IET Renewable Power Generation Research Article
Wind turbine reliability estimation for different assemblies and failure severity categories
ISSN 1752-1416 Received on 15th January 2015 Revised on 19th June 2015 Accepted on 28th June 2015 doi: 10.1049/iet-rpg.2015.0020 www.ietdl.org
Christos Kaidis 1 ✉, Bahri Uzunoglu 2, Filippos Amoiralis 1 1
MECAL Independent Experts, Capitool 15 NL-7521 PL, Enschede, The Netherlands Uppsala University, Campus Gotland, Cramergatan 3 SE-62167, Visby, Sweden ✉ E-mail:
[email protected]
2
Abstract: This study discusses the life-cycle analysis of wind turbines through the processing of operational data from three modern European wind farms. A methodology for supervisory control and data acquisition data processing has been developed combining previous research findings and experience from operational wind farms followed by statistical analysis of the results. The analysis was performed by dividing the wind turbine into assemblies and the failures events in severity categories. Depending on the failure severity category a different statistical methodology was applied, examining the reliability growth and the applicability of the ‘bathtub curve’ concept for wind turbine reliability analysis.
1
Introduction
With the continuous growth of wind power efforts have been made to optimise the cost of all the aspects constituting a wind power project. In general, operation and maintenance (O&M) costs constitute a sizeable share of the total annual costs of a wind turbine. For a new machine, O&M costs might easily have an average share over the lifetime of the turbine of approximately 20– 25% of total levelised cost per kWh produced – as long the WT is fairly new, the share might constitute 10–15% increasing to at least 20–35% by the end of its life [1]. The estimation of the cost of some aspects of O&M is straight forward (e.g. scheduled service) but for the unscheduled service and the spare parts replacements the prediction becomes more complicated. One of the major elements of the cost modelling of unscheduled maintenance is the reliability estimation for the wind turbines under discussion. This paper presents a methodology for making use of supervisory control and data acquisition (SCADA) data, extracting downtime events, categorising them and performing statistical analysis of the results using a different approach depending on the failure category.
2
Data processing
Information concerning the operation and maintenance of wind turbines can be derived from several different sources with the level of detail and the usefulness deferring .The scarcity of wind turbine failure data has been pointed out by several researchers in the past [2]. This was of the main reasons that the use of SCADA data was selected; SCADA data is easier to acquire and more easily manageable compared with hand-written maintenance logs. In this section the basis of the methodology is presented followed by a detailed description of the SCADA processing algorithm development. 2.1
Failure classification
Before starting a wind turbine reliability study it is important to define the event types that will be considered as failures and the way that the failure events will be classified. In this section the definitions of wind turbine taxonomy and failure are presented and explained.
IET Renew. Power Gener., pp. 1–8 & The Institution of Engineering and Technology 2015
Wind turbine taxonomy is a structure that names the main features of a wind turbine generator (WTG) in a standardised terminology [3]. The definition of taxonomy before starting a WTG reliability research project is necessary to define accurately failure locations and also describe turbines from different WTG manufacturers in a common way [4]. There have been several efforts of developing a wind turbine taxonomy differing on their principal structure and level of detail. The main criteria for the development of these taxonomies have been the information availability (so that the level of detail of the taxonomy will correspond to the level of detail of the information available) and the function of each component with the components performing the same function grouped together [5]. For this research the taxonomy developed for the ReliaWind project will be used because the most detailed wind turbine taxonomy available in literature (comprised of a total of 257 components) and was developed to focus on SCADA and service log data [3], a fact that meets the needs of this project which will focus on SCADA data and alarm logs for reliability analysis. Failure is defined to be the inability of a subassembly to perform its required function under defined conditions; the item is then in a failed state, in contrast to an operational or working state [5]. Moving from the general definition to implementing a reliability study limits should be customised to be precise on what will be considered a failure. In recent WTG reliability projects the limitations stated for a downtime event to be considered a failure were [4]: i. The total duration of the event is ≥1 hour ii. Human intervention is required to set the turbine back to operational state Other researchers have tried to quantify the severity of a failure event according to its duration by dividing failures in minor (duration ≤1 day) and major (duration >1 day) considering that for a failure event of duration longer than 1 day the service team will travel at least twice to the site [6]. The main difference compared with previous researchers is that this project does not pose any duration limit to the failure events, that is, failure events of total downtime ≤1 hour that required a manual restart are also taken into consideration. The reason for that is that failure events that require only a manual restart and can possibly last less than 1 hour (for an onshore and easily accessible
1
Table 1 O&M information sources and their usability O&M data type
Information derived
Disadvantages
A. Maintenance logs
† Accurate failure info † Information for downtimes † Cost of repair
† Sometimes available only in hardcopies † Can be difficult to read or incomplete
B. Operation and alarm logs
† Failures and duration
† Unknown alarm codes † Numerous stops for the same failure † No environmental conditions info
C. 10-minutes SCADA and Alarms
† Failure data † Information for further analysis (e.g. Root cause analysis) † Environmental parameters † Comparison/ verification of logs (if both available)
† Large amount of data, require time-consuming processing † Not all alarms indicate failures † No maintenance activity described
D. Service provider bills
† Maintenance cost † Indications for the kind of failures
† Less detailed info about failures
E. Component purchase bills
† Information for component replacements
† No downtime information † No failure information
wind farm) can be considered insignificant onshore but can cause long downtimes offshore were accessibility is a major issue. 2.1.1 Algorithm development: For this research project 10-minute SCADA data in combination with the relevant alarm logs were processed to extract the failure events of operational wind farms and perform further statistical analysis. More specifically, the following columns of the 10-minute SCADA data were used: SCADA counters (or timers), timestamp, power generated, average wind speed 2.1.2 Turbine state: Initially, the algorithm defines the state of the WTG according to the SCADA counters. The SCADA counters are indications showing how many seconds the WTG was in each state (operational, alarm and service) in every 10-minute span (thus taking values from 0 to 600); a relevant example is provided in Table 2. The three possible states that a WTG can be in are:
† Operational: When the WTG is generating or is capable of generating electricity. The turbine OK counter has values greater than 0 and the alarm counter is 0. † Alarm: When a failure has occurred and the WTG cannot perform its function. The alarm counter has values greater than 0. † Service: When repairing or maintenance action takes place. The service on counter has values greater than 0. The distinction between these different turbine states is mainly based on the SCADA counters but there are some special cases that are treated in a different way. They can be summarised as: † One of the alarm descriptions that appear when the WTG is in alarm state (according to the SCADA counters) is ‘Pause pressed on keyboard’. In this case the algorithm inserts a correction and the turbine is considered to be in service state since the description indicates the presence of a technician in the turbine. † There are cases when the WTG appears to be operating normally according to the SCADA counters (i.e. Turbine OK = 600), the wind speed is between cut-in and cut-out but the WTG is not generating energy. In these cases, the algorithm considers the turbine be in alarm state regardless the counter indication. 2.1.3 Short running periods: As short running periods are defined the situations when the WTG is in alarm state for a period of time, briefly operates again, returns to alarm state and eventually starts operating normally again. After examining some of these cases and comparing them with the relevant maintenance logs it was concluded that the alarm periods that are interrupted by short running periods in most of the cases belong to the same failure event. Thus, the short running periods are ignored and the events (alarm or service) before and after merged. The maximum duration of a short running period is one hour. Other authors mention similar events as ‘back-to-back’ events and consider them as separate failure events [7]. In Table 3 an example of a short running period is provided. 2.1.4 Event indicators: As event indicators are defined the moments when the WTG changes from one state to another. Depending on the initial and final state a different event indicator occurs. The event indicators are defined as (Fig. 1): † Service start: The WTG state changes from operational to service † Service end: The WTG state changes from service to operational † Pause start: The WTG state changes from operational to alarm † Pause end: The WTG state changes from alarm to operational † Pause end/service Start: The WTG state changes from Alarm to Service In the scope of this research project the total downtime is divided into ‘Alarm duration’ and ‘Service duration’. As alarm duration is
Table 2 Example of WTG state definition according to SCADA counters
Table 3 Example of short running period for a detected event
SCADA columns
SCADA columns
TimeStamp
Turbine OK counter
Service on
Alarm
Turbine state
TimeStamp
Turbine OK counter
Service on
Alarm
Turbine state
2009-06-01 09:50 2009-06-01 10:00 2009-06-01 10:10 2009-06-01 10:20 2009-06-01 10:30 2009-06-01 10:40 2009-06-01 10:50
600
0
0
Operating
0
0
600
Alarm
600
0
0
Operating
0
0
600
Alarm
100
0
500
Alarm
100
0
500
Alarm
0
0
600
Alarm
600
0
0
Operational
0
0
600
Alarm
600
0
0
Operational
0
400
200
Service
249
0
351
Alarm
0
600
0
Service
2010-06-27 03:00 2010-06-27 03:10 2010-06-27 03:20 2010-06-27 03:30 2010-06-27 03:40 2010-06-27 03:50 2010-06-27 04:00
0
0
600
Alarm
Flag
Short run Short run
IET Renew. Power Gener., pp. 1–8
2
& The Institution of Engineering and Technology 2015
The time limits were decided in cooperation with the WTG inspection team of MECAL. 1 hour was considered as the time needed to perform a visual check of the turbine and a manual restart without any repairing action. The division between Minor and Major repair was made under the assumption that a repair that needs the technician crew to be present for more than a working day (i.e. 8 hours) is a major one. Any repairing action that can be performed within a working day is considered a minor repair.
Fig. 1 Event indicators between WTG states
defined the initial logistic delay time, that is, the time needed from the moment the WTG stops until the first human intervention (Service state). When the WTG state changes to Service then the assumption that the repairing action lasts until the turbine starts operating normally again is made. For this reason, there is no event indicator for the state change from Service to Alarm state. Even though Service to Alarm can be observed, this does not indicate that the service action is terminated. Making this assumption information concerning logistic delay after the first service action (e.g. waiting time for spare parts, technicians unavailability) cannot be distinguished. Thus, the actual repairing time is possibly shorter than what is estimated as ‘Service duration’. 2.1.5 Downtime events: The purpose of defining the event indicators was to be able to distinguish and categorise the downtime events that occurred during the period the SCADA data of which is examined. The different types of downtime events are defined according to the event indicators as following: † Failure (pause start – pause end/service start – service end): A failure event starts when the turbine state changes to Alarm (Pause Start) followed by a downtime period until human intervention is detected (Pause End / Service Start) and ending when the WTG starts operating again. o The duration between pause start and pause end/service start is defined as ‘larm duration’ o The duration between pause end/service start and service is defined as ‘service duration’ † Auto-restart (pause start – pause end): Downtime event which is solved by the WTG itself or with a remote restart, without the natural presence of a technician needed. † Scheduled service (service start – ervice End): Downtime event during which the turbine was in service state without any alarm
2.1.6 Failure events: For the division of the failures to severity sub-categories the initial logistic delay (i.e. the time needed from the start of the failure event until the technician reaches the WTG) is ignored and only the service time is taken into consideration. With these assumptions the failure events are divided to three severity categories as shown in Table 4. Table 4 Failure categorisation Service time Manual restart Minor repair Major repair
≤1 hour 1 hour ≤ Service Time ≤ 8 hours ≥8 hours
IET Renew. Power Gener., pp. 1–8 & The Institution of Engineering and Technology 2015
2.1.7 Classification of failures to WTG assemblies: The 10-minute SCADA data are used as described in the previous sections of this chapter to define the failure events and categorise them according to their duration. Alarm logs contain additional information concerning the kind of the failures through the alarm numbers and descriptions provided by WTG Control and Communication System. The columns used from the alarm log are: event detected timestamp, error number, error description. To connect the information extracted from the 10-minute SCADA data with the alarm logs some data modifications were needed. The timestamp of the alarm log is given in accuracy of 1 min while the SCADA has 10-minutes accuracy. For this reason, the alarm log timestamp was rounded-up to the next 10 min timestamp. For each failure event the alarm that initiated the event is considered responsible for the failure, which means that the assembly from which the WTG Control System received a signal is considered the one that have failed. As pointed out also by other researchers, the fact that a failure occurred in a component does not necessarily mean that the component itself is responsible for the failure [8]. Further research that exceeds the scope of this project would be needed to identify the root cause of each failure. There have been cases that the 10-minute time span when a failure event occurred did not agree with the alarm log indication. In these cases the previous and next 10-minutes span was examined. If there still was no match the failure event defined by the SCADA data processing was marked as ‘unknown’. The categorisation of the failure events to the different parts of the WTG that they occurred was decided to be made at the assembly level of the taxonomy that was selected. The reasons for this choice are: † The available data for this project would not be enough to have enough failure events in each category of a more detailed level (sub-assembly or component) † The taxonomies used in previous research in wind turbine reliability are closer to the assembly level of the Reliawind taxonomy used for this project. Thus it would be easier to compare the results of this project with other results from literature. The alarm codes that appeared in the results of the SCADA data analysis were assigned to the different wind turbine assemblies. This was done according to the description given in the alarm log for each error code, additional information from the manufacturer (e.g. troubleshooting manual) when available and the experience of MECAL’s inspection crew.
3
Results of the SCADA analysis
The data analysis methodology described in chapter 2 was applied to SCADA data available in MECAL from three modern onshore European wind farms. The data used start from the commissioning of the wind farm having removed the first 2 months. It is common in new wind farms that during the first months after commissioning control adjustments and initial troubleshooting (mainly to fix installation issues) take place. In the wind farms under discussion there were several downtime events due to this reasons and since no detailed qualitative information was available (maintenance logs, service action description etc.) it was decided to remove this period of data. The details of the dataset used for the analysis are presented in Table 5.
3
Table 5 Dataset used for the analysis Wind farm A B C
Number of WTGs
Rated power, kW
Days of data
Turbine × days
23 36 4
3000 850–1750 2000
944 760a 1441
21,712 25,381 5764
a Some of the wind turbines in this wind farm have been erected earlier than the rest. Thus, for most of the WTGs there are 760 days of data available but for some others there is less data. On average, there are 705 days of data for each wind turbine
Due to confidentiality reasons, the wind turbine manufacturer could not be disclosed. The main technical characteristics of the wind turbines of the data set are: † † † † †
Pitch-regulated upwind turbines Active yaw Three-bladed rotor Hydraulic pitch Geared drive
From the total amount of failures that have been extracted by the data analysis, 17% could not be attributed to any assembly for one of the following reasons: † There was no relevant alarm for the time period that the SCADA data indicated a failure † The alarm related to the failure was not clearly indicating the assembly It should also be mentioned that the periods when the SCADA system was not available were removed from the data set. The amount of time when the SCADA system was not giving signals was less than 1% of the total data set.
For the results presented in this section the unknown failures have been removed. Thus, the percentages presented in Figs. 3 and 4 are percentages over the 83% of the failures that could be attributed to a wind turbine assembly. The downtime of the failure events identified for each WTG assembly was initially separated to the time when the WTG was in alarm state (logistic duration) and the time when repairing actions were performed (service duration). The results are shown in Fig. 2. The failure events identified were distributed to the WTG assemblies and were separated to failure types. The results are shown in Fig. 3. In Fig. 4 the distribution of the downtime to the WTG assemblies and failure event types is shown. In Fig. 3 it can be seen that the failures of electrical components are more frequent that those of mechanical components. This result can be justified by the age of the wind farms under discussion; in early life stages more failures of electrical assemblies are expected compared with mechanical failures that occur in later stages due to fatigue related issues. Another element to be taken into consideration is that the dataset examined is relatively small, thus case-specific problems can have a big influence on the outcome. For example, in one of the three wind farms examined in this project, high vibrations in the tower of the WTG resulted in downtime events that required a manual restart (Fig. 3). To the authors’ experience, this is not a common issue and in larger datasets the downtime events due to the tower are expected to be less.
4
Reliability analysis
The first research projects on wind turbine reliability [6] focused on counting the failure occurrence and extracting reliability results in terms of failure rates (failures per wind turbine assembly per year). This was mainly based on the assumption that the failure rate of wind turbine assemblies follows the ‘bathtub curve’ shape, that is, having a constant failure rate during the useful life period.
Fig. 2 Downtime distinction between service duration and Logistic duration
IET Renew. Power Gener., pp. 1–8
4
& The Institution of Engineering and Technology 2015
Fig. 3 Percentage of identified failures occurring per assembly and failure type for three wind farms
Fig. 4 Percentage of downtime occurring per assembly and per failure type for three wind farms
IET Renew. Power Gener., pp. 1–8 & The Institution of Engineering and Technology 2015
5
In more recent research projects efforts have been made to examine the evolution of the failure rate during the lifetime of a wind turbine. Spinato et al. used the power law process (PLP) to model the reliability growth of Danish and German wind turbines but also the reliability growth of several wind turbine assemblies [5]. In addition, Andrawus used the Weibull distribution to model the failures of operational wind farms examined [9]. Moreover, recent findings from failure data of two operational wind farms have demonstrated failure behaviour different than the bathtub curve. The author of that report expresses his doubts about the assumption of constant failure rate [10].
be considered that the condition of the turbine has improved after a manual restart and thus using a distribution would not be appropriate for modelling manual restarts. For modelling inter-occurrence of manual restarts the PLP model is used under the assumption that the system is ‘as-bad-as-old’ after the failure. For the power law the waiting time to the next failure, given a failure at time T, has distribution function (FT(t)) and rate of occurrence (μ(t)) respectively [14]: FT (t) = 1 − e−l·[(T +t)
b
−T b ]
(1)
m(t) = l · b · t b−1 4.1
In reliability engineering a probability distribution is used to describe one lifetime of a component and does not allow for more than one failure. Thus, it is required that no failures have occurred before time ‘t’ and after each failure the component is as good as new has subsequently been replaced by a new component [11]. Given these conditions, using a probability distribution is suitable for reliability analysis of non-repairable systems. One of the common mistakes is analysing inter-arrival data of failures for repairable systems [12]. A point process is a stochastic model describing the occurrence of discrete events in time or space. In reliability analysis, failures of repairable systems can be described with point processes [13]. 4.2
(2)
Probability distribution vs. point process
Methodology for different failure severity categories
For the statistical analysis of the failure events extracted with the use of the SCADA data processing algorithm, depending on the event type, the following methods were selected: † PLP model for the manual restarts and minor repairs † Weibull distribution for the major repairs That indicates that in the cases of Manual Restart and Minor Repair the wind turbine assembly was considered to have been brought back to the condition it was before the failure event. If the Weibull distribution was used for Manual Restarts or Minor Repairs, it would indicate that the assembly is starting a new operational life after the failure which is not a realistic assumption to make. 4.2.1 Statistical processing of manual restarts: Manual restarts of a wind turbine are failure events that require the presence of the technical crew but no repairing action takes place. The only intervention is rebooting the turbine controller. It cannot
A general maximum likelihood estimation for the parameters of the power law model is given by Crow in the AMSAA report no. 138 [15]. The parameters (β, l) are calculated by the equations: K
q=1 Nq b b q=1 (Tq − Sq )
l = K
K
b=
l·
K q=1
q=1
Nq
[Tq b · Ln(Tq ) − Sq b · Ln(Sq )] −
(3)
K q=1
Nq i=1
Ln(Xiq ) (4)
where, K: the number of systems (WTGs) examined; Sq: the starting time for each system; Tq: the end time for each system; Nq: the total number of failures for a system; X: the age of the system when the failure occurred. This statistical processing methodology was applied to two of the wind farms for which SCADA data was available. The failure rate function plot is shown in Fig. 5. 4.2.2 Statistical processing of minor repairs: Minor repairs are defined as the failure events for which less than 8 hours of repair time is required (Table 4). During these 8 hours it is considered that the WTG assembly is not entirely replaced by a new one but only corrective maintenance is performed and possibly components of the WTG assembly are replaced. The result of a Minor Repair is that the WTG assembly is back to operational state, in a better condition than it was before the failure but not ‘as-good-as-new’. A methodology to model imperfect maintenance of complex is suggested by Kallen using superposed renewal processes [16]. The aim of this project is to introduce a methodology for extracting WTG reliability information using only SCADA data and the relevant alarm logs. From this source of information it is
Fig. 5 Failure rate plot function, manual restarts
IET Renew. Power Gener., pp. 1–8
6
& The Institution of Engineering and Technology 2015
Fig. 6 Failure rate plot function, minor repairs
not possible to extract details on the extent of the repairing action performed. Thus, the application of a renewal process to model the Minor Repairs is beyond the scope of this research project. For this reason, the simplification that the WTG assembly is back to its original (before the failure event) state after a minor repair was made. Having made this simplification the methodology of modelling minor repairs was the same as in the case of manual restarts described in Section 4.2.1. Because of the relatively small turbine population and time length of the sample used for this report, the minor repairs for each wind farm are grouped together to estimate the parameters of the PLP model. Though, it is suggested to model the minor repairs of each assembly separately if a larger dataset is available. From the current dataset the PLP model was applied to the minor repairs of
the pitch system which was the most critical assembly (and thus the amount of minor repairs was sufficient for the analysis). The results for the minor repairs in the two wind farms under discussion are presented in Fig. 6. 4.2.3 Statistical processing of major repairs: For the major repairs the assumption that the assembly is ‘as-good-as-new’ after the repairing action is considered realistic to be made. In this case there is no inter-occurrence of failure events but a new lifetime of the assembly starts after each major repair. Thus, the major repairs can be modelled with the Weibull distribution. For the estimation of the Weibull shape and scale parameters (β, l) ‘Dr. Bob’s reliability calculator’, an Excel-based tool developed by NASA was used [17]. Because of the relatively small turbine
Fig. 7 Weibull probability plot for major failures of pitch system of wind farm A
IET Renew. Power Gener., pp. 1–8 & The Institution of Engineering and Technology 2015
7
population and time length of the sample used for this project only major failures of assemblies for which there was sufficient number of events. Especially for wind farm B for which the dataset was shorter no more than 2 major failures were detected for the same assembly. Thus, it was considered of little statistical value to perform Weibull analysis in such a small sample. The Weibull Probability plot for the major failures for the pitch system of wind farm A is presented in Fig. 7. The horizontal orange line denotes the 63,2nd percentile to calculate the characteristic life (η parameter). The slope of the plot (red line) indicates the shape parameter
5
Conclusions
In this research project an algorithm was created to extract the failure history with the use of 10-min SCADA data and the relevant Alarm logs. Following the data processing, the results went through a different statistical analysis process depending on the failure type. The following conclusions can be drawn: † Processing SCADA data only (along with the alarms logs) can provide a sufficient description of the failure history. 83% of the failures were identified for the three wind farms examined in the project. † The assemblies with the higher failure frequency in the wind farms examined were the pitch system, the frequency converter and the control and communication system. † The assemblies that cause the longer downtime in the wind farms examined are the frequency converter, the pitch system and the power electrical system. † Wind turbine assemblies which are complex systems operating in very different conditions. Consequently, the bathtub curve for their failure rate should not be taken for granted and should be analysed on base-to-base cases. † Using the Weibull distribution and NHPP can model reliability more precisely and if the failure rate is constant it can be
concluded (then we get an exponential distribution and HPP respectively).
6
References
1 EWEA: ‘Costs & prices’, Wind Energy Facts, 2010, 2, pp. 100 2 Wennerhag, P., Bertling, L.: ‘Wind turbine operation and maintenance, Survey of the development and research needs’. Vindforsk III, Elforsk report 12:41, Stockholm, 2012 3 Tavner, P.: ‘Offshore wind turbine: reliability, availability and maintenane’ (The Institution of Engineering and Technology, 2012) 4 Wilkinson, M.: ‘Measuring wind turbine reliability – results of the reliawind project’. European Wind Energy Association Annual Event, Brussels, 2011 5 Spinato, F., Tavner, P., van Bussel, G., et al.: ‘Reliability of wind turbine subassemblies’, IET Renew. Power Gener., 2009, 3, (4), pp. 387–401 6 Faulstich, S., Hahn, B., Tavner, P.: ‘Wind turbine downtime and its importance for offshore deployment’, Wind Energy, 2010, 14, (3), pp. 327–337 7 Peters, V.A., Alistair, O.B., Bond, C.R.: ‘Continuous reliability enhancement for wind (CREW) database: wind plant reliability benchmark’ (Sandia National Laboratories, Livermore, 2012) 8 Tavner, P., Xiang, J., Spinato, F.: ‘Reliability analysis for wind turbines’, Wind Energy, 2007, 10, (1), pp. 1–18 9 Andrawus, J.A.: ‘Maintenance optimisation for wind turbines’. PhD Thesis, The Robert Gordon University, Aberdeen, 2008 10 Buckley, S.: ‘Forecasting wind farm component failures and availability post-warranty’. EWEA Annual Event, Vienna, 2013 11 Crow, L.H.: ‘Practical methods for analyzing the reliability of repairable systems’, Reliability EDGE, 2004, 5, (1), pp. 4–9 12 Hacker, L.: ‘Avoiding a common mistake in the analysis of repairable systems’, Reliability EDGE, 2004, 7, (1), pp. 3–8 13 Tavner, P.: ‘Offshore wind turbines. Reliability, availability and maintenance’ (The Institution of Engineering and Technology, London, 2012, 1st edn.) 14 NIST/SEMATECH: ‘e-Handbook of statistical methods’, April 2012. Available at http://www.itl.nist.gov/div898/handbook/apr/section1/apr172.htm, accessed August 2013 15 Crow, L.H.: ‘Reliability analysis for complex, repairable systems’. Technical report No. 138, U.S. Army Material Systems Analysis Activity, Aberdeen Proving Ground, Maryland, 1975 16 Kallen, M.J.: ‘Modelling imperfect maintenance and the reliability of complex systems using superposed renewal processes’, Reliability Eng. Syst. Safety, 2011, 96, (6), pp. 636–641 17 NASA: ‘NASA official website’, 2013. Available at http://kscsma.ksc.nasa.gov/ Reliability/Default.html, accessed 6 August 2013
IET Renew. Power Gener., pp. 1–8
8
& The Institution of Engineering and Technology 2015