After-sales services optimisation through dynamic opportunistic maintenance: a wind energy case study

After-sales services optimisation through dynamic opportunistic maintenance: a wind energy case study A. Erguidoa,b, A. Crespo Márquezb, E. Castellanoc, J. L. Floresd aDepartamento de Organización Industrial y Gestión de Empresas I, Escuela Superior de Ingenieros, Universidad de Sevilla. bIK4-Ikerlan Technology Research Centre, Operations and Maintenance Technologies Area, 20500 Gipuzkoa, Spain cMIK Research Centre, Mondragon University, 20560 Gipuzkoa, Spain dDependable Embedded Systems Area, IK4-Ikerlan Technology Research Centre, Gipuzkoa, Spain *Asier Erguido (corresponding author) [email protected] +34 943 712 400 Adolfo Crespo [email protected] +34 954 487 215 Eduardo Castellano [email protected] +34 943 718 009 Jose Luis Flores [email protected]s +34 943 712 400 Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was performed within the context of the SustainOwner (‘Sustainable Design and Management of Industrial Assets through Total Value and Cost of Ownership’), a project sponsored by the EU Framework Programme Horizon 2020, MSCARISE- 2014: Marie Sk1odowska-Curie Research and Innovation Staff Exchange (RISE) (Grant number 645733-Sustain-Owner-H2020- MSCA-RISE-2014) and the EmaitekPlus 2017–2018 Program of the Basque Government. After-sales services optimisation through dynamic opportunistic maintenance. A Wind energy case study. Journal Title XX(X):1–13 ©The Author(s) 2017 Reprints and permission: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/ToBeAssigned www.sagepub.com/ Asier Erguido1,2, Adolfo Crespo2, Eduardo Castellano3and Jose Luis Flores4 Abstract After-sales maintenance services can be a very profitable source of incomes for original equipment manufacturers (OEM) due to the increasing interest of assets’ users on performance-based contracts. However, when it concerns the product value-adding process, OEM have traditionally been more focused on improving their production processes, rather than on complementing their products by offering after-sales services; consequently leading to difficulties in offering them efficiently. Furthermore, both due to the high uncertainty of the assets’ behaviour and the inherent challenges of managing the maintenance process (e.g. maintenance strategy to be followed or resources to be deployed), it is complex to make business out of the provision of after-sales services. With the aim of helping the business and maintenance decision makers at this point, this paper proposes a framework for optimising the incomes of after-sales maintenance services through: 1) implementing advanced multi-objective opportunistic maintenance strategies that sistematically consider the assets’ operational context in order to perform preventive maintenance during most favourable conditions, 2) considering the specific OEMs’ and users’ needs, and 3) assessing both internal and external uncertainties that might condition the after-sales services’ success. The developed case study for the wind energy sector demonstrates the suitability of the presented framework for optimising the after-sales services. Keywords After-Sales Services, Life Cycle Cost, Uncertainty Assessment, Dynamic Opportunistic Maintenance, Multi-Objective Optimisation, Wind Energy Sector 1 Introduction After-sales service is fast becoming a key instrument in the relationship between the Original Equipment Manufacturers (OEM) and the assets users. In general, assets users are more frequently asking for such services, and the OEMs are willing to satisfy them due to the several benefits that they are able to obtain, such as: recurrent stream of revenues generated throughout the life cycle of the assets, which usually exceeds the profit margins of new equipment sales1; extra value added to sold equipment, used as a competitive differentiator2; increase of the assets users’ satisfaction and loyalty3,4, etc. Accordingly, many OEMs have already successfully integrated the after-sales services within their business, having transformed it in a business core2. Nevertheless, some others, such as machinery fabrication companies, have traditionally been more focused on new equipment design and sale rather than on offering after-sales services to their clients; having now difficulties in properly deploying such services5. The main problems when defining the after-sales services arise when the key factors that drive the system performance have to be identified and their influence on operational availability has to be meassured6. Furthermore, there are several uncertainty sources that have to be dealt with during the after-sales services deployment, such as cost or repair processes, which make it difficult to guarantee a determined service level and a price for providing it7,8. In this context, the development of maintenance models plays a key role, since they enable to calculate the quality of the after-sales service (through reliability, availability and maintainability analysis), and the cost associated to that service (through life cycle cost (LCC) analysis); allowing to find a trade-off between the service level to be offered and its price. Moreover, when such maintenance models are developed, the impact of uncertainty sources can also be meassured, accurately providing the decision-maker with the necessary information to anticipate the risks to be handled within the after-sales service contracting. Accordingly, the after-sales service success and the satisfaction of every stakeholder involved in the contract will be fostered. To the best of the authors knowledge, there is not previous research that 1) categorises the uncertainty sources to be dealt within the after-sales services, 2) analytically derives 1IK4-Ikerlan Technology Research Centre, Operations and Maintenance Technologies Area, 20500 Gipuzkoa, Spain 2Departamento de Organización Industrial y Gestión de Empresas I, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, España 3MIK Research Centre, Mondragon University, 20560 Gipuzkoa, Spain 4IK4-Ikerlan Technology Research Centre, Dependable Embedded Systems Area, 20500 Gipuzkoa, Spain Corresponding author: Asier Erguido, IK4-Ikerlan Technology Research Centre, Operations and Maintenance Technologies Area, 20500 Gipuzkoa, Spain Email: [email protected] Prepared using sagej.cls [Version: 2016/06/24 v1.10] 2Journal Title XX(X) Figure 1. Proposed approach (figures are shown in detail during the paper) their impact in terms of both the after-sales service level and its profitability and 3) provides managerial insights illustrated through a numerical experiment based on realfield data, enriching its practitioning approach. Therefore, it is the aim of this paper to address these specific issues, for which different steps have been taken, classified into 3 main phases (see Figure 1): 1. Problem definition. Within this phase the maintenance problem is defined, identifying the maintenance constraints for deploying the after-sales service and the main objectives of both the OEM and the asset user. Likewise, the maintenance policy to be followed during the after-sales service is established and the main uncertainty sources are identified. 2. Simulation-based optimisation. Simulation techniques are used in order to handle the several stochastic processes to be born within the after-sales maintenance services and to evaluate the different strategies9,10. Since both the interests of OEM and assets users should be met by the defined after-sales maintenance services, a multi-objective metaheuristic is implemented for finding the efficient frontier of the service level vs cost curve (non-dominated optimal maintenance strategies), in a simulation-based optimisation approach11. 3. After-sales Service optimisation. Before offering the after-sales service, the asset users are characterised and their requirements are identified. Based on the two previous phases and with the aid of a sensitivity analysis, the impact of uncertainty sources on the aftersales service is analyzed, in order to be able to assess the economical risk of the after-sales service to be offered. The paper is organized as follows. In section 2 a brief summary of the literature is performed. Section 3 addresses the uncertainty impact and assessment on the after-sales service. In section 4 the system model for managing the after-sales services in the wind energy sector is developed. In section 5 the computational results based on real field data are shown. Finally, section 6 summarizes the main conclusions of the research and establishes future research lines. 2 State of the art The present work is associated with multiple literatures, but the three most directly related literatures are on aftersales services, uncertainty assessment and maintenance optimisation models (specifically applied to the wind energy). 2.1 After-sales services To date, the literature has distinguished two different types of after-sales services6,7: material contract and Performance Based Contracting (PBC). While under a material contract the asset users pay to the OEM the services related to the maintenance activity (i.e. spare parts or labour time), under the PBC a service level of the assets is ensured by the OEM at the asset user site. Traditionally the most traditional service agreements have been related to material contracts. However, the paradigm is currently changing to PBC, due to the interest of assets users on the availability of their systems, rather than on the resources used for maintaining them7. Therefore, on this new context, the asset users will explicitly define the service level that they require, and the OEMs will determine how to fulfill that requirement13, e.g. defining their after-sales maintenance strategy. The most widely used PBC payment forms can be classified as fixed or variable price: 1. Fixed payment method. There are two basic approaches according to the uncertainty related to the sold asset14: fixed price, where the OEM assumes all the risk of the contract (asset with lower uncertainty), and cost plus fixed price, where the risk is assumed by the asset user (asset with higher uncertainty). In both cases, the OEMs will prefer to minimize the LCC of the commited service in order to maximize their profits15. 2. Variable payment methods. The OEMs will be awarded if certain goals related to the service level are Prepared using sagej.cls Erguido et al. 3 Figure 2. Uncertainty framework for after-sales services, adapted from12 achieved. Thus, OEMs will be focused on maximizing both their interests and the asset users’ interests16. In wind power industry, maintenance activities are usually performed by the OEM under a material contract, which implies lucrative revenues for the OEM. Nevertheless, such contract model generates financial pressures on the wind farmers and does not ensure the OEMs’ efforts on improving their assets’ reliability, which suggests that a change of paradigm to PBC will be given14. Under a PBC, the asset users would be able to focus on their core business (delivering reliable and clean energy), while the OEMs would keep longer service agreement14. 2.2 Uncertainty assessment There are plenty of uncertainty sources that might condition the after-sales service, jeopardising its success, and thus, the OEMs’ profits and assets ussers’ service level7. These uncertainty sources might be classified in endogenous, when the OEM has influence over the uncertainty source to a greater extent (technology, data quality, system model accuracy, etc.), and exogenous, when there is lesser influence over them (political and cultural context)17. Both endogenous and exogenous uncertainties should be considered within the uncertainty analysis. However, the decision-makers’ efforts should be rather focused on minimising the formers12 in order to reduce the risk of the after-sales service deployment; understanding the risk as the effect of uncertainty impact on OEMs’ and assets users’ objectives18. Generally, these uncertainties, which are quantified through statistical analysis and confidence or tolerance intervals19,20, should be assessed in industrial practice at different levels12 (see Figure 2): 1. The system model, which aims to numerically describe the real industrial problem and obtain some outputs (variables of interest) according both to fixed and uncertain inputs (developed in Section 4). 2. Uncertainty sources, which might appear both in the inputs parameters and in the system model, and will propagate the uncertainty until the output (respectively studied in Sections 3and 5). 3. Actions related to the decision making process regarding the feedback process based on the analysis of the uncertainty impact on the quantities of interest (see Section 5). Likewise, the general goals when assessing them can be classified in12: to understand the influence of uncertainty on model in order to improve the decision making-process; to accredit a certain level for accepting the use of a model; to compare relative performance and select the best maintenance policy or operation of the system; and to comply or demonstrate that a certain criterion is met. For the present research, the main goals will be related to identify and assess the main uncertainty sources related with the after-sales services, mainly generated by the maintenance processes and strategies adopted7. Therefore, it will be possible to meassure the risk of the different after-sales services to be deployed, comparing them and selecting the most appropriate one. Likewise, as a further result, the decision-maker will be able to rank the uncertainty sources, and thereby guide their decisions in order to reduce them. 2.3 Maintenance optimisation models As stated, in order to succesfully structure the after-sales service, it is necessary to develop adequate maintenance Prepared using sagej.cls 4Journal Title XX(X) Table 1. Nomenclature and Acronyms definition Nomenclature LCC Life Cycle Cost LP Loss of Power OF Objective Function WF Wind Farm WT Wind Turbine FM Failure Mode CM Corrective Maintenance PM Preventive Maintenance OEM Original Equipment Manufacturer AU Asset user TTF Time To Failure MT Maintenance Team vtAverage wind speed in period t GPtGenerated Power in period t RP Rated Power of the WT Rik(VA)Reliability of system i and FM k at virtual age VA SRTikj Fixed Reliability Threshold for applying perfect or imperfect PM jon system iand FM k SRTikjt System Reliability Threshold in period tfor applying perfect or imperfect PM jsystem iand FM k DRTik Fixed Dispatch Reliability Threshold DRTikt Dispatch Reliability Threshold in period t VWind speed threshold for determining reliability thresholds variation pPeriods of time considered for wind speed forecasting wik Reactivity weight KNumber of FM considered for each system JLevels of PM types considered for each FM GRP Generalized Renewal Process VA hikt Virtual age associated to FM kin system iin WT hin period t ↵ik Weibull scale parameter of FM kof system i ik Weibull shape parameter of FM kof system i qpr ikj Restoration factor of jPM level on system ifor FM k qc ik Restoration factor of CM on system ifor FM k NT Number of MTs cc ik Cost of tools and materials needed for performing CM of FM kin system i cpr ikj Cost of tools and materials needed for performing PM j of FM kin system i cteam Cost of MT cet Extra time cost cdisp cost of maintenance dispatch cna cost of No Availability or opportunity cost cpPenalty cost due to unplanned maintenance mc ik Maintainability of CM for FM kin system i mpr ik Maintainability of PM for FM kin system i CCapacity of each MT (in hours) NTmax Maximum number of MTs TMaximum iteration periods models that find the efficient frontier of the service quality vs cost curve2. Wang’s comprehensive review21 about the maintenance optimisation models classifies them into two main categories: single-unit systems and multiple-unit systems. In both cases, the maintenance decision making process relies on the usual indicators, such as, assets’ age, reliability, number of failures, etc. However, the formers tend to overlook the fact that the assets are very complex, consisting of several systems and subsystems, which can present economical, structural or stochastic dependences among them that condition the maintenance performance (see22). In this context, multiple-unit maintenance policies, which consider such dependencies, enable to find more suitable maintenance solutions21. Accordingly, there has been a growing interest in the utilisation, modelling and optimisation of such maintenance policies. It is the case of opportunistic maintenance, which due to its capacity for including short term information in order to improve maintenance performance23, has been widely researched lately24. According to Ba et al.25, the short term information included within the opportunistic maintenance can be both regarding internal, e.g.. assets dependences, and external factors, e.g. production schedule. In the specific context of the after-sales service offer, external factors play a key role, since beyond the dependences among the assets, the needs of the assets users should be continuously regarded within the maintenance decision making process. On the particular case of the wind energy sector, opportunistic maintenance policies have been widely researched as well, mainly favoured by the economical dependences among the wind turbines26. Nevertheless, to date, researches on opportunistic maintenance in the wind energy sector have been mainly related to the internal factors, rather than to external factors: redundancies27, condition monitoring systems26,28,29, multi-level maintenance30,31, etc. Therefore, on this specific research, the novel dynamic opportunistic maintenance prosposed by the authors has been adopted, since it enables to consider both internal and external factors, more suitable for the after-sales service context. 3 Uncertainty assessment on the after-sales service In order to be able to manage the several uncertainty sources that might jeopardize the success of the afer-sales service deployment, the framework for assessing the uncertainty in industrial practices proposed by Rocquigny et al.12 has been adopted and particularised for this specific application in Figure 2. In the particular case of the after-sales services, the propagation and impact of the uncertainty sources in the variables of interest should have a double perspective, since the output of the model should consider both the OEMs’ and the asset users’ interests, which could respectively be the minimization of service cost and minimization of service disruptions (see Figure 2). Figure 3illustrates the impact that the uncertainty sources might have in practice: whereas the model should give an after-sales strategy that optimises both the OEMs and the assets users interests (non-dominated solution), in the practice, this solution will not be so accurate -due to the Prepared using sagej.cls Erguido et al. 5 (a) Uncertainty influence on OEM s’ and Asset Users’ Interests (b) Service Appeal for the asset user VS Risk of the after-sales service success Figure 3. Uncertainty impact on the after-sales service uncertainty sources-, being probable to provide a final output that does not meet stakeholders’ interests. Accordingly, the uncertainty might lead to different scenarios depending on the output variables results: both the OEM and the asset user are satisfied, neither of them are satisfied, or only one of them is satisfied (see Figure 3a). Since every stake has to be satisfied by the after-sales service in order to consider it successfull, it is essential to meassure the impact of the uncertainty sources within the interest variables; otherwise the success of the after-sales service will be jeopardised. This impact, which in Figure 3 has been represented through the diameter of the circle, can be meassured by analyzing the joint probability distribution function of the interest variables (see Figure 2). The OEM should be aware of this uncertainty impact within the definition of the after-sales service, in order to search an scenario where both the OEM and the asset user are satisfied. In fact, decisions very conservative from the OEM perspective (higher service cost, lower service level) might lead to an after-sales service less appealing for the asset users, and viceversa (see Figure 3b). Thus a trade-off should be found between offering an appealing service for the assets users and a successfull after-sales service. Furthermore, once the OEM is able to quantify the uncertainty impact, they will be able to rank the uncertainty sources according to their impact on the variables of interest through sensitivity analysis. Consequently, they will be able to focus their research efforts on reducing these uncertainties and their impact, specially regarding the endogenous uncertainties, and offering more appealing and less risky after-sales services in the future. 4 System model for managing after-sales services in the wind energy sector On this section, the whole system for managing the aftersales service in the wind energy sector is modelled, defining the specific problem, maintenance policy to be followed, deriving the analytical formulation of OEMs and asset users quantities of interest and the optimisation problem. 4.1 Problem definition The wind farm (WF) consists of Hwind turbines (WTs) of similar characteristics that have Ncritical systems connected in series. Each system might fail in kdifferent failure modes (FMs) classified according to their severity (k=1,2,...,K), for which in case of failure, kcorrective maintenance (CM) will be performed. Likewise, prior to a failure occurrence, systems can undergo different preventive maintenance (PM) levels, either perfect or imperfect (j=1,2,...,J). When the PM activity restores the system to an operational condition worse than the new one but better than just before the maintenance task is performed, it will be considered an imperfect action. However, if the PM restores the system to an operational condition as good as the new one, i.e. replacement, it will be considered a perfect action (see32 for further information). Accordingly, in this research j=J is considered a perfect repair and j=1the most imperfect repair. Among the several studies that have investigated the restoration effect of maintenance (see32), the Generalized Renewal Process (GRP) proposed by Yañez et al.33 is specifically utilised in the present problem. The GRP provides flexibility for modelling both the behaviour of the systems before failures and the quality of repairs during the different life stages of the systems by the definition of two main concepts (see Eq.1): • Rejuvenation parameter (qij =[0,1]), which is associated to the efficiency of the restoration effect of the maintenance activity jon the system i(q=0for the most imperfect maintenance and q=1for perfect maintenance) • Virtual age (VA), which identifies the system’s age after being repaired, and thus, it’s reliability. Prepared using sagej.cls 6Journal Title XX(X) VA new i=VA old i(1 qij)(1) Accordingly, after an imperfect repair, failure probability distribution conditioned to the survival of the new virtual age is calculated through Eq.2. Due to the suitability of the Weibull distribution when modelling the WTs’ systems’ reliability34,35, Eq.2has been ad hoc particularized in Eq.3 according to the scale (↵ik)and shape parameters (ik)that define the Weibull distribution for each FM kof system i(the reader is addressed to33 for further information): F(t|VA new i)=P[Tij t|Tij >VA new i] =F(t)F(VA new i) 1F(VA new i)(2) R(t|VA new hik )=1F(t|VA new hik ) =exp "✓VA new hik ↵ik ◆ik ✓t ↵ik ◆ik #(3) Likewise, both fixed and variable maintenance costs are considered in the problem. According to the formers, performing any maintenance implies a relevant dispatch cost (cdisp), a material cost (cc ik,cpr ik ), an opportunity cost (cna) in terms of not produced energy, a penalty cost (cp)in case a failure hinders the distribution of commited energy, and an extra cost (cet) regarding outsourced maintenance activities if there are not own resources available for performing CM. In fact, own human resources, which consist of a number of maintenance teams (NTmax) with a certain capacity (C), are considered to be the main fixed cost (cteam). Both own and outsourced resources will directly depend on the required time to repair the systems, according to the maintainability of each FM (mc ik,mpr ik ). Finally, without loss of generality, some assumptions have been made for the problem formulation: 1. Degradation processes of the systems are considered independent from each other and they are associated to the operation time (ageing systems, with increasing failure rate). 2. Data pooling procedure has been followed for performing the reliability analysis, since the fleet of WTs within a WF can be considered identical according to the coupling factors proposed by Stamatelato et al.36 3. Reliability of the FMs follows the Weibull distribution, with scale parameter ↵and shape parameter . 4. Maintenance activities should be finished during the period of time in which they are started. 5. A maintenance dispatch is considered per period of time, where several maintenance teams (MTs) can be dispatched. 6. PM is assumed to be less resource-consuming than CM. 7. WF maintenance managers make decisions in discrete time and frequently37. 4.2 Dynamic opportunistic maintenance policy In this study, the dynamic opportunistic maintenance policy proposed by the authors38 is followed, since it enables to consider within the maintenance decision making process short term information regarding both internal and external factors, through the economic dependency among the WTs39,40 and their specific operational context respectively. To this aim, the maintenance decision making process relies on two different dynamic reliability thresholds levels, which will release the maintenance activities based on the reliability of the FMs (see Figure 4): • Dispatch reliability threshold (DRTikt): it determines whether a maintenance team should be preventively dispatched to the WF for performing PM, ensuring a minimum reliability for each FM and system. • System reliability threshold (SRTikjt): once a maintenance team has been dispatched to the WF, it determines whether PM level jshould be performed during period tfor preventing FM kof system i. The novelty of the dynamic maintenance policy remains on systematically considering the operational context of the assets, dynamically recalculating the reliability thresholds’ value in order to release the maintenance activities during most suitable operational contexts. In the particular case of the wind energy case study, there are several reasons for trying to avoid the performance of PM during high wind speed periods:1) WTs must be stopped during PM, 2) the profits of the WF are directly related to the wind speed41 and 3) maintenance activities should be released during low wind speed periods for workers’ safety42. Accordingly, the dynamic maintenance policy proposed is focused on fostering the PM activities’ release during low wind speed periods by increasing the reliability thresholds; and on the contrary during high wind speed periods, where PM activities’ release is hindered by decreasing the reliability thresholds. Therefore, usually two conflicting objectives to be born in the wind energy sector are achieved43: to reduce the wind energy power losses while reducing the total maintenance cost. In order to define the thresholds variation with regards to the specific operational context, it will be determined by the following factors (see Eq.4-6): 1. Wind speed threshold (V): determines if the reliability threshold should be decreased or increased by analyzing the forecasted wind speed for the next p periods; if the mean of forecasted wind speed is above Vthe threshold will be decreased in order to hinder PM, and on the contrary if it is below V(Eq.6). 2. Generated power (GPt)and reactivity weight (wik): determine the gradient of the reliability thresholds, being directly proportional to the difference between the generated power at each time period (GPt)and the rated power of WTs (RP)(Eq.4,5). SRTikjt =SRTikj +(2Wt1) ·SRTikj ·wik ·(RP GPt+RP ·Wt )(2Wt1) (4) Prepared using sagej.cls Erguido et al. 7 (a) Decision-making structure for the dispatch of the maintenance teams (b) Decision-making structure for performing PM. Example with 3 PM levels per FM Figure 4. Decision-making structure for the dynamic opportunistic maintenance model DRTikt =DRTik +(2Wt1) ·DRTik ·wik ·(RP GPt+RP ·Wt )(2Wt1) (5) Wt=(1Pt+p l=t vl pV 0Pt+p l=t vl p>V (6) 4.3 LCC and LP analysis In order to make profits from the after-sales service, the OEMs should be able to accurately estimate both the whole LCC of their assets and the service level that they are able to offer to the assets’ users, concerning among others: reliability, availability and maintainability (RAM). Accordingly, the main costs to be born in the wind energy sector regarding maintenance and after-sales service, i.e. CM, PM, dispatch and human resources costs, and the offered service level, through the energy-based availability, have been analitycally derived in this Subsection. According to the CM and PM cost (see Eq.7and Eq.8 respectively), material and tools requirements ⇣cc ik,c pr ikj⌘ and costs due to non availability caused by maintenance have been considered, according to the downtimes ⇣mc ik,m pr ikj⌘ and the non-generated power during the maintenance period (GPt), modelled as in Karki and Patel41. Whereas in the CM a penalty cost should be considered for commited but not provided power (cp), in the PM the unique cost associated to the non-available periods is the opportunity cost of not being producing energy (cna). As in other reviewed studies44,45, the cost of imperfect maintenance has been associated to the restoration factor of the maintenance activity (q). zhikt·hcc ik ·(qc ik)2+mc ik ·GPt·(cna +cp)i(7) yhikjt·cpr ikj·⇣qpr ikj⌘2+mpr ikj ·GPt·cna(8) Likewise, every time that maintenance has to be performed, a maintenance team should be dispatched to the WF (Eq.9), which implies a cost cdisp. Accordingly, a number of maintenance teams (NT)will be internally hired at a cost (cteam)by the company in order to perform maintenance. However, if a failure happens and there are no own maintenance teams available for maintenance, external resources (ETt)should be hired at an extra cost (cet)(Eq.10). (t+✓t)·cdisp (9) ETt·cet +NT ·cteam (10) Thereby, considering the long term nature of the LCC analysis, for which the cost has to be properly updated to present value according to the interest rate (ka), the LCC can be defined as follows (Eq.11). LCC (DRTik,SRTikj )="X t (t+✓t)·cdisp X hX iX kX t zhikt hcc ik (qc ik)2+mc ik ·GPt(cna +cp)i+ X hX iX kX jX t yhikjt cpr ikj ⇣qpr ikj⌘2+mpr ikj ·GPt·cna X t ETt·cet +X t NT ·cteam#·(1 + ka)t(11) As stated, the OEM should as well be aware of the service level that is able to provide at the mentioned cost. Particularly, in the wind energy sector the service level can be meassured according to the lost power (LP)46 (Eq.12). Prepared using sagej.cls 8Journal Title XX(X) Table 2. Intermediate Binary variables utilised in the model zhikt =8 > < > : 1if CM k is performed in system i of W T h in period t 0otherwise ✓t=(1if a MT is correctively dispatched to W F in period t 0otherwise yhikjt =8 > < > : 1if P M j is performed in F M k of system i of W T h in period t 0otherwise t=(1if a MT is preventively dispatched to W F in period t 0otherwise LP =X t GPt· X hX iX k mc ik ·zhikt+ X hX iX kX j mpr ikj ·yhikjt1 A(12) 4.4 Dynamic opportunistic maintenance optimisation model The general mathematical formulation of the considered dynamic OM policy (see Figure 4) will take the following form, considering the DRT and SRT modelling (Eq.15-17); only a maintenance per WT at a time Eq.18); and the overal long term maintenance strategy performance according to LCC (Eq.11) and Lost Power (LP) (Eq.14): OFOEM =Minimize LCC(X)(13) OFAU =Minimize LP(X)(14) S.T. 0DRTik SRTik1... SRTikj  ... SRTikJ 1i✏I, k✏K, j✏J;t✏T(15) 0wik 1i✏I, k✏K(16) 0DRTikt SRTik1t... SRTikjt  ... SRTikJt 1i✏I, k✏K, j✏J;t✏T(17) X j yhikjt +zhikt 1h✏H, i✏I, k✏K, t✏T(18) zhikt,y hikjt✏{0,1}h✏H, i✏I, k✏K, t✏T, 8j=1,2 4.5 Multi-objective Simulation-based Optimisation: NSGA II Several stochastic processes have to be born within the maintenance model, such as failure occurrence, repair processes and weather conditions; which difficults to analitically solve the presented maintenance problem30,44. Thus, in order to accuratelly evaluate the different maintenance strategies and find optimal solutions, most of the problem has been firstly analitically derived, and secondly implemented in simulation techniques, as commonly done in other researches31,44,47. Particularly, an agent-based simulation has been modelled due to its suitability to handle engineering problems with multi-agent systems48, such as the wind energy sector. The simulation process modelled can be summarized in 6 main steps (see Figure 5): Figure 5. Simulation process for LCC and Energy-based availability evaluation Step 1. In the simulation initialization the parameters needed for the selection of the maintenance policy and the solution of the maintenance problem are specified. On the one hand, the formers will determine the after-sales service management, namely: reliability and wind speed thresholds, number of maintenance teams, etc. On the other hand, the latters will condition the maintenance solution that are not under the influence of the decision-maker, such as: FMs’ failure and maintainability distributions or costs related to maintenance. Step 2. The simulation clock and virtual age of each FM of the systems are updated, identifying their new reliability according to their age (Eq.3). Likewise, the dynamic Prepared using sagej.cls