likelihood estimation, Bayesian, maximum entropy. Propagation of uncertainty also affects the results. Several methods exist for uncertainty propagation including Monte Carlo simulation, response surface method, method of moments and bootstrap sampling [29]. Monte Carlo simulation is used here for propagation of uncertainties. This method is designed based on probabilistic models and statistical sampling. Monte Carlo method procedure is composed of sampling from CDF of each xi parameter that is involved in availability estimation (reliability distribution functions and

maintenance policies). Random variable sampling is designed for variables with considering the dependency among them if significantly available. This process is repeated for sufficient sample size to estimate availability values. A typical sampling for k elements in n iterations for estimating of availability function is given by

 x11 , x12 , , x1k  A(t )1   x12 , x22 , , xk2  A(t ) 2     x n , x n , , x n  A(t ) n k  1 2

(10)

where xkn is k-th parameter in n-th iteration, and A(t) is the availability value. Confidence intervals method is utilized for

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presenting uncertainty of the estimated results. In this method, a boundary with acceptable confidence level is associated with the estimated response variable. The confidence bounds are calculated by Fisher Matrix approach on censored data [36]. According to this method, the mean and variance of the availability function is determined. Maximum likelihood estimation is used for point estimation of statistical parameters. Determination of variance and covariance of the MLE parameters matrix is obtained by the inverse of Fisher Matrix: cov( x1 , x2 )  cov( x1 , xi )   var( x1 ) cov( x , x ) var( x2 )  cov( x2 , xi ) 1 2   F 1         var( xi )   cov( x1 , xi ) cov( x2 , xi ) 

 2 Λ  2  x1  2 Λ   x x  1 2    2 Λ   x1 xi

(11)

1

2 Λ    x1 xi  2 Λ   1  (12) F x2 xi  x22     2 Λ 2 Λ    x2 xi xi2  where xi is the statistical parameters, F−1 is inverse of the Fisher Matrix, Λ is the log-likelihood function. The upper and lower intervals for mean availability values at 12000 operation hours by using Monte Carlo simulation uncertainty propagation method with considering 500 iterations and confidence interval 95% are given in Fig. 8. 2 Λ x1 x2 2 Λ

centered maintenance is evaluated for the Komatsu mining trucks at the Sungun Copper Mine. The analysis process is comprised for both repairable and nonrepairable items. The reliability analysis is implemented for each sub-system at various mission time. The probabilistic failure process modeling is performed for repairable and non-repairable items using the GRP and RP methods, respectively. The importance measure analysis indicates that the wheels are the most critical component. Later, the analysis based on the availability indicates that the mean availability of the dump truck is 91.8% at 12000 operation hours. The uncertainty analysis is done to find the confidence interval of the estimated equipment reliability and availability. Research findings are provided to the maintenance management team for planning better decisions about the maintenance operation, condition monitoring of the critical items, inventory of the spare parts and their re-order level which leads to reduction in the equipment downtime. This leads to an improvement of the equipment productivity and reduction of the operating costs. The future researches are planned about maintenance optimization and preventive maintenance intervals.

Acknowledgment Authors wish to appreciate the support of the Maintenance Department of Mobin Co. and Sungun Copper mine.

Nomenclature and abbreviations CMD

Complete data

CND

Censored data

CDF

Cumulative distribution function

DFI

Decreasing failure intensity

EXP

Exponential

GRP

Generalized renewal process

IFI

Increasing failure intensity

IID

Identical and independent distribution

K-S Test Kolmogorov-Smirnov test

Fig. 8 Boundary intervals for mean availability function at 12000 operation hours

5 Conclusions The RAM analyses are essential in the maintenance of the heavy machinery as productivity of the equipment strongly depends on it. In this work, the reliability-

LK

Likelihood value

ML

Log-mean

NL

Log-normal

SL

Log-standard deviation

M

Mean

MLE

Maximum likelihood estimation

NHPP

Non-homogenous Poisson process

N-2P

Normal-2 parameters

PLP

Power law process

PDF

Probability density function

RAM

Reliability, availability and maintainability

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RF

Restoration factor

RP

Renewal process

RRX

Rank regression on x

S

Standard deviation

TBF

Time between failures

TTR

Time to repair

W-2P

Weibull-2 parameters



Correlation coefficient

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