DOC TOR A L T H E S I S
Department of Civil, Environmental and Natural Resources Engineering
Division of Operation, Maintenance and Acoustics
Reliability and Life Cycle Cost Modelling
of Mining Drilling Rigs
Hussan Saed Hamodi Al-Chalabi
ISSN 1402-1544 ISBN 978-91-7583-043-8 (print)
ISBN 978-91-7583-044-5 (pdf) Luleå University of Technology 2014
Hussan Saed Hamodi Al-Chalabi Reliability and Life Cycle Cost Modelling of Mining Dr illing Rigs
ISSN: 1402-1544 ISBN
978-91-7583-XXX-XSe i listan och fyll i siffror där kryssen är
Reliability and Life Cycle Cost Modelling of Mining Drilling Rigs
Hussan Saed Hamodi Al-Chalabi
Division of Operation, Maintenance and Acoustics Luleå University of Technology
SE -- 971 87
Sweden
Printed by Luleå University of Technology, Graphic Production 2014 ISSN 1402-1544
ISBN 978-91-7583-043-8 (print) ISBN 978-91-7583-044-5 (pdf) Luleå 2014
www.ltu.se
Dedicated
to my parents, Khalida and Saed,
to my family, Amani, Abdulmalek and Yaman,
for allowing me to be part of their life and love.
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ACKNOWLEDGMENTS
The research work presented in this thesis has been carried out during the period 2011 to 2014 at the Division of Operation, Maintenance and Acoustics at Luleå University of Technology (LTU). The research programme was financed by Atlas Copco, Boliden Mineral AB and LTU.
First of all, I would like to express my deepest gratitude to my main supervisor, Professor Jan Lundberg, who has enriched my knowledge through stimulating discussions and fruitful guidance. You have always believed in me and shown a positive attitude.
I would like to express my sincere gratitude to Alireza Ahmadi and Behzad Ghodrati, my co- supervisors, for their invaluable guidance, suggestions and support.
My sincerest gratitude is extended to Professor Uday Kumar, Head of the Division of Operation, Maintenance and Acoustics at LTU, for providing me with the opportunity to pursue my research at the Division of Operation and Maintenance Engineering.
I would like to express my sincere gratitude to the Iraqi Ministry of Higher Education and Scientific Research for providing a scholarship which made it possible for me to pursue doctoral research at LTU.
I am grateful to all the group members in the drilling rig project for their valuable time in meetings, sharing their experiences and suggestions for design improvement. Specific gratitude is extended to Arne Vesterberg, Tommy Öhman, Curt Lindblad, Mats Johansson, Mikael Anderson, Lars Karlsson, Andreas Nordbrandt, Ulf Sundberg and Jesus Retuerto for sharing their expertise.
I would like sincerely and gratefully to acknowledge my colleagues (present and past) at the Division of Operation, Maintenance and Acoustics for providing a friendly and open-minded working environment. Special thanks are due to Malin Shooks, Rajiv Dandotiya, Mustafa Aljumaili, Christer Stenström, Stephen Famurewa, Yasser Ahmed and Yamur Aldouri for their discussions. Gratitude is also extended to my friend Hassan Ali. The administrative support from Cecilia Glover and Marie Jakobsson is also gratefully acknowledged.
I wish to express my sincere gratitude to my dearest parents, Saed and Khalida, who have always offered their full support throughout my life and who taught me the meaning of life.
Gratitude is extended to my siblings too. I am really thankful for all the support given to me.
Finally, I would like to express my deepest gratitude to my loving wife, Amani, and our beloved sons, Abdulmalek and Yaman, for their enormous understanding and endless support during my studies and research. It would not have been possible to complete this journey without you by my side.
Hussan Saed Hamodi Al-Chalabi December, 2014
Luleå, Sweden
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ABSTRACT
In the context of mining, drilling is the process of making holes in the face and walls of underground mine rooms, to prepare those rooms for the subsequent operation, which is the charging process. Due to the nature of the task, drilling incurs a high number of drilling rig failures. Through a combination of a harsh environment (characterised by dust, high humidity, etc.), the operating context, and reliability and maintainability issues, drilling rigs are identified as a major contributor to unplanned downtime.
The purpose of the research performed for this thesis has been to develop methods that can be used to identify the problems affecting drilling rig downtime and to identify the economic lifetime of drilling rigs. New models have been developed for calculating the optimum replacement time of drilling rigs. These models can also be used for other machines which have repairable or replaceable components. Based on an analysis performed in a case study, a life cycle cost (LCC) optimization model has been developed, taking the most important factors affecting the economic replacement time of drilling rigs into consideration. To this end, research literature studies and case studies have been performed, interviews have been held, observations have been made and data have been collected. For the data analysis, theories and methodologies within reliability, maintainability, ergonomics and optimization have been combined with the best practices from the related industries.
Firstly, this thesis analyses the downtime of the studied drilling rigs, with the precision and uncertainty of the estimation at a given confidence level, along with the factors influencing the failures. Secondly, the thesis identifies components that significantly contribute to the downtime and the reason for that downtime (maintainability and/or reliability problems).
Based on the failure analysis, some minor suggestions have been made as to how to improve the critical components of the drilling rig. Thirdly, a new method is proposed that can help decision makers to identify the replacement time of reparable equipment from an economic point of view. Finally, the thesis proposes a method using the artificial neural network (ANN) for predicting the economic lifetime of drilling rigs through a series of basic weights and response functions. This ANN-based method can be made available to engineers without the use of complicated software.
Most of the results are related to specific industrial and scientific challenges, such as planning for cost-effectiveness. The results of the case study are promising for the possibility of making a significant reduction in the LCC by optimizing the lifetime. The results have been verified through interaction with experienced practitioners from both the manufacturer and the mining company using the drilling rig in question.
Keywords: Cost-optimization; Decision making; Drilling rig; Economic model; Life cycle cost analysis; Mining industry; Optimal replacement time; Reliability analysis; Replacement decision; Underground mining rig
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SAMMANFATTNING
Borrning är den process inom gruvdrift som åstadkommer hål i berg för att förbereda för laddning och sprängning. Denna process innebär hård belastning på de borriggar som utför borrningarna, vilket resulterar i oplanerade och kostsamma driftstopp. Dessa driftstopp beror bland annat på damm och hög luftfuktighet, handhavande, samt borriggarnas inbyggda funktionssäkerhet och underhållsmässighet.
Huvudsyftet med detta forskningsprojekt är att utveckla metoder att beräkna ekonomisk livslängd för borriggar i gruvmiljö. Dessa metoder skall även lämpa sig för beräkning av ekonomisk livslängd av andra typer av maskiner som består av utbytbara eller reparabla komponenter. Därvid har en livscykelkostnadsmodell tagits fram baserat på en fallstudie, där de viktigaste maskinpåverkande faktorerna tagits i beaktande. För att kunna utveckla dessa metoder och denna modell har litteraturstudier, fallstudier, intervjuer, observationer, datainsamlingar och modellering genomförts. Den så utvecklade modellen baseras på rådande teorier och metoder inom driftsäkerhet, underhållsmässighet, ergonomi och optimering för industriella applikationer.
De komponenter som väsentligt bidrar till driftstopp med avseende på funktionssäkerhet och underhållsmässighet har kartlagts. Baserat på analys av tillgänglighet, ges också några förslag på hur dessa kritiska komponenter kan förbättras. Slutligen föreslås en metod för att förutsäga den ekonomiska livslängden hos borriggar, genom användning av så kallad viktning, och utan krav på komplicerad programvara.
Resultaten är i första hand relaterade till industriella applikationer och förväntas hjälpa beslutsfattare att ta kostnadseffektiva beslut. Resultaten från fallstudien gör det också möjligt att uppnå betydande besparingar genom optimering av livslängden på borriggar. Resultaten har verifierats genom kontinuerlig interaktion med både tillverkare av borriggar och gruvbolag. Ur vetenskaplig synvinkel har också kunskapen ökats beträffande kritiska komponenters tillförlitlighet.
Nyckelord: Optimering av kostnad; beslutsfattande; borrigg; borrmaskin; ekonomisk modell;
livscykelkostnadsanalys; gruvindustri; livslängd; tillförlitlighet; tillgänglighet; funktionssäkerhet;
underhållsmässighet; underjordsbrytning
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LIST OF APPENDED PAPERS
Paper I
Al-Chalabi, H., Lundberg, J., Wijaya, A. and Ghodrati, B. (2014), ‘‘Downtime analysis of drilling machines and suggestions for improvements’’, published in the Journal of Quality in Maintenance Engineering, 20(4), 306-332.
http://dx.doi.org/10.1108/JQME-11-2012-0038
Paper II
Al-Chalabi, H., Lundberg, J., Jonsson, A. and Ahmadi, A. (2014), ‘‘Case Study: Model for economic lifetime of drilling machines in the Swedish mining industry’’, published in the Engineering Economist.
http://dx.doi.org/10.1080/0013791X.2014.952466
Paper III
Al-Chalabi, H., Ahmadzadeh, F., Lundberg, J. and Ghodrati, B. (2014), ‘‘Economic lifetime prediction of a mining drilling machine using artificial neural network’’, published in the International Journal of Mining, Reclamation and Environment, 28(5), 311-322.
http://dx.doi.org/10.1080/17480930.2014.942519
Paper IV
Al-Chalabi, H., Lundberg, J., Al-Gburi, M., Ahmadi, A. and Ghodrati, B. (2014), ‘‘Model for economic replacement time of mining production rigs including redundant rig costs’’, submitted for publication in the Journal of Quality in Maintenance Engineering.
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DISTRIBUTION OF WORK
The content of this section has been shared and accepted by all the authors who have contributed to the papers. The contributions of each named author to the scientific papers
included in this thesis can be divided into the following main activities:
1. formulating the fundamental ideas of the study (initial idea and model development);
2. performing the study (data collection and analysis);
3. writing the paper and analysing the results;
4. revision of important intellectual content;
5. final approval for inclusion in the PhD thesis.
Table 1. Contributions of the main authors and co-authors of the appended papers
Paper I Paper II Paper III Paper IV
Hussan Al-Chalabi 1, 2, 3 1, 2, 3 1, 2, 3 1, 2, 3 Jan Lundberg 1, 4, 5 1, 4, 5 1, 4, 5 1, 4, 5
Alireza Ahmadi 4 4 4
Behzad Ghodrati 4 4 4 4
Andi Wijaya 4
Adam Jonsson 1, 4
Majid Al-Gburi 2 2
Farzaneh Ahmadzadeh 3
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ABBREVIATIONS
ANN Artificial neural network BPP Branching Poisson process
CMMS Computerised maintenance management system DFR Design for reliability
DMC Decreasing maintenance cost (%) DOC Decreasing operating cost (%) DRC Decreasing redundant rig cost (%) ERT Economic replacement time (months) GSI Geological strength index
GUI Graphical user interface HME Heavy mobile equipment IAC Increasing acquisition cost (%)
IFPP Increasing factor of the purchase price (%) iid Independent and identically distributed IPP Increasing purchase price (%)
K-S Kolmogorov-Smirnov test
LCC Life cycle cost MC Maintenance cost (cu)
NHPP Non-homogenous Poisson process OC Operating cost (cu)
ORT Optimal replacement time (months) PP Purchase price (cu)
RFMC Reduction factor of the maintenance cost (%) RFOC Reduction factor of the operating cost (%) TBF Time between failures (h)
TOC Total ownership cost (cu)
TOCvalue Total ownership cost value (cu)
TTF Time to failures (h) TTR Time to repairs (h)
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NOTATION
α Significant level cu Currency unit
µx Mean time to repair (h) µy Mean time to failure (h) DTLL Lower limit of downtime (h) DTM Mean downtime (h) DTUL Upper limit of downtime (h) TTRLL Time to repair lower limit (h) MTTR Mean time to repair (h) TTRUL Upper limit of time to repair (h) mLL Lower limit of number of failures mM Mean number of failures
mUL Upper limit of number of failures cu/h Currency unit per hour
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TABLE OF CONTENTS
ACKNOWLEDGMENTS ... V ABSTRACT ... VII SAMMANFATTNING ... IX LIST OF APPENDED PAPERS ... XI DISTRIBUTION OF WORK ... XIII ABBREVIATIONS ... XV NOTATION ... XVII
1 INTRODUCTION ... 1
1.1 Background ... 1
1.1.1 Mining drilling rig ... 2
1.1.2 Reliability literature review ... 3
1.1.3 Optimal replacement time literature review ... 4
1.2 Basic concepts and definitions ... 5
1.2.1 System reliability and performance ... 5
1.2.2 System availability ... 5
1.2.3 System maintainability ... 6
1.2.4 System life cycle costing ... 6
1.2.5 Life cycle costing fundamentals ... 7
1.3 Industrial motivation of the study ... 8
2 THE APPROACH OF THE THESIS ... 11
2.1 Research problem description ... 11
2.2 Overall research goal ... 11
2.3 Research questions... 12
2.4 Scope and limitations of the study ... 12
3 RESEARCH METHODS ... 15
3.1 Data collection and analysis ... 15
3.1.1 Research objects ... 18
3.1.2 Failure and cost data... 18
3.2 Method used in Paper I... 21
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3.3 Method used in Papers II-IV ... 21 4 SUMMARY OF APPENDED PAPERS ... 23 4.1 Paper I ... 23 4.2 Paper II ... 23 4.3 Paper III ... 24 4.4 Paper IV ... 24 5 RESULTS AND DISCUSSIONS ... 25
5.1 Results and discussion related to research question 1 ... 25 5.2 Results and discussion related to research question 2 ... 30 5.3 Results and discussion related to research question 3 ... 34 5.4 Results and discussion related to research question 4 ... 35 6 CONCLUSIONS ... 41 7 SCIENTIFIC & INDUSTRIAL CONTRIBUTIONS ... 43 8 SCOPE OF FURTHER RESEARCH ... 45 REFERENCES ... 47
1
1 INTRODUCTION
1.1 Background
Mining is ranked as the second basic industry of early civilization after agriculture. Since prehistoric times, mining has been an essential part of human existence, i.e. mining in the broadest sense of the term, meaning the extraction of any naturally occurring mineral substances from the earth or other heavenly bodies for utilitarian purposes (Hartman, 1987).
Humans began mining approximately 450,000 years ago (Hartman and Mutmansky, 2002).
Nowadays, mining is the foundation of the world’s industrial development.
Minerals have been mined in Sweden for over 1,000 years. Metals from these minerals and other substances are important for society and are used in daily life. The mining industries contribute nine percent of the Swedish gross domestic product and employ 0.5 percent of the total industrial labour force (Lithander, 2004). In 2010, mining accounted for 13 percent of all industrial investments and contributed SEK 26 billion to Sweden's gross domestic product. In 2012, the Swedish Trade Council stated that the Swedish mining industry had annual sales of approximately SEK 70 billion and more than 30,000 employees, making the mining industry an important engine for growth in Sweden (Swedish Trade Council, 2012). The year 2013 was a record year for the Swedish ore production, as it reached almost 80 million tons that year, an increase of ten percent compared with 2012. Today, there are 17 mines in production in Sweden, 15 metal mines and two clay mines.
In modern mining, there are five stages in a mine’s life in the utilization of a mineral deposit.
The first stage is the search for ores or other valuable minerals, which is called the prospecting stage. The second stage in the life of a mine is determining as precisely as possible the value and volume of the mineral deposit found. This stage is called the exploration stage.
Development is the third stage in the mine’s life and it involves the work of opening a mineral deposit for exploitation. Exploitation, the fourth stage of mining, is associated with the actual recovery of minerals from the earth. The final stage in the operation of most mines is reclamation, the process of closing the mine (Hartman, 1987).
Mining can be classified into two main types based on the excavation technique. Type one is surface mining, which is performed on the surface by removing layers of bedrock to reach stone, coal, or ore deposits. Type two is underground mining, which concerns the exploitation of geological materials or other minerals by extracting them beneath the surface of the earth.
Underground mining consists of making incisions into the earth in the form of underground tunnels to reach ore deposits, and can be classified into three main types based on the access type: slope mining, shaft mining and drift mining. Slope mining is a form of underground mining used where the mineral deposits are located very deep. This type of mining is normally carried out when there are problems drilling shafts vertically downward. Shaft mining is a type of underground mining where shafts are driven vertically into the earth to access ore deposits (Wijaya, 2012). Drift mining involves the use of a drift or horizontal access tunnel driven into the earth for extracting or transporting ore or minerals; drilling rigs are used for face drilling in this type of underground mining. This thesis focuses on drilling rigs used in underground mines. A typical drift mining process cycle consists of six processes, namely drilling, charging, blasting, scaling, loading and rock bolting. These processes form a cycle illustrated in Figure 1.1.
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Figure 1.1. A typical drift mining process cycle
The process cycle starts with drilling, the process of making blasting holes in the mining room face by crushing the rock. The next process, charging, is the process of filling the blasting holes with an explosive, for example dynamite. The subsequent process is blasting, the action of breaking rock using the charged explosives. After this the scaling process will start, in which loose material is cleared from the roof, face and walls to make the mining room completely safe. This is followed by the loading process, in which the broken rock is gathered and loaded onto trucks for removal to a central loading area. After the loading process is finished, the mining room has been cleared from broken rocks and prepared for the final process, which is bolting. Bolting involves the insertion of steel rods into holes drilled into the mining room’s roof or walls to provide support for the roof or sides of the mining room.
1.1.1 Mining drilling rig
A mining drilling rig is a machine used to create holes in the ground. Mobile drilling rigs can be used to make tunnels and underground facilities, and small or medium-sized mobile drilling rigs are utilized in mineral exploration, for example. Mining drilling rigs are used for two main purposes, namely production drilling (for processes in the mining production cycle such as bolting) and exploration drilling (for identification of the location of minerals).
As the description of the process cycle for drift mining shows, drilling is an extremely important step in the workplace. From an economic viewpoint, drilling rigs make an important contribution to the mine’s production rate, have a high acquisition, maintenance and operating cost, and represent a possible critical bottleneck for production. The L2C drilling rig is used as the object of a case study in this thesis and its components are presented in Figure1.2. This rig is manufactured by Atlas Copco and is used by Boliden AB in Sweden.
In 1898 Atlas manufactured its first drill, driven by compressed air, and then in 1915 the company produced drills equipped with four-cylinder single-acting piston motors. These drills had a design that offered many advantages over those of Atlas’ competitors, including fewer parts and good balance. The first mobile rig arrangement for underground drilling was designed for sub-level caving in Kiruna in 1952. In 1973 Atlas Copco presented the first heavy-duty impact hydraulic rock drill. The hydraulic rock drilling technique made it possible to increase the drilling output. In 1998 the company launched a new generation of underground drill rigs called boomers. Based on a modular design, this rig concept set new standards for automation, computerization and performance.
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Figure 1.2. Mining drilling rig (source: Atlas Copco Rock Drills AB)
Economic competition has pressurized mining companies into achieving higher production rates by enhancing the techniques of drilling and blasting and increasing mechanisation and automation. Boliden’s historical data over a period of one year (2008) from one of their underground mines in Sweden show that more than 15% of the unplanned downtime of mobile rigs is related to drilling rigs, the greater part of whose downtime is attributed to the poor reliability of their components. Thus, the drilling rig is a bottleneck in the production cycle and is becoming an important object of research in underground mining. Due to a combination of a harsh environment, the operation context, and reliability and maintainability issues, the drilling rig is a major contributor to unplanned downtime.
In the following subsections, an account is given of literature reviews performed to identify the current status of research on reliability and optimal replacement times, as documented in the available literature.
1.1.2 Reliability literature review
A mine production system consists of many subsystems. To make a mining system profitable, the optimization of each subsystem in relation to other subsystems should be considered (Barabady and Kumar, 2008). To achieve this aim, reliability and maintainability analysis should be performed for each subsystem in the mine production system. Since the mid-1980s, reliability analysis techniques have been essential tools in automatic mining systems (Blischke and Murthy, 2003).
Many researchers have studied the reliability and maintainability of mining equipment and its failure behaviour. For example, Kumar et al. (1989) analysed the operational reliability of a fleet of diesel-operated load-haul-dump (LHD) machines in Kiruna Mine in Sweden. They divided the LHD machines into four main subsystems. They did separate failure analysesand the reliability of the fleet was modeled. Kumar et al. (1992) performed reliability analysis on the power transmission cables of electric mine loaders in Sweden. They used a proportional hazards model to investigate the effects of two different designs on the reliability of a power transmission cable of an electric mine loader. They have found that the proportional hazards model can be used as an explanatory tool to seek explanations for undiscovered facts and on that basis decisions for selecting the suitable design for a component can be taken. Kumar and Klefsjö (1992) analysed the maintenance data of one subsystem (the hydraulic system) of a fleet of six LHD machines divided into three independent groups at Kiruna Mine.
1 Cabin 6 Front jacks 11 Cable reeling unit
2 Boom 7 Hydraulic pump 12 Diesel engine 3 Rock drill 8 Rear Jack 13 Hydraulic oil reservoir 4 Feeder 9 Electric cabinet 14 Operator panel 5 Service platform 10 Hose reeling unit
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Reliability assessment of mining equipment was performed by Vagenas and Nuziale (2001);
using genetic algorithms, they developed and tested reliability assessment models for mobile mining equipment. They found that the application of genetic algorithms in reliability engineering may contribute to a better understanding of the reliability characteristics of industrial systems. Vayenas and Xiangxi (2009) used reliability-based maintenance to study the availability of 13 LHD machines in an underground mine. They were interested in the influence of machine downtime on the productivity and operation costs of these machines.
They found that mechanical breakdowns and planned maintenance consume most of the repair time of the fleet. Wijaya et al. (2011) developed a method for visualising downtime by using a jack-knife diagram; they applied the method on a scaling machine at a mine in Sweden.
Gustafson et al. (2012) analysed the reliability of automatic and manual LHD machines and performed a comparison between them. They found that the hydraulic and electric systems are the biggest reasons for the downtime of both manual and automatic LHD machines.
In addition, many studies have considered reliability, maintainability and optimum replacement decisions; readers are referred to Ahmadi and Kumar (2011) and Dandotiya and Lundberg (2012), for example, for further studies on the recent literature in this field. The first study to have been made regarding the downtime analysis of mining drilling rigs is presented in this thesis.
1.1.3 Optimal replacement time literature review
Standard models for economic replacement time (ERT) decisions contain an estimation of the discounted costs by minimising the total cost of the equipment. The assumption of these models is that equipment will be replaced at the end of its economic lifetime by a continuous sequence of identical equipment (Hartman and Tan, 2014). Bellman (1955) developed the first optimal asset replacement model for a variable lifetime of assets. Wagner (1975) offered dynamic programming formulation for the equipment replacement problem in which the state of the system is the time period and the decision at each period is to keep the equipment for N periods. His formulation has been extended by researchers to deal with the realities of technological changes, for example see Oakford et al. (1984), Bean et al. (1985), Hartman and Rogers (2006), and Hritonenko and Yatsenko (2008). These authors assumed a finite horizon in their approaches to the problem of equipment replacement under non-stationary costs.
In 1976, Elton and Gruber (1976) showed that an equal life policy was optimal on an infinite horizon under technological changes. In contrast, Hartman and Murphy (2006) studied an asset replacement problem for a stationary finite horizon; they illustrated how a bound on the number of times an asset is retained in its economic life can be obtained, thus suggesting that it is optimal to replace the asset during its economic lifetime.
Dynamic programming models have been utilized in real cases of calculating equipment replacement time because of the important uncertainties associated with life cycle costs (Richardson et al., 2013). The net present value of all the life cycle costs associated with an infinite sequence of equipment life cycles has also been used to make equipment replacement decisions (Bethuyne, 1998; Scarf and Bouamra, 1999; Hartman, 2005; Yatsenko and Hritonenko, 2005). Other researchers have used different equipment replacement models to analyse a variety of equipment, such as forklifts, buses, and aircraft (Eilon et al., 1966; Keles and Hartman, 2004; Bazargan and Hartman, 2012). Although Tanchoco and Leung (1987) found that replacement decisions could be influenced by capacity considerations, others have noted that technological changes can encourage decision makers to utilize equipment beyond its economic lifetime (Cheevaprawatdomrong and Smith, 2003). The first study to have been made regarding the optimal replacement time of mining drilling rigs is presented in this thesis.
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1.2 Basic concepts and definitions 1.2.1 System reliability and performance
In this section we present the basic definitions of reliability and discuss the relationship between reliability and performance. System or product reliability is defined as the ability of a product or system to perform as intended (i.e. without failure and within specified performance limits) for a specified period of time and in its life cycle conditions (Kapur, 2014).
Reliability is an important attribute of a system or product. In the case of the drilling rig, the user expects the rig to operate properly for a specified period of time beyond its purchase date, which usually depends on the purpose and cost of the rig. At a low cost, a throwaway rig may be used as a redundant rig just for a limited period of operation. A reliable rig may be expected to last for many years of operation when it is properly maintained. The behaviour or the future performance of the system depends on its reliability. Thus, reliability has been considered as a term that concerns quality (Kapur, 1986; O'Connor, 2000). In the past few decades, system reliability has been defined in many ways, including the probability that a system, product, or device will not fail for a given period of time under specified operating conditions (Shishko and Aster, 1995). System reliability can be defined as the capability of a product to meet customer expectations of product performance over period of time (Stracener, 1997).
The performance of equipment is typically associated with the functionality of that equipment, what the equipment can do and how well it can do it. For example, the functionality of an underground mining drilling rig involves drilling holes in the face and walls of mining rooms.
How it drills the holes and the quality of the holes involve functional performance parameters such as rotational speed, feeding speed, ease of drilling hard rocks, and steering adjustments.
Improving the performance of equipment usually requires adding technology and complexity.
This can make the desired reliability difficult to achieve.
To summarize the relationship between reliability and performance, it can be stated that the reliability of equipment refers to its ability to perform its function without failure for a certain period of time in its life cycle application under specified working conditions and within certain limits of performance. The performance parameters usually describe the functional capabilities of the equipment. Finally, it can be stated that the performance of equipment is related to its reliability.
1.2.2 System availability
Availability is defined as a percentage measure of the degree to which machinery and equipment are in an operable and committable state at the point in time when they are needed. This definition includes committability and operability factors which are contributed to by the equipment itself, the process being performed, and the surrounding facilities and operations (Katukoori, 1995). There are different classifications of availability and different ways to calculate it. A common classification is based on the span of time to which the availability refers and the types of downtime used in the computation. There are a number of different classifications of availability, such as the following:
point availability, defined as the probability that the system is in an operable state at a specified time;
interval availability, defined as the expected fraction of an interval of a specified length of time during which the system or equipment is in an operable state;
steady state availability, defined as the expected fractional amount of time in a continuum of operating time during which the system or equipment is in an operable state.
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For further discussion about the classifications and ways to calculate the system availability, see Katukoori (1995), Kumar and Akersten (2008), and Stapelberg (2009).
1.2.3 System maintainability
The maintainability of an item is defined as its ability, under stated conditions of use, to be retained in, or restored to, a state in which it can perform its required function when maintenance is performed under stated conditions and using prescribed procedures and resources (Rausand, 2004). System maintainability is a main factor which can be used to determine the availability of the system.
The maintainability of a system depends on design factors such as ease of reinstallation, ease of dismantling, ease of access to the system, and so on. Maintainability is primarily determined by the design of the system or the item and can be greatly enhanced if the repair procedure and fault detection and isolation are worked out during the design stage of the system itself. The objective of maintainability is to restore the function of the system in a minimum period of time.
1.2.4 System life cycle costing
The life cycle cost of a system can be defined as the sum of all the acquisition and ownership costs incurred during the useful life span of the system. These costs include direct, indirect, recurring, nonrecurring, and other related costs incurred, or estimated to be incurred, in design, research and development, investment, operations, maintenance and other support of the system, and retirement of the system. The ownership costs represent the total of all costs other than the acquisition or initial cost during the life span of a system. The term life cycle costing was used for the first time in 1965 in a report entitled "Life Cycle Costing in Equipment Procurement" (Dhillon, 2010). This report was prepared by the Logistics Management Institute, Washington, D.C., for the Assistant Secretary of Defense for Installations and Logistics, the U.S. Department of Defense, Washington, D.C. According to many studies, the system ownership cost (i.e. operating and logistic cost) can vary considerably and amount to 10-100 times the original acquisition cost (Ryan, 1968). Determining the system’s life cycle cost is an important issue, because the acquisition is a small part in relation to the total costs associated with owning and operating the system.
The life cycle cost of a system can be determined through one of three general methods (Farr, 2011). These methods are the engineering build-up, the analogy and the parametric method.
The engineering build-up method involves direct estimation at the component level leading to a detailed engineering build-up cost estimate of the system. This can be achieved by using machine element and mechanics theories for estimating the lifetime of equipment and practical lifetime tests, see, for instance, Norton (2011). The engineering build-up methodology can be used for individual estimates for each item, element, or component, and these estimates are then combined into the overall cost estimate. Therefore, this methodology is sometimes classified as a "bottom-up" estimating method. It involves computation of the cost of each element by estimating costs at the lowest level of detail and computing quantities and levels of effort to determine the total system cost.
In the analogy method an estimate is made using historical results from a similar system or product. Analogy estimates are performed on the basis of comparison and extrapolation using similar systems or items. In many instances this can be accomplished using simple relationships or equations representative of detailed engineering build-up estimates of past projects. The preferred means to conduct a cost estimate early in the system life cycle is to use data from programmes that are technically representative of the programme to be estimated. The cost
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data are then subjectively adjusted upward or downward, depending on whether the subject system is felt to be more or less complex than the analogous programme (Farr, 2011).
The parametric method is based on mathematical models or equations. Simple mathematical relationships such as nonlinear and linear regression are mostly utilized. Excel software, for example, can be easily utilized to fit these relationships (Farr, 2011). In this thesis, the parametric method is used to calculate the total ownership cost of the drilling rig and to estimate its economic lifetime.
1.2.5 Life cycle costing fundamentals
Life cycle costing can be defined as a method for estimating the total life cycle cost of an acquired item or acquired equipment. The total life cycle cost includes equipment procurement and ownership costs. The equipment ownership cost could be quite significant and in most cases exceeds the procurement cost. For example, various studies indicate that the operating and maintenance costs over the life span of equipment could be many times greater than its procurement cost (Ryan, 1968). There are many reasons why the industrial sector all around the world is being compelled increasingly to use life cycle costing to make different types of decisions that indirectly or directly concern engineering systems. Examples of these reasons are increasing operation and maintenance costs, budget limitations, competition, and the high cost of investment (Seldon, 1979). There are six primary areas where life cycle costing can be used: comparing competing projects, controlling on-going projects, long-term planning and budgeting, selecting a successful candidate among bidders competing for a project, comparing logistics concepts, and deciding the optimal replacement of aging equipment (Seldon, 1979). The focus of this thesis is directed on the economic replacement time of mining drilling rigs. To perform life cycle costing studies, different types of information are required, such as the costs connected with the acquisition, operation, maintenance, installation, and transportation (delivery) of the equipment, the taxes to be paid, the disposal cost, the second-hand value, and the useful operational life of the equipment or systems ( Brown, 1979).
There are many activities associated with life cycle costing, including the following (Earles, 1981):
o conducting appropriate sensitivity analysis;
o defining activities that generate a product’s or an item's ownership costs;
o establishing discounted life cycle costs;
o identifying all the cost drivers;
o defining a product's or an item's life cycle.
Over the years, many authors have proposed steps for performing life cycle cost analysis (Wynholds and Skratt, 1977; Coe, 1981; Dhillon, 2013). The following ten steps have been considered quite effective in performing life cycle cost analysis (Greene and Shaw, 1990):
1. determine the life cycle cost analysis objective, 2. define the scope of the system,
3. choose the effective models for estimating the life cycle cost,
4. obtain all the essential data and make the appropriate inputs into the selected model, 5. conduct sanity checks for outputs and inputs,
6. conduct essential sensitivity analysis, 7. formulate the life cycle cost analysis results, 8. document the life cycle cost analysis,
9. present the life cycle cost analysis as is appropriate, 10. update the life cycle cost analysis as is appropriate.
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In order to perform effective life cycle cost analysis, availability of reliable cost data is necessary.
This means that the existence of good cost data banks is very important. Thus, in developing a new cost data bank, careful attention must be given to factors regarding the data such as uniformity, volume, responsiveness, flexibility and comprehensiveness (Dhillon, 2010).
Although data for life cycle cost analysis can be obtained from many sources, their quality and amount may vary quite considerably. Therefore, prior to starting a life cycle cost study, it is vital to examine carefully factors such as data applicability, data availability and data bias (Dhillon, 1999).
In 2010 Dhillon discussed the advantages and disadvantages of life cycle costing, stating that the important benefits of life cycle costing are that they are useful for the following purposes:
o reducing the total cost, o controlling programmes,
o comparing the cost of competing projects,
o making decisions associated with equipment replacement, planning, and budgeting.
In contrast, some of the main disadvantages of life cycle costing include the following:
o it is costly;
o it is time-consuming;
o the acquisition of data for analysis is a trying task, o it has doubtful data accuracy.
For more details, see Dhillon (2010). The specific purposes of life cycle costing in product acquisition management are to estimate the total ownership cost (TOC) of the product and to decide when to buy a new one. Reducing the TOC by using LCC analysis is an important issue in the development process of the product, and understanding TOC implications is necessary to decide whether to continue to the next development phase, as well as to control costs and assist the procurement decisions (Farr, 2011).
Life cycle cost analysis is an economic estimation technique that determines the total cost of owning, operating, maintaining and disposing of a system over its life span. It must be used to understand fully how to determine and interpret the total ownership cost of a system (Farr, 2011). A simple process for developing an LCC model is shown in Figure 1.3.
1.3 Industrial motivation of the study
Industrial companies, or more specifically mining companies, put huge funds, often millions of dollars, into their annual budgets to purchase heavy mobile equipment (HME) such as drilling rigs, scaling rigs, wheel dozers, wheel loaders, dump trucks, etc. Given the enormous costs of acquiring, operating, and maintaining their HME, it is important for mining companies to optimise their replacement and procurement strategies (Richardson et al., 2013). With increased mine production, the HME operating hours will increase and, as a result, the operating and maintenance cost will increase also. At some point in the equipment’s life span, these costs will be too high and, since it will then no longer be economically viable to continue using the old equipment, it should be replaced (Verheyen, 1979). An essential economic consideration in industrial companies is that a model must be found for identifying this point (i.e. the point at which the equipment replacement time is expected to yield a minimal life cycle cost). Obviously, for mining companies, one of the most important decisions concerns determining the ERT of capital equipment; this can be accomplished with the help of life cycle cost analysis. The main reason for the increasing use of the life cycle costing concept for HME is that at some point the operating and maintenance costs will exceed the acquisition costs.
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Figure 1.3. Process for developing an LCC model (adapted from Farr, 2011)
Since the 1960s most of the research conducted in the field of mining equipment has concerned the reliability and maintenance of such equipment. Nowadays, modern mining machines have a higher technology level and a higher complexity in comparison with the old ones (Hoseinie, 2012). Reliability analysis techniques have been gradually accepted as standard tools for the planning and operation of complex and automatic mining equipment (Barabady and Kumar, 2008). Generally, the downtime costs of mining equipment are too high due to high production losses (Dandotiya, 2012). In order to enhance equipment reliability and to reduce mining equipment downtime, a large amount of research has been conducted using various methods to ensure the improvement of equipment design and maintenance procedures.
Reliability analysis can be used in identifying the sensitive subsystems and critical components of mining machinery. Moreover, reliability analysis has been acknowledged as the basic requirement for all maintenance planning, prediction of the remaining useful life, and life cycle cost analysis of machinery. Therefore, we need to analyse the reliability of operating machinery at the first stage of any comprehensive field studies.
A preliminary study performed by the author of this thesis in one underground mine in Sweden revealed that more than 15 percent of the unplanned downtime of mobile equipment is related to drilling rigs. This high amount of unplanned downtime leads to monetary losses, which need to be minimized. Since drilling is the first process of a typical mining cycle and is a key factor for production, it is also important to find solutions for drilling rig problems and reduce the downtime. To minimize losses related to downtime, the reliability of the drilling rig should be improved and the economic replacement time of the rig should be determined. The replacement of rigs should be carried out in a cost-effective way.
The present study has focused on the development of a model that can be used by the manufacturer and the operator companies for easy estimation of the optimal replacement time of drilling rigs from an economic point of view. This model can in principle be used for other machinery used in the mining industry or other industries. Furthermore, the study has also aimed to calculate the downtime of drilling rigs to assist the manufacturer and operator companies in identifying the problems affecting rig downtime and to provide solutions that will reduce it. This collaborative research has been jointly conducted by Luleå University of Technology, a mining company operating the drilling rig and the manufacturing company which developed the rig.
Understand the manufacturer
and operator requirements
Define the
scope Collect data
Sensitivity analysis
Conduct LCC analysis
Evaluate and normalize the
data
Select the variables
Data analysis and correlation Regression
and curve fit
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2 THE APPROACH OF THE THESIS
2.1 Research problem description
Meeting an increasing demand for higher production, reducing the production equipment’s downtime and increasing its productivity are the major concerns of the collaborating mining company. Economic competition is pressurizing the mining company into achieving higher production rates by enhancing its drilling and blasting techniques and increasing its mechanisation and automation. This means that improving the availability of the company’s production rigs should be investigated.
The production rigs are those rigs which contribute directly to the mine production rate and create value for the company. One of these production rigs is the drilling rig. The maintenance department at the mining company aims to reduce the number of failures and the downtime of production rigs. The financial department at the company aims to reduce the costs associated with the drilling rig’s acquisition, operation and maintenance by implementing a cost-cutting strategy. There are many reasons why the mining company is being compelled increasingly to use life cycle costing to make different types of decisions that indirectly or directly concern production rigs. Examples of these reasons are increasing operation and maintenance costs, budget limitations, competition, and the high cost of investment. The overall goal of the mining company is to increase its mine production and the company profit.
To achieve the goal of the maintenance department, the engineers at this department asked the following questions: which components of the drilling rig have mostly contributed to its downtime and which problems have the greatest effect on the downtime of the rig? To achieve the goal of the financial department, the financial experts at this department asked the following question: what is the best time to replace the rig and buy a new one from an economic point of view, with a view to reducing the total ownership cost of the rig? To achieve the overall goal of the mining company, downtime analysis should be performed for the drilling rig to identify the rig components that contribute most to its downtime, to identify the problems affecting the downtime of those components, and, if possible, to make suggestions for the solution of these problems. Another measure which would help the company to achieve its overall goal would be to perform life cycle cost analysis for the drilling rig in order to estimate the optimal replacement time of this rig, with a view to reducing the ownership cost from an economic point of view and increasing the company profitability.
The main reason for an increased use of the life cycle costing concept for production machinery is that at some point of its life span the operating and maintenance costs will exceed the acquisition costs. To this end one should consider focusing one’s attention on optimization models, techniques and tools which can help the decision makers in the mining company to optimize their equipment lifetime.
2.2 Overall research goal
The overall research goal has been to develop methods for downtime analysis and replacement time optimization. These methods should be useful for machinery in general and specifically for drilling rigs in mining applications.
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2.3 Research questions
To fulfil the overall research goal of the thesis, the following research questions (RQs) have been formulated.
1. Which critical components make a large contribution to the downtime of the drilling rig? What are the dominant problems influencing the drilling rig downtime, reliability problems and/or maintainability problems?
2. How should a model be constructed that can calculate the optimum replacement time of a drilling rig? Moreover, which cost factors have the largest impact on the replacement time?
3. How should the above model be improved with respect to easy and accurate prediction of the economic lifetime of this rig, with a high level of certainty and with a view to enhancing decision making in this regard?
4. How should a model be constructed for estimation of the economic lifetime of mining production rigs when also the costs from one redundant rig are considered?
These research questions are answered by the four appended papers, each of which makes its own contributions toward the research questions (see Table 2.1).
Table 2.1. Relationship between the appended papers and research questions
Paper I Paper II Paper III Paper IV
Research question 1 (RQ 1) X
Research question 2 (RQ 2) X X X
Research question 3 (RQ 3) X
Research question 4 (RQ 4) X
The research framework appears in Figure 2.1. Paper I analyses and compares the downtime of four drilling rigs used in two underground mines in order to identify the critical components of these rigs. Paper II develops a practical model to calculate the optimal replacement time of the drilling rigs. Paper III develops a new model for easy and accurate prediction of the economic replacement time of mining drilling rigs by using an artificial neural network technique. Paper IV develops a model to determine the economic replacement time of production rigs used in the mining industry when also the costs from one redundant rig are considered.
2.4 Scope and limitations of the study
The scope of this thesis is limited to the drilling rig and, more specifically, to the study of the replacement time of drilling rigs used in underground mines in Sweden, as well as the issues related to the downtime of these rigs. The thesis is based on manually entered failure, repair and cost data from the collaborating mines.
The limitations of this thesis can be described as follows. Firstly, the reliability of human beings is an important area to consider, but is beyond the scope of this thesis. Secondly, the data are related to specific mobile mining equipment, with specific environmental and operating characteristics and working in specific underground mines. Thirdly, the results obtained from this research are limited to the information that could be extracted from the collected data.
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Fourthly, the results are limited to case studies of L2C drill rigs. Fifthly, the operating conditions, for example the working environment, are not considered in the downtime analysis. Sixthly, the influence of production performance of the drilling rig is not considered in the model of the optimal replacement time. The model is only considering the costs.
Finally, in the present thesis, the replacement time analysis was performed based on the cost data obtained from only one drilling rig operated in a single underground mine in Sweden.
Consequently, the operating conditions should be taken into consideration before applying the study’s results, especially when the operating conditions are not similar to those in the present study.
Figure 2.1. Research framework Reliability and Life Cycle Cost Modelling of Mining
Drilling Rigs
Paper I Downtime analysis and
comparison between different subsystems
Paper II
Optimal replacement time estimation
Paper III Economic replacement
time prediction using artificial neural network Paper IV
Model for ERT considering different cost
factors
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3 RESEARCH METHODS
3.1 Data collection and analysis
The data were collected from the database of the computerized maintenance management system (CMMS) of the mining company participating in the present study. The literature survey was carried out based on relevant peer-reviewed papers in conference proceedings and journal articles from online databases. Some of the papers and articles were searched for on the basis of references of other relevant articles, and some of the known papers and articles were retrieved directly from the journal databases. Relevant books and reports were searched for in Lucia (Luleå University Library’s online catalogue), and PhD and licentiate theses from various universities were studied. Specific keywords were used to search for information in well- known online databases, including Science Direct, Elsevier, Emerald, Springer and Google Scholar. Moreover, discussions were held with reference groups.
The present research was performed on two underground mines in the north of Sweden.
Failure and repair data for two years (August 2009-August 2011) were collected to answer research question one. These data were collected from the two mines for four drilling rigs.
Three rigs were working in the first mine and the fourth rig was working in the second mine.
Cost data for around four years (March 2009-January 2013) were collected to answer research questions two, three and four. The cost data were collected for a single rig operating in the second mine.
The analysis of failure data which can be used in reliability analysis should be based on the assumption that the times between failures (TBFs) are independent and identically distributed in the time domain. The magnitude of the recorded TBF data was valid for fitting the various distributions for representing the population of the TBFs. However, before any reliability analysis for Paper I was performed, trend and serial correlation tests had to be carried out to check whether the usual assumption of independent and identically distributed TBF data in the data sets would be contradicted or not (Kumar, 1989; Kumar and Klefsjö, 1992). The Laplace trend test was used in this study to test the hypothesis that a trend did not exist within the TBF data. We calculated the test statistic U for the TBFs of the drilling rig subsystems to be at a significant level of 0.05. From the standard normal tables, with a significant level of 0.05, the critical value is equal to 1.96. If -1.96<U<1.96, then we would accept the hypothesis of no trend within the TBF data. After applying the trend test for the critical components of the studied rigs, we found that there was no trend within the TBF data; for example, U was equal to 0.55 in the feeder of the drilling rig used in the second mine.
The serial correlation test of the TBF data of the drilling rigs and their subsystems was carried out to check the dependence of the TBF data. This test was performed by plotting the ith TBF against the (i-1)th TBF. We tested the significance of the correlation by calculating the (r) value and comparing it with the critical (r) value, which could be obtained from the correlation tables. For example, the results of the serial correlation test of the above component (i.e. the feeder) are given in Figure 3.1. Since the points are randomly scattered, the failure data can be assumed to be independently distributed. The (r) value is equal to 0.05, while the critical value of (r) from the correlation tables at the significance level alpha = 0.05 and a degree of freedom of 30 for a two-tailed test is equal to 0.364. We can conclude that the correlation between the TBFs of this subsystem is statistically not significant (i.e. no correlation
16
exists), since r < the critical r. Different types of statistical distributions were examined and their parameters were estimated by using the Easy Fit and Minitab software.
0 100 200 300 400
0 50 100 150 200 250 300 350 400
ith TBF
(i-1)th TBF Serial correlation test
Figure 3.1. Serial correlation test for the feeder of the drilling rig
As mentioned earlier, the cost data for the single machine used in one mine were collected for a period of around four years. Figures 3.2 and 3.3 illustrate the maintenance and operating cost for this period.
Figure 3.2. Maintenance cost Figure 3.3. Operating cost
With reference to Papers II-IV, since the user company planned to use the machine for 120 months, extrapolation was performed on the operating and maintenance cost data. Figures 3.4 and 3.5 illustrate the maintenance and operating costs determined by data extrapolation.
Figure 3.4. MC after extrapolation Figure 3.5. OC after extrapolation In Figures 3.4 and 3.5, the dots represent the real historical data for the maintenance and operating costs. Curve fitting was performed using the Table Curve 2D software to show the behaviour of these costs before and after the time when the data were collected. Note that the fitting would have been better if more data had been available for a time period of more than
Maintenance cost
70 80 90 100 110 120
Time (month) 0
25 50 75 100 125 150
Maintenance cost (cu)
Operating cost
70 80 90 100 110 120
Time (month) 15
25 35 45 55
Operating cost (cu)
Maintenance cost
0 50 100 150 200
Time (month) -200
-100 0 100 200 300 400
Maintenance cost (cu)
Operating cost
0 50 100 150 200
Time (month) -50
0 50 100 150
Operating cost (cu)
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four years. This software uses the least squares method to find a robust (maximum likelihood) optimisation for nonlinear fitting. It is worth mentioning that the drilling rig in this case study had no multi-level preventive maintenance programme. The main reason why the maintenance cost was quite low in the earlier months was that the rig was new at the start of its utilization. The history shows that the user company began to keep track of cost data by using CMMS when the maintenance costs started growing. This observation can be compared with the three phases in the conventional bathtub curve (see Figure 3.6) used in reliability studies (Blischke and Murthy, 2003).
Figure 3.6. Bathtub curve (adapted from Blischke and Murthy, 2003)
The first phase of this curve represents the period with a relatively large number of early failures. This phase is not included in Figure 3.4 because the failures are considered to have been identified and resolved before the delivery of the rig to the mining company. The rig is assumed to have been delivered to the mining company while in the second phase. In this phase the rig has random failures at a low and almost constant failure rate. This phase is visible in the period between 0 and 76 months in Figure 3.4, where the cost is low and relatively constant. The final phase represents a period with an increasing number of failures that are related to the aging of the system. This corresponds to the period between 76 and 120 months in Figure 3.4.
There was no information regarding the number of failures and the maintenance cost at the beginning of the lifetime of this rig and up to the time when the company started to record these data in its CMMS. Therefore, the ‘‘Lorentzian Cumulative’’ equation was used to perform the extrapolation for the maintenance cost data.
The fitted curve for the maintenance and operating costs (in the second and third phases) using the Lorentzian extrapolation is assumed to represent the behaviour of our data adequately, since r2 (adj.) = 0.97 and 0.91 for the two costs, respectively. In Figures 3.4 and 3.5, the inflection point after 120 months of operation is due to a change in the usage profile of the rig, as the rig was to be used as a redundant rig. This was confirmed by the engineers at the collaborating mine. The rig was to be used after 120 months of operation only when any of the production drilling rigs should fail, and therefore the planned service and corrective maintenance were assumed to be relatively constant.
In Paper IV, MATLAB code was used to generate data sets for different time scales for using a redundant rig, after discussion with an expert group at the collaborating mining company (see Figure 4 and Table 3 in Paper IV).
18 3.1.1 Research objects
The present research was performed on four drilling rigs working in two different underground mines in Sweden. The first underground mine began operating in 1940 and is classified as one of the oldest operating mines in Sweden. The predominant mining method used in this mine is cut-and-fill mining with hydraulic backfill (Krauland et al., 2001). The geology of the mine is irregular and complex. The complex ore is presently extracted at a depth of 900-1,400 m below the surface. The ores extracted from the first mine are lead, gold, copper, zinc, gold-copper and silver ores (Rådberg et al., 1992). In this mine, the uniaxial compressive strength of the intact host rock varies from 65-150 MPa and the geological strength index (GSI) varies between 50 and 80 (Edelbro, 2008). The second underground mine began operating in 1952 and is located in northern Sweden. The extraction process in this mine is the cut-and-fill method. The extracted ore is polymetallic and contains copper, gold, silver, lead and zinc. The geological strength index of the rock varies between 70 and 80 at a depth level of •1115-1130 m and the rock mass is of high quality, while at a depth level of
•1130-1185 m, the rock mass quality is lower, with a geological strength index equal to 30-50 (Edelbro, 2009).
The drilling rig investigated in the present research is the L2C drilling rig, which is a model typically used in underground mining in Sweden. The dimensions of this rig are as follows:
length 14.5-16.6 m; width 2.5 m; width of the rig with side platforms 2.9 m; height of the rig with the cabin 3.15 m; weight 26-33 tons (see Figure 1.2). The rig has four retractable stabilizer legs and an articulated four-wheel drive chassis. It can be operated by a water-cooled turbocharged diesel engine with 120 kW at 2,300 rpm or by electric power with a capacity of 158 kW (Atlas Copco Rock Drills AB, 2010).
3.1.2 Failure and cost data
The failure data used in this research (see Paper I) were collected over a period of two years (2009-2011). The source of the data is the database of the two underground mines in Sweden participating in the study. This database belongs to the MAXIMO system, which is a computerized maintenance management system (CMMS). In this research study, the time to failure data (TTF data) and the time to repair data (TTR data) of four drilling rigs and their subsystems were arranged in chronological order so that statistical analysis could be used to determine if there was any trend in the failure and repair data. The framework for the basic methodology used in this study for the analysis of the failure and repair data is presented step- by-step in Figure 3.7.
The first step in analysing the data was calculation of the times between failures (TBFs) for the system. In the CMMS, the failure data are recorded based on calendar time. Since drilling is not a continuous process, the TBFs were estimated by considering the utilization of each rig.
Reliability and maintainability data analysis is usually based on the assumption that the TBF and TTR data are independent and identically distributed (iid) in the time domain. Therefore, it was critical to conduct a formal verification analysis of the assumption that the TBF and TTR data were iid; otherwise completely wrong conclusions could be drawn (Ascher and Feingold, 1984; Kumar and Klefsjö, 1992). The next step, after sorting and classifying the TBF and TTR data based on the component level, was validation of the iid assumption. The failure data were tested for trends using the Laplace trend test. This trend test is used to determine whether the data set is identically distributed (Klefsjö and Kumar, 1992). If such a trend is observed, then classical statistical techniques for reliability analysis may not be appropriate.
Therefore, a non-stationary model such as the non-homogenous Poisson process (NHPP) must be fitted (Ascher and Feingold, 1984; Kumar and Klefsjö, 1992; Modarres, 2006; Birolini,
