Delft University of Technology
FACULTY MECHA NICAL, MARITIME AND MATERIALS ENGINEERING
Department Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl
This report consists of 35 pages and 0 appendices. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning
Specialization: Transport Engineering and Logistics Report number: 2015.TEL.7982
Title: System reliability analysis of ship to shore cranes
Author: D.M. van Campen
Title (in Dutch) Systeem betrouwbaarheidsanalyse van schip-naar-kade kranen
Assignment: Literature thesis Confidential: no
Initiator (university): Dr. ir. X. Jiang Supervisor: Dr. ir. X. Jiang
Delft University of Technology
FACULTY OF MECHANICAL, MARITIME AND MATERIALS ENGINEERING
Department of Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl
Student: Assignment type: Literature Supervisor: Dr. X. Jiang Report number: 2015.TEL.xxxx Specialization: TEL Confidential:
Creditpoints (EC): 10
Subject: System reliability analysis of ship to shore cranes*
Ship to shore cranes (abbreviation thereafter the crane) are typically deployed to load and offload ships of all types and classes at harbors. In general, the crane consists of large numbers of components and subsystems; the status of those components and subsystems would change with time and operation process. The complexity of both internal organization and operation processes of the crane makes it very complicated and thus difficult to evaluate the safety and the reliability of the crane. In those regards, it is essential to introduce system reliability method to the design, evaluation and optimization of the crane in order to maintain its safety and operating process effectiveness. In this literature assignment, the student is demanded to review the development of system reliability method and its application on the design, evaluation, maintenance and optimization of the crane. The following aspects are required to be illustrated in the report:
• Explain the basic theory of system reliability and available approaches /methods.
• Identify the main components and subsystem of the crane, their failure modes inter-relationship between those failure modes (dependent or independent? )
• Identify the main operation processes and their distribution in time domain; the status of components and subsystem with related to each operation process.
• Illustrate the state of the art: application of system reliability to design, evaluate, inspect and optimize the crane.
•
(*Note: The type of crane is not necessarily limited to a ship to shore crane)
This report should be arranged in such a way that all data is structurally presented in graphs, tables, and lists with belonging descriptions and explanations in text.
The report should comply with the guidelines of the section. Details can be found on the website. If you would like to know more about the assignment, you may contact with Dr. X. Jiang through x.jiang@tudelft.nl.
The supervisor, X. Jiang
System reliability analysis
of ship to shore cranes
Literature Assignment
Delft University of Technology
Faculty of Mechanical, Maritime and Materials
Engineering
Transport Engineering and Logistics
System reliability analysis of ship to shore cranes
Literature Assignment
in partial fulfilment of the degree of Master of Science
at the Delft University of Technology
by ing. D.M. van Campen
Delft, the Netherlands
November 10, 2015
Contents
1 Introduction 2
2 Theory and General Definitions 3
2.1 Reliability . . . 3 2.2 Failure . . . 5 2.2.1 Failure prevention . . . 6 2.3 Redundancy . . . 6 2.4 Maintenance . . . 8 2.5 Probability . . . 8 3 Reliability Analysis 10 3.1 Reliability prediction . . . 10
3.2 Load strength analysis . . . 11
3.3 FMECA . . . 12
3.4 FTA . . . 14
3.5 ETA . . . 15
3.6 Multi-state system modelling . . . 16
4 Reliability of a STS gantry container crane 20 4.1 Crane lay-out . . . 20
4.2 System analysis . . . 22
4.3 Operation process . . . 24
4.4 Reliability and risk evaluation . . . 26 5 Conclusions and recommendations 30
Chapter 1
Introduction
This document presents the results of a literature study performed by Daan van Campen in partial fulfilment of the degree of Master of Science at the Delft University of Technology. The subject of the study is system reliability analysis of ship to shore cranes and is initiated by Dr. ir. X. Jiang of the Department of Marine and Transport Technology. The goal of this assignment is to research the theory of system reliability with information that is found in literature and to apply this on a crane which is a large and complex system.
Chapter two of this document focuses on the basic theory and general def-initions in reliability theory. First a definition of reliability is given with an motivation to apply this theory in engineering. This is followed by a descrip-tion of failure, redundancy, system configuradescrip-tions, dependency, maintenance and probability. These are all basic concepts used in reliability theory.
In chapter three a variety of methods to perform reliability analysis are presented. The theories that are found in literature and discussed in this chapter are reliability prediction, load strength analysis, FMECA, FTA, ETA and Multi-state system modelling. For each of the mentioned methods the basic concepts and theory are explained and the applications are discussed.
Form the study on reliability analysis methodologies it is concluded the multi-state modelling method is the most suitable one for the analysis of a complex system such as a crane. An example of the reliability assessment is presented. First the basic components, characteristics and operations of a ship to shore gantry crane are presented. This is followed by a system analysis, iden-tifying all systems which influence the reliability and the components which this system contains. Based on the system analysis a operation process is formed, completed with statistical data. A reliability and risk evaluation is performed, including the system risk function of the critical state and unconditional lifetime results.
In chapter five, the conclusions and recommendation of the research can be found. Finally, in chapter six the used literature is presented in the bibliography.
Chapter 2
Theory and General
Definitions
Many engineering structures are designed according to standards, the design process is deterministic. With a set of requirements and constraints the engineer designs a solution which is in accordance to the predefined standards. The in the standards defined requirements are considered to be adequate and sufficient. However, standards do not guarantee success nor imply failure of the structure will not occur. The probability of failure is not impossible but is on an acceptable level [7].
Standards do not include all engineering problems, and even if they did the desire to further decrease the probability of failure will remain existent. Failure often results in an increase of costs, inconvenience or a threat to the safety. Reliability is a term that indicates the absence of failure, the ability to perform the intended function or task. A clear definition of the concept reliability is needed for this research. A wide variety of research field specific definitions can be found in literature.
2.1
Reliability
A general definition which can also be found in ISO8402 is given by M.Rausand and Høyland "Reliability is the ability of an item to perform a required function, under given environmental and operational conditions and for a stated period of time." [12].
M.Rausand and Høyland state that the reliability of the components which make a system determine the reliability of the system. It is not possible to compensate low reliability by maintenance, however reliability engineering can increase the safety, quality and operational availability of a system. Carter emphasises this and states that "success is achieved when the weakest or least adequate individual component of a system if capable of coping with the most severe loading or environment to be encountered" or "the strength of a chain is
that of its weakest link"[3].
An other definition of reliability, defined specially for engineering purposes, is given by Lewis, "Reliability is defined as the probability that a component, device, equipment, or system will perform its intended function for a specified period of time under a given set of conditions" [10]. This definition is very general as well and can be applied to any object. Engineering is a trade-off between reliability, performance and costs, the approach and outcome of this trade-off strongly depends engineering character and goal.
By use of an example of a race car in the Indianapolis 500 and a com-mercial aircraft this trade-off is further clarified by Lewis. Each year race car performance is increased, however the reliability of the car, measured as the probability that it will finish the race, remains very poor. Performance has the priority and high probability of breakdown is tolerated if there is to be any chance of winning the race. This is in contrast with the design of a commercial airliner where breakdown could result in a catastrophic accident. Reliability is of utmost importance and therefore the main design consideration. Decreased aircraft performance such as fuel efficiency, speed and payload are accepted to maintain small probability of failure.
For many products the reliability trade-off can be viewed in more economic terms. Increased costs for higher reliability of the parts versus increased costs of repair and loss of production as a results of lower reliability. Reliability is an aspect of uncertainty. Whether the object performs its intended function, it works, is a matter of probability.
Reliability theory is not only of importance during the design phase but can be used in the systems complete life cycle. There is a theoretical optimum for the increase of reliability compared to the additional benefit. Forecasting this is almost impossible. The relation between the costs of a item and the reliability is shown in Figure 2.1. A badly run reliability program does not increase reliability but does however bring significant costs.
Figure 2.1: Reliability and life cycle costs [14]
Unfortu-nately a design according the latest knowledge is not always the case, especially for old systems. The benefit of assessing the reliability of existing system is the availability of much more data regarding the system [5].
2.2
Failure
As can be read from the definition, reliability is the probability a system will per-form as intended. The system should not fail, failure could therefor be defined as the point where the system is no longer functional. Failure on component level does not necessary results to failure of the complete system, this is fur-ther explained later in this document. The most important variable to express reliability, and thus also failure, is time.
A parameter to characterise reliability is the mean time to failure or MTTF. Failure rate, denoted as λ, is defined as the number of failures per time unit. This parameter is strictly only applicable for objects that are repairable. Non repairable items do not have a failure rate but a probability of survival over the expected life time.
Figure 2.2: Bathtub curve of time dependent failure rate [10]
The behaviour of failure rate (repairable items) as a function of time λ(t) is typically described by a so called bathtub curve. An example of such curve can be found in Figure 2.2. The curve shows a high failure rate on the left hand side. This high initial failure rate is very typical and can be explained by a variety of reasons. For example incorrect installation, missing components, production errors, exceeded tolerances or damaged during transport. The centre part of the curve shows a constant failure rate, this resembles the useful life of the object and here failure is rather random. The right hand side of the curve has an increase of failure rates, typically caused by ageing of the item.
As stated earlier in this paragraph, the failure rate as a function of the time is only valid for repairable items. The pattern described by this curve is however also valid for non-repairable items, but the plotted failure rate should be replaced by a hazard rate.
Mechanical equipment typically show a more sloped middle section of the curve, since these items are for instance subjected to mechanical wear, corrosion and fatigue. The failure rate is therefor increased in magnitude when operational time continues. Failure rates of computer software however show the opposite behaviour, the curve asymptotically approaches a failure rate of zero on the right side. Examples of such failure rate curves for different types of equipment can be found in Figure 2.3. The described time dependent failure rates are all for systems without redundant components.
Figure 2.3: Time dependent failure rate equipment types [10]
2.2.1
Failure prevention
Preventing failure as much as possible is the first step in creating a reliable design. Design of components should be checked with a load-strength analy-sis and margins of safety. Combinations, optionally factorised, of all possible loads during operation and life of the component should be taken into account. Tolerances have a large influence on the margin of safety, the design should be based on the least favourable conditions of margins. When a adequate margin of safety can not be obtained one should consider testing to obtain the necessary reliability.
If possible extreme loads should be prevented. This can be achieved by for example overpressure valves, electrical overload limiters or mechanical load indicators. With the application of overload protection the maximum load is known and can therefor used directly in the reliability analysis. However, one should keep in mind failure of the overload protection is possible.
Strength degradation can be difficult to prevent since it is often influenced by a wide range of parameters. Quantifying these parameters and the effects they cause are hard to forecast. Prevention of strength degradation can therefor be difficult. If prevention is not possible, maintenance procedures or scheduled replacement should be implemented to ensure a reliable design.
2.3
Redundancy
The reliability of a system is clearly a combination of the component reliability it contains. Systems with a high number of components have the tendency of poorer reliability compared to less complex systems. To maintain the same
reliability of a system with an increased number of components, the reliability of the individual components should be improved. This is visualised in Figure 2.4 where the system reliability is plotted as a function of number and reliability components.
Figure 2.4: System reliability as function of number and reliability components [10]
Systems with components that are in series are sometimes referred as weakest link systems. Component failure result in failure of the system [13]. Alterna-tively, system reliability can be increased by implementation of redundancy of components, subsystems or complete system redundancy. This can prevent that component failure results in system failure. The most basic form of redundancy is a parallel component configuration. This can be a single redundancy layout where two components are redundant, or a multiple redundancy layout where a higher number of components are redundant. During the reliability assessment it is essential to investigate the dependence of the redundant components or subsystems. A multiple redundancy lay out is very beneficial for the system reliability, however if failure of the components is dependent the increased relia-bility is basically nullified. Failure dependency of components and sub systems is very common, since they often share power sources and are subjected to the
same environmental conditions.
The question if redundancy is a feasible or optimal method depends on the properties of the system. Systems where minimum size or weight is essential are less suitable for implementation of redundant components. In these cases higher component reliability is obviously preferred, imposed by economic reasons.
Redundancy can be implemented in different levels of the system hierarchy. High level redundancy is a duplication of the entire system, where low level redundancy is implemented on a component or subsystem level.
2.4
Maintenance
The vast majority of systems require maintenance, maintenance can be cat-egorised in two basic types. The first type is preventive maintenance, here actions are taken at a moment while failure still is absence. The goal of pre-ventive maintenance is to reduce wear related issues and so increase long term reliability. Corrective maintenance is carried out after failure with the goal to restore functionality of the system.
The extend of maintenance implementation depends on the characteristics of the system. The effects of failure, which can be financial but is often a matter of safety, determines the level and type of maintenance. The quality of maintenance depends strongly on human factors.
2.5
Probability
To quantify reliability one must involve statistical models. However as stated by O’Conner, quantifying probability values for failures increase uncertainty. Data about reliability and quality is difficult to obtain and contains many sources of uncertainty and variability.
It is not the goal of this research to extensively describe all failure rate distri-butions. However to illustrate the large number of possibilities of probabilistic distributions an enumeration of common used distributions are given [17][13][6]:
• Unimodel distribution • Binominal distribution • Poisson distribution
• Normal/Gaussian distribution • Inverse gaussian distribution • Lognormal distribution • Exponential distribution • Gamma distribution
• Pareto Distribution • Chi-square distribution • Weibull distribution • Extreme value distribution • Triangular distribution • Double trapezium distribution • Quasi-trapezium distribution • Chimney distribution • Rayleigh distribution • Erlang distribution • Birnbaum-Saunders distribution • Auxilary distribution Statistical confidence
To assess if the used data is representative for the population analysed the statistical confidence can be determined. The fraction of data that is included by the true data gives the confidence interval.
Chapter 3
Reliability Analysis
The goal of a reliability-conscious project team is to deliver a failure free design. Therefore the design should not fail, both when manufactured and when used according to specifications given by the designer.
Design analysis methods are developed to review design reliability and point out potential shortcomings critical parts. Literature often states these analysing methods are very time consuming and laborious, or even considered to be ex-hausting and tedious. However, experience show that finding these potential shortcoming of the design in an early design stage has a considerable effect on future costs. O’Conner states that well managed design analyses are extremely cost effective and the expense can be strongly reduced by good preparation and planning.
To successfully and efficiently apply any of the analysing methods one should have a comprehensive understanding of the design and its functions. All avail-able information should be collected and organised, a functional block diagram forms the basis of the analysis. While performing the analysis one should keep in mind the viewpoint of the analysis. O’Conner states for example that the viewpoint has an influence on the criticality number of a component. Viewpoints can for instance be safety, mission success, availability, repair cost, failure mode or effect detectability.
To endeavour effectiveness, the process of a reliability analysis should be started as early as possible. If the reliability analysis is embedded with the design process it will result in a iterative process where the analysis has an influence on the design.
3.1
Reliability prediction
Prediction of reliability is for obvious reasons the preferred method to assess the reliability. However, the challenge is to perform an accurate and trustworthy predication of reliability. Experience in reliability analyses is essential when one wants to predict the reliability and the best approach is to make use of data of
earlier reliability assessments.
Based on available data of comparable objects one could predict the reli-ability of new objects. The differences between the two objects could result in a higher or lower reliability, this is where the experience of the engineer is required. Comparisons can be made on part level, subsystem level or complete system level, each comparison contributes to the prediction quality.
The quality of the predicted reliability is furthermore strongly dependent on the quality of the used mathematical models. In science behaviour of physical systems is described by certain deterministic and empirical laws. These physical laws have limitations in their validity. These limitations become more distinctive when applied with models which contain large number of actions, the error of the law is passed on and increased.
3.2
Load strength analysis
M.Rausand and Høyland make the distinction between hardware, software and human reliability. Hardware reliability, the reliability of technical components and systems, is defined according to the following equation:
R = P r(S > L)
Where reliability (R) is the probability (P r) that the strength (S) is greater than the load (L). The reliability of a component can be illustrated by a graph with distributions for load and strength, such a distribution can be found in Figure 3.1.
Both load en strength values are described by a distribution, when these distributions do not overlap failure will not occur. The end of the distributions are called "tails", overlap of these tails implies an item with poor strength is subjected to a high load and thus failure occurs.
The shape of the distributions depends on the scatter, or standard deviations of the load en strength of an object. In Figure 3.2 three examples of scatter are shown.
A small scatter of the load distribution represents a load that is considered to be smooth. Case 1 is an example of such a smooth load, contrary to the load distribution of case 2. A small scatter of strength distribution can be found in case 2. For case 1 the scatter of the strength distribution is relative large. In case 3 the scatter of the strength distribution is approximately equal to the scatter of the load distribution.
It is evident that the overall reliability of a construction, which contains a number of components, is influenced by the reliability of its individual nents. The relation of overall reliability as a function of this number of compo-nents for the 3 cases described earlier can be found in Figure 3.3. The number of components the structure contains is a degree of complexity of the structure. Case 1 has a strictly defined load distribution but high scatter of the strength distribution, the reliability is described by the product of all components, hence the strong drop for a higher number of components. In case 2 the scatter of
Figure 3.1: Distribution of load and strength [3]
the component strength distribution is relative small, hence all elements have approximately the same strength. Thus the overall reliability is barely changed when complexity is increased and could be considered to be constant. Case 3 is an intermediate situation which shows intermediate results.
The load-strength analysis is a method to analyse reliability of hardware components. An example of a load-strength analysis is given in Figure 3.4
The goal of a load strength analysis is to guarantee that all load and strength aspects of the design are taken into consideration.
3.3
FMECA
The most commonly used reliability analysing technique is the failure modes, effects and criticality analysis, or FMECA in short. FMECA is a method that gives insight in effects on the system of each failure mode. All identified failure modes are granted a class to express the severity if failure occurs. Depending on the stage of the project the FMECA method is performed according a hardware or on a functionality approach. With the hardware approach failure of physical components are taken into account, so the effects of a part failure is analysed. The functional approach can be implemented in an earlier design stage where hardware components are not yet completely defined but only their function is described.
The methodology of FMECA is described by MIL-STD-1629 in two meth-ods. A non quantitative method, method 101, identifies the effects of failure regarding severity, detectability, maintainability or safety. The critical analysis
Figure 3.2: Scatter strength and load distributions [3]
Figure 3.4: Load-Strength analysis example [14]
method, method 102, "includes consideration of failure rate or probability, fail-ure mode ratio and a quantitative assessment of criticality, in order to provide a quantitative criticality rating for the component or function." The failure mode criticality number Cmis defined by O’Conner as:
Cm= βαλpt
Where β is the conditional probability of loss of function, α the failure mode ratio, λp the part failure rate and t the operational time, or at-risk time
of an item. As stated earlier in this document, only repairable objects can have a failure rate. Non repairable items have a probability of survival over an expected life time. Therefore the failure mode criticality number is different for non-repairable items:
Cm= βα(1 − e−αt/M T T F)
Where MTTF is the mean time to failure. The summation of all failure mode criticality numbers of an item is called the item criticality number.
The process of the FMECA is according a worksheet which is followed as described by the standard. Using a computerised version of the required work-sheets, speeds up the process significantly and increasing accuracy and con-venience. Furthermore enables a computerised version of the worksheet the possibility to do quick tests with a variety input data and configurations. An example of a computerised worksheet, performed in FMECA PREDICTOR, is shown in Figure 3.5
3.4
FTA
The fault tree analysis, or FTA, is a method to receive insight in how failures are caused. Failures can be caused by individual events or a combination of events, categorised in different levels of failure in the FTA. FTA shows in a graphical manner the connections and levels of events according to standardised symbols, hence it shows the components which contributed to one specific failure [4].
A course with detailed application and information of the fault tree analy-sis can be found in Cursus Risico Analyse voor Werktuigbouwkundige
Ontwer-Figure 3.5: Load-Strength analysis example [14]
pers(dutch)[15]. Avontuur gives an example of a FTA on a hydraulic system, this system can be found in Figure 3.6.
Figure 3.6: Hydraulic system[2]
The result of the FTA performed on Figure 3.6 can be found in Figure 3.7, the failure mode is placed on top of the graph and is the top event.
The connections between events can be expanded with their probability. Enabling the option to determine the probability of a failure of a certain set of events. An FTA is only applicable for one main event, a shown on top of the FTA, so each failure mode requires its own FTA.
3.5
ETA
Even tree analysis, ETA, is a method that defines all states of a system. This method is very useful when a structure can partly fail and is still operational. Thus ETA is able to include redundant components. FTA is not a suitable technique for this situation since this method can only analyse a total failure of the system. ETA can only be used for analysing small sets of component, which is considered to be a disadvantage.
Figure 3.7: FTA of a hydraulic system[2]
failure mode, also called an event, which can be true or false. The reliability is determined by calculating the probability of each branch at the left side of the graph.
3.6
Multi-state system modelling
Large technical systems are commonly complex and therefore reliability assess-ment with the methods described so far can be very difficult. For multi-state systems, which are typically complex, a convenient method is system modelling by an asymptotic approach. The key benefit of this approach is that it does not require a complex, difficult to determine, initial formula for the system re-liability. The methodology described in this chapter is based on information found in Reliability and Safety of Complex Technical Systems and Processes [9] by Kołowrocki and Soszyńska-Budny and Reliability of Large and Complex
Figure 3.8: Event Tree Analysis example[2] Systems [8] by Kołowrocki
The approach identifies the system components and multi-state reliability functions. This requires determination of the mean values and variances of lifetimes in each state. The method is one of a mathematical nature and the following notations are defined by Kołowrocki and Soszyńska-Budny:
• n is the number of components
• Ei, where i = 1, 2...., n, are the components of a system
Each of the components within the system, and the system itself has a reliability state where 0 is the worst state and z is the best state. A reliability state can, by definition, only degrade in time.
• {0,1,....,z}, z ≥ 1
Furthermore the following notations are used:
• Ti(u), i = 1, 2...., n, are the independent random variables representing the
lifetimes of components Ei in the reliability state subset {u, u + 1, ...., z}.
while they were in the reliability state z at the moment t = 0
• Tuis a random variable representing the lifetime of a system in the
relia-bility state subset {u, u + 1, ...., z} while it was in the reliarelia-bility state z at the moment t = 0
• Ei(t)is a component Eireliability state at the moment t, t ∈ h0, ∞), given
that it was in the reliability state z at the moment t = 0
• St is a system S reliability state at the moment t, t ∈ h0, ∞), given that
is was in the reliability state z at the moment t = 0
Now the multi-state reliability function of a component Ei is formulated as:
Ri(t, · ) = [Ri(t, 0), Ri(t, 1), ...., Ri(t, z], t ∈ h0, ∞), i = 1, 2, ..., n,
where
Ri(t, u) = P (Ei(t) ≥ u | Ei(0) = z) = P (Ti(u) > t), t ∈ h0, ∞), u = 0, 1, ...., z,
Each system, or subsystem, has a critical state. The critical reliability state dictates the acceptable value of the risk function. The risk function is the prob-ability a system reliprob-ability state is worse than the critical state r, r ∈ {1, ...., z}, where the original state was z and the state can only degenerate:
r(t) = P (S(t) < r|S(0) = z) = P (T (r) ≤ t), t ∈ h0, ∞)
The reliability of a multi-state system can be structured according to a certain lay-out. The reliability structures with time degrading components as identified by Kołowrocki and Soszyńska-Budny are enumerated below.
• Series • Parallel • "m out of n" • Consecutive "m out of n: F" • Series-parallel • Parallel-series • Series-"m out of k" • "mi out of li"-series • Series-consecutive "m out of k: F" • Consecutive "mi out of li: F"-series
For each of these structures the reliability function is given by Kołowrocki and Soszyńska-Budny, additionally these functions are also given for compo-nents with an exponential reliability function.
By applying the Semi-Markov process a general probabilistic model of the systems operation process is constructed. This model gives the main character-istics of the system operation process. Kołowrocki and Soszyńska-Budny states that this requires the definition of the following items:
• Probability of the system operations process deviation at the initial oper-ation state
• Probability of the system operation process transitions between operation states
• Conditional distribution functions
• Conditional density functions of the systems operation process conditional sojourn times at the operation state
Examples of types of distributions that can be used to describe the probabilities in a suitable way can be found in paragraph 2.5.
Finding all exact parameters to adequately describe operation process, and judge what distribution should be used, is however very difficult.
pbl is the probability of process transition from operation state zb into the
operation state zlwhere b, l = 1, 2, ...., v. This is a matrix of probabilities where
b 6= lsince a that would not be a transition of an operation state.
The mean value of the system operation process conditional sojourn times (θbl) at a particular operation state can be determined for a specific distribution.
This value is defined as: Mbl= E[θbl].
Similar, the mean values of the system operation process unconditional so-journ times is defined as: Mb= E[θb]
Now the limit values of the system operation process transient probabilities at a particular operation state can be found by:
pb= πbMb v P l=1 πlMl , b = 1, 2, ...., v
Where π are the steady probabilities. The expected values of the total sojourn times of the system operation process at a particular operation state is calculated by:
E[ˆθb] = pbθ, b = 1, 2, ...., v
By linking the general system operation process model obtained by the Semi-Markov process to the reliability and safety model obtained by the asymptotic modelling approach, an analytical model of complex multi-state systems related to their operation process is generated.
Chapter 4
Reliability of a STS gantry
container crane
To propose a state of the art application of system reliability of a crane a ship to shore (STS) container gantry crane is used as an example. The Multi-state system modelling methodology as described in this document is followed to assess the reliability of an STS gantry crane. The analyses is strongly based on an example performed in Reliability, Risk and Availability Analysis of a Container Gantry Crane [16] which is performed according to the exact same methodology. The work of Soszyńska-Budny is used since all relevant required data is collected in this example by experts. An example with realistic real life data is preferred for educational purposes.
4.1
Crane lay-out
Ship to shore cranes operate in container terminals and transfer containers be-tween the quay and container ships. A transfer is called a move, so a move is the activity where a container is moved from the quay to the container ship or moved from the container ship to the quay. The first quay installed ship to shore crane was introduced in 1966 by Sealand [1].
An example of a typical STS crane can be found in Figure 4.1. This image is edited by Achterberg with numbers and letters identifying the main components and characteristics of the crane. For the reliability assessment in this chapter a crane with this typical lay out is used.
The STS crane has the following global parameters[11]: • A: Gantry span
• B: Outreach • C: Backreach • D: Lift height
Figure 4.1: Liebherr STS crane lay-out [1][11] • E: Clearance under sill beam
• F: Travel wheel gauge • G: Buffer to buffer
The STS crane has the following main components[1]: • 1: Main boom
• 2: Trolley • 3: Spreader • 4: Cabin
• 5: Water side leg • 6: Land side leg • 7: Cable reel • 8: Topping line • 9: Machinery house • 10: Beam • 11: Boogie set • 12: Wheels
The following three paragraphs refer to items that correspond with the com-ponents in Figure 4.1. The STS crane is designed to transfer standardised containers. The interaction between the crane and container is performed by the spreader unit (item 3). Each corner of the container is equipped with holes where twistlocks can lock the container to the spreader. The spreader is at-tached to the headblock, which is equipped with sheeves on top. By use of ropes going via the trolley (item 2) to the machinery house (item 9) the height of the spreader can be altered.
Movement of the trolley (item 2) enables horizontal positioning of the spreader unit along the main boom (item 1) and beam (item 10), this is a translation between water side and land side. The trolley is controlled via a rope system as well and is driving along a rail track located on the main boom and beam. The trolley is able to drive over the full length of the outreach (item B), gantry span (item A) and backreach (item C).
Horizontal translation along the quay is performed by driving the complete crane along a rail track. Each of the crane’s four legs are via a boogie set (item 11) equipped with a series of wheels (item 12). The wheels have a driving unit and can drive the crane along perpendicular rails. The distance between these rails is called the gantry span (item A). Transferring the crane along this track is required to change loading or unloading position and can be performed while a container is attached to the spreader.
As can be seen in Figure 4.1 the main boom (item 1) of the crane is equipped with a hinge point close to the water side leg (item 5). The angle of the boom can be altered from a horizontal position where the boom angle is equal to 0° to an upward position. When the main boom is in an upward position it is not possible to transfer containers from and to the ship since the trolley cannot drive on the track of the main boom. This upward position is required when the clearance under the main boom is not sufficient for large ships to pass or when the crane is driving along its rail track with insufficient clearance under the main boom. Transferring the crane along the rail track is possible with the boom in both positions, with or without a container attached to the spreader.
4.2
System analysis
The reliability of the system, the ship to shore gantry crane, is determined by the reliability of the crane’s subsystems. Soszyńska-Budny identifies the following subsystems which influence the reliability of the crane:
• S1:Power supply system
• S2:Control and monitoring system
• S3:Boom hoist system
• S4:Crane transfer system
Each of the subsystems consists of a number of components. In the next section the components per subsystem are given:
Power supply system (S1):
• E(1)
1 - High voltage cable from the power station to the crane
• E(1)
2 - Cable reel (Figure 4.1 item 7)
• E(1)
3 - Interior power supply cable
• E(1)
4 - Device transmitting energy from the high voltage cable to the
inte-rior power cable • E(1)
5 - Energy transformers (Figure 4.1 item 9)
• E(1)
6 - Low voltage interior power supply cable
• E(1)
7 - Relaying and protective electrical components
Control and monitoring system S2:
• E(2)
1 - Crane control software, analysing the situation and take action if
required. • E(2)
2 - Measuring and diagnostic device sending data about the crane state
to the software controller • E(2)
3 - Signal transmitter from controller to executing crane components
• E(2)
4 - Components that carry out the control orders
• E(2)
5 - Control panels (Figure 4.1 items 4 and 9)
• E(2)
6 - Control connections
Boom hoist system S3:
• E(3)
1 - Propulsion unit; engine, rope drum, transmission gear, clutch,
breaks, rope • E(3)
2 - Rollers and multi-wheels
• E(3)
3 - Main boom (Figure 4.1 item 1); Boom, hinge, locking mechanism
• E(4)
1 - Driving unit; engine, clutch, breaks, transmission gear, wheels
(Fig-ure 4.1 item 12), boogie set (Fig(Fig-ure 4.1 item 11) Loading and unloading system S5:
• E(5)
1 - Spreader unit (Figure 4.1 item 3); propulsion unit, headblock,
spreader, twistlocks, stabiliser unit • E(5)
2 - Trolley unit (Figure 4.1 item 2); propulsion unit, rails in main beam,
trolley
The subsystems of the gantry crane, are structured in a series lay-out as can be shown in Figure 4.2.
Figure 4.2: Subsystems scheme STS crane
4.3
Operation process
The reliability of the crane, its subsystems and the components is different for each operation state. Soszyńska-Budny identifies the following six operation states:
• z1: Standby with the power supply on and the control system off
• z2: Prepared either to start or to finish the work with the crane boom in
an upward position
• z3: Prepared either to start or to finish the work with the crane boom in
an horizontal position
• z4: Transfer the crane along the quay with the crane boom in an upward
position
• z5: Transfer the crane along the quay with the crane boom in an horizontal
position
• z6: Loading and unloading of a container with the crane boom in an
The identified states are operational states, hence transition from one state to one of the other states is possible. These transitions are a matter of proba-bility. The data required to fill the probability matrix for transitions between operational states, pbl, b, l = 1, 2, ...., 6, is obtained from statistical data by
Soszyńska-Budny and have fixed probabilities:
pbl = 0 0.648 0.336 0.008 0 0.008 0.525 0 0.373 0.093 0 0.009 0.105 0.111 0 0 0.118 0.666 0.417 0.583 0 0 0 0 0.005 0 0.220 0 0 0.775 0.012 0 0.628 0 0.360 0
It is evident the probability matrix shows a diagonal filled with probabilities equal to zero, this would not be a change of the operation state. Certain transi-tions of state will never occur since they are not physical possible, for instance the operation state transition from z6 to z2 or z4. Loading and unloading
con-tainers, z6, is only possible when the boom is in a horizontal (0°) position,
therefore a operation state transition to a state where the boom is in an upward position is impossible.
Figure 4.3: STS crane operation state transitions
All operation state transitions with a possibility unequal to zero are illus-trated in Figure 4.3. A double arrow means the transistion is possible in both ways, however the probabilities are not necessary equal. A single arrow repre-sents a transition that is only possible from one operation state to the other.
The mean values of the system operation process conditional sojourn times, Mbl= E[θbl], b, l = 1, 2, ...., 6, b 6= l, per operation state are defined.
Soszyńska-Budny presents the following data:
Mbl = − 456.98 36.86 50 − 3 7.89 − 9.12 1.55 − 16 5.50 4.34 − − 6.82 7.86 2 2.14 − − − − 10 − 2.9 − − 24.68 22.60 − 23.12 − 20.51 −
Now the mean values of the system operation process unconditional sojourn times can be calculated with Mb = E[θb]. Resulting in the following:
Mb ≈ 308.93 7.83 7.09 2.08 19.82 22.17
By determining the steady state probabilities the limit values of the system oper-ation process transient probabilities for each operoper-ation state can be determined by: pb= πbMb 6 P l=1 πlMl , b = 1, 2, ...., 6 Soszyńska-Budny founded the following values:
pb(t) = 0.6874 0.0187 0.0515 0.0005 0.0717 0.1702 T
4.4
Reliability and risk evaluation
By use of experts Soszyńska-Budny comes to four component reliability states of the ship to shore gantry crane. As discussed, 0 is the worst state a component can be in, and z is the best state, therefore z = 3 for a situation with four states:
• State 3: Fully effective operations
• State 2: Less effective operations due to ageing
• State 1: Less effective operations due to ageing and an increased danger level
• State 0: Not operational, destroyed
By definition reliability states can only degenerate. The critical reliability state is a measurement for the acceptable value of the risk function r(t), which is set by Soszyńska-Budny at r = 2. It is assumed, again by help of experts, all components are four-state components with exponential reliability distributions in each of the operational states.
In operation state z1the crane is standby with the power supply on and the
S1, the power supply system. This subsystem has n = 7 components which are
in series. Operation state z1is a four-state series system, the reliability function
for such multi-state system is given by Kołowrocki and Soszyńska-Budny. In operation state z2the crane is preparing to start or to finish the work with
the main boom in an upward position. This state is very similar to z3since only
the crane angle differs. Both states or composed of subsystems S1, S2 and S3.
Respectively the power supply system, the control and monitoring system and the boom hoist system. Subsystem S1 is, as discussed before, a series system
with n = 7 components. Subsystems S2and S3 are both series systems as well,
however S2 is composed of n = 6 components and S3 is composed of n = 3
components. The operation state z2 and z3 are series systems composed of
subsystems S1, S2 and S3.
Operation states z4 and z5 are also very similar, transferring either to or
from the loading and unloading area with the crane boom in a horizontal or upward position. Both states are composed of subsystems S1, S2, S3 and S4.
Respectively the power supply system, the control and monitoring system, the boom hoist system and the crane transfer system in a series layout.
Operation state z6is the loading and unloading of a container with the crane
arm angle of 0 degrees. This state is composed of subsystems S1, S2, S3and S5.
Respectively the power supply system, the control and monitoring system, the boom hoist system and the loading and unloading system, also in series.
For each of the operation states the expected values of the system conditional lifetimes in the reliability states is calculated by Soszyńska-Budny according to the reliability functions for a multi-state system given in Reliability and Safety of Complex Technical Systems and Processes[9]. Reliability state 0 is not deter-mined since the system is destroyed and not operational. The results, all values in years, are: µ1(1) ≈ 5.24, µ1(2) ≈ 3.79, µ1(3) ≈ 2.76 µ2(1) ≈ 1.93, µ2(2) ≈ 1.53, µ2(3) ≈ 1.13 µ3(1) ≈ 1.19, µ3(2) ≈ 1.52, µ3(3) ≈ 1.12 µ4(1) ≈ 1.83, µ4(2) ≈ 1.43, µ4(3) ≈ 1.05 µ5(1) ≈ 1.84, µ5(2) ≈ 1.46, µ5(3) ≈ 1.06 µ4(1) ≈ 1.62, µ4(2) ≈ 1.28, µ4(3) ≈ 0.98
Now the multi-state reliability function of the complete system can be deter-mined as can be found in Reliability and Safety of Complex Technical Systems and Processes by Kołowrocki and Soszyńska-Budny with the values and stan-dard deviations of the unconditional lifetimes. The reliability function is given by a vector, the coordinates are plotted by Soszyńska-Budny in Figure 4.4 with tin years.
In section 3.6 the function for the risk function is defined as: r(t) = P (S(t) < r|S(0) = z) = P (T (r) ≤ t), t ∈ h0, ∞)
Figure 4.4: Reliability function Rt,·coordinates[16]
The critical reliability state for this system was set to r = 2, therefore the risk function for the STS crane can be written as:
r(t) = 1 − R(t, 2)
The graph of R(t, 2) was already plotted in Figure 4.4. From this graph the risk function r(t) is plotted in Figure 4.5 with t in years.
Figure 4.5: Risk function r(t)[16]
With the risk function for the critical sate of the STS gantry crane known one can predict the crane availability. In Reliability, Risk and Availability Analysis
of a Container Gantry Crane [16] Soszyńska-Budny calculates expected value and standard deviation of the STS crane unconditional lifetime for reliability state r = 2 with the following results:
µ(2) ≈ 3.04years σ(2) ≈ 3.43years
The prediction of renewal and availability characteristics are determined for the system which is repairable in a situation where renovation time is ignored and a situation where renovation time is included. In the case this renova-tion time is included, the time required is according to a certain probability distribution. Soszyńska-Budny calculates the distribution for the duration un-til the next time exceeding the system reliability state including the expected value and standard deviation. Furthermore the distribution of the number of exceeding of the reliability state in time with the expected value and standard deviations is determined. Finally the distribution for the number of required renovations and a function for the system steady state availability is given. All this data combined provides the engineer with the relevant data for inspection of the crane.
Chapter 5
Conclusions and
recommendations
This document is written as literature assignment with the goal to research the system reliability of ship to shore cranes. After the basic theory a variety of common reliability analysis methods are described. Older methods found in lit-erature and described in this document are able to predict component reliability and the relibility of small systems. However these theories have difficulties to predict the reliability of large and often complex systems. Since the assignment demands a state of the art reliability assessment a more modern and mathemat-ical approach is introduced, the multi-state modelling.
The multi-state modelling methodology is explained. An example of a ship to shore gantry crane reliability assessment according this methodology found in literature is presented and supplemented. However, unregarded the chosen methodology, the quality and correctness of the reliability assessments in general are highly subjected to the available data. The crane operation data presented in this document are according to the author of the source of high quality since statistical data was available. Nevertheless, statistical reliability data on component level was much less thorough and predominantly based on experts opinions. The presented example showed the methodology of the reliability, risk and availability characteristics of the STS gantry crane and are not necessary representative for a real world problem.
A general conclusion from this research is that reliability of large systems is very difficult to predict and requires complex methodologies. Performing relia-bility analysis really is a specialised engineering task and extensive knowledge of both theory and the system itself is definitely required. Something that could only be obtained by years of experience in the field of system reliability.
All literature used during this research agrees that reliability assessments are very sensitive for engineering judgements and available data. Each reliability methodology is developed for a specific purpose with a certain philosophy, one could not simply give a general proposal for a reliability assessment. Mastering
reliability theory and use this to write a detailed plan for a complex system such as a ship to shore crane could literally be someone’s life work.
Chapter 6
Bibliography
[1] F.F. Achterberg. Trends in ship-to-shore container cranes. TU Delft, Mar-itime and Transport Technology, 2012.
[2] G.C. Avontuur. Reliability Analysis in Mechanical Engineering Design. Technische Universiteit Delft, 2000.
[3] A.D.S. Carter. Mechanical Reliability. The MacMillan Press Ltd., 1872. ISBN 333138317.
[4] E.J.Henley, , and H.Kumamoto. Reliability Engineering and Risk Assess-ment. Prentice-Hall Inc., 1981. ISBN 0-13-772251-6.
[5] M.H. Faber. Reliability based assessment of existing structures. John Wiley & Sons Ltd., 2000.
[6] Arnljot Høyland and M.Rausand. System Reliability Theory: Models, Sta-tistical Methods. John Wiley & Sons Ltd., 1994. ISBN 978-0-470-31774-7. [7] W van Hengel J.K. Vrijling and R.J. Houben. Acceptable risk as a basis
for design. Elsevier Science Limited., 1998.
[8] Krzysztof Kołowrocki. Reliability of Large and Complex Systems. Elsevier Ltd., 2014. ISBN 978-0-08-099949-4.
[9] Krzysztof Kołowrocki and Joanna Soszyńska-Budny. Reliability and Safety of Complex Technical Systems and Processes. Springer, 2011. ISBN 978-0-85729-693-1.
[10] E.E. Lewis. Introduction to Reliability Engineering. John Wiley & Sons Ltd., 1987. ISBN 04718119985.
[11] Liebherr Container Cranes Ltd. Technical Description Ship to Shore Gantry Cranes. Liebherr Container Cranes Ltd., 2014.
[12] M.Rausand and Arnljot Høyland. System Reliability Theory: Models, Sta-tistical Methods, and Applications. John Wiley & Sons Ltd., 2004. ISBN 047147133.
[13] Andrzej S. Nowak and Keven R. Collins. Reliability of Structures. McGraw-Hill Companies Inc., 2000. ISBN 0-07-048163-6.
[14] Patrick D.T. O’Conner. Practical Reliability Engineering. John Wiley & Sons Ltd., 1985. ISBN 047190659.
[15] C.G. Avontuur R.C.A. Beem and L.M.A. Claes. CURSUS RISICO ANAL-YSE voor Werktuigbouwkundige Ontwerpers. Bouwdienst Rijkwaterstaat, 1998.
[16] Joanna Soszyńska-Budny. Reliability, Risk and Availability Analysis of a Container Gantry Crane. Gdynia Maritime University, Gdynia, Poland, 2012.
[17] Shelemyahu Zacks. Introduction to Reliability Analysis. Springer-Verlag, 1992. ISBN 0-387-97718-X.
