Review on Energy Resilience

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International Journal of Production Economics

journal homepage: www.elsevier.com/locate/ijpe

A simulation-based optimization approach evaluating maintenance and spare parts demand interaction effects James M. Wakirua,∗, Liliane Pintelona, Peter N. Muchirib, Peter K. Chemwenoc a Centre of Industrial Management/Traffic and Infrastructure, KU Leuven, Celestijnenlaan 300, 3001 Heverlee, Belgium b Department of Mechanical Engineering, Dedan Kimathi University of Technology, Nyeri, Kenya c Department of Design, Production and Management, University of Twente, Drienerlohaan 5, 7522 NB Enschede, Netherlands

A B S T R A C T

Industrial facilities frequently experience significant production losses due to unanticipated failures, sub-optimal maintenance, operational and spare parts logistics challenges. These among other factors directly affect the plant's performance measures such as availability, repair time and costs. Consequently, optimization addresses such challenges. However, a fundamental problem presented here relates to the need for a framework that assists in the determination of critical system to be optimized, variables that significantly impact the performance of such systems, and subsequently undertake optimization. To realistically model such com- plexities, a framework that applies the discrete simulation model of critical repairable subsystems, undergoing deterioration is proposed. The study utilises empirical maintenance data, where Pareto analysis is employed to identify critical subsystems, while expert input is incorporated to derive model variables. A full factorial Design of Experiment (DOE), is employed to establish the variables with significant main and interaction effects on the total repair time and subsequently employed as decision variables for a simulation-based optimization. The proposed framework is demonstrated in a case study of a thermal power plant. Simulation results highlight the turbocharger as the critical subsystem, while spares availability, the time between overhaul (TBO) and reliance on different maintenance strategies exhibit most significant main and interaction effects. The optimization results obtained demonstrate that TBO, spares availability and reliance on various main- tenance strategies, provide a significant impact on the reduction of the repair time. The framework enhances maintenance decision making by optimizing the plants' operational and maintenance related factors identified.

1. Introduction

1.1. Background

It is essential industrial facilities such as power plants can supply electric power to the population consistently without interruptions. This requirement is amplified when a plant supporting critical in- stallations, such as in the health and security sectors, where an inter- ruption, could lead to significant risks along with both social and eco- nomic losses. Moreover, most facilities supplying utility grids maintain contracts specifying hefty penalties in the event of deviation from the supply agreement, which makes it imperative for such power plants to address factors likely to cause interruption of power production and supply. Besides natural disasters and short-supply of consumables like fuel, downtime retains a pivotal role in contributing to power produc- tion interruption. A growing body of literature recognizes the sig- nificant role of maintenance-related downtime, contributing to power plant downtime and subsequently, reduced profitability (Alabdulkarim et al., 2011; Bouslah et al., 2018). It follows that addressing main- tenance-related downtime will considerably reduce power generation interruptions and Operational and Maintenance (O&M) cost. A survey

carried out by Jardine and Tsang (2013) reports that maintenance budgets on average are 20.8% of the total plant operating budget. In- tegrating such measures would ultimately drive the facility towards achieving the expected plant economics due to savings in maintenance and operational costs. Optimal maintenance leads to maximized effi- ciency and productivity as well as reduced waste in both equipment and personnel usage, which leads to the significance of joint optimization modelling of maintenance, inventory, and manpower also suggested by Van Horenbeek et al. (2013). Distinct from maintenance strategies optimization, operational and other aspects such as inventory man- agement, manpower planning, procedures and outsourced main- tenance, likewise require to be optimized to ensure successful plant operations. While addressing these aspects, consideration of main- tenance quality is vital, because it is influenced by various aspects, while it impacts the equipment reliability and consequently reduced productivity.

1.2. Notations

Throughout this paper, the following notations are adopted.

https://doi.org/10.1016/j.ijpe.2018.12.014 Received 12 April 2018; Received in revised form 11 October 2018; Accepted 11 December 2018

∗ Corresponding author. E-mail address: [email protected] (J.M. Wakiru).

International Journal of Production Economics 208 (2019) 329–342

Available online 13 December 2018 0925-5273/ © 2018 Elsevier B.V. All rights reserved.

T

Decision variables Ao Engine operational availability Tr Total repair time (hrs. per year) Model parameters i Number of maintenance actions n Subsystems modelled =n {1,2,3,4,5} FSj Failure severity for jth severity level

n Random time to next failure for nth subsystem Tdi Random diagnosis time for ith maintenance action (hrs.) Tdn Total diagnosis time for n

th subsystem (hrs.) Tln Total lead-time for nth subsystem (hrs.) Oc Number of Outsourced contractors t Simulation time (hrs.) tstn Initial time to failure for nth subsystem j Severity levels as per ISO 14224:2016; =j {1,2,3,4}

i Impact factor for ith maintenance action I Engine operating time/Running hours γ, β, η Location, scale and shape parameters for WEIB (λn) f Spares availability or spares fill-rate Ri Maintenance actions ( =i i; {1,2,3,4,5}) Trn Total repair time for nth subsystem (hrs.) Tri Random repair time for ith maintenance action tbo Time between overhauls (TBO) tn Simulation time (years) Mtech Mechanical technicians DT Downtime (hrs.)

1.3. Study aim and motivation for the research

Power plant system reliability represents an essential factor in the success of a power generation project. A decline in reliability due to critical equipment downtime directly affects both, the availability to generate power and consequently its profitability. Increased downtime can be attributed to several reasons influencing O&M aspects such as increased failure frequency, protracted lead times in sourcing critical spares, imperfect maintenance, human errors in diagnosis and main- tenance, and lack of enough maintenance personnel. These factors de- monstrate a significant impact on the installation's economics, tactical and strategic planning. The factors above, both individually as well as interactively affect maintenance, where optimizing them would im- prove the availability of a given power plant and reduce repair and subsequent maintenance time, hence improving the economics and performance of the plant. Moreover, in the plants that retain main- tenance records, deriving maintenance optimization programs utilizing knowledge embedded in this data is not straightforward. The primary challenge faced by many practitioners is the establishment and selec- tion of significant optimization variables affecting equipment perfor- mance, from the empirical data, and further implementing an optimi- zation of the variables. The challenge of undertaking maintenance optimization based on significant decision variables derived from em- pirical data, with the objective of offering maintenance decision sup- port, presents the motivation to this study.

This study proposes a discrete event simulation (DES) model fra- mework that considers the utilization of empirical maintenance data to derive critical subsystems, modelling parameters, and variables. We model a repairable system, whose deterioration is assumed to follow a Semi-Markov Decision Process (SMDP). Design of Experiment (DOE) approach is utilized to quantify the effects and interactions of the variables on equipment availability and total repair time. Markedly, optimization is performed applying the identified significant variables, with an objective of minimizing the total repair time. DES is utilized due to its robustness in dealing with complex, highly variable and un- certain events as a decision support tool also corroborated by (Alrabghi and Tiwari, 2015).

The remaining part of the paper proceeds as follows: Section 2 presents a brief literature review of relevant studies, while Section 3 describes the methodology used for this study. Section 4 presents the

results, with a brief evaluation, whereas a summary discussion is pre- sented in Section 5. Finally, Section 6 contains concluding remarks and the proposed future work.

2. Relevant literature review

The British Standards Institute defines maintenance as, “a combi- nation of all technical, administrative and managerial actions during the life cycle of an item destined to preserve it in or restore it to, a state in which it can fulfil the required function” (EN13306, 2010). This definition enlarges the sphere of maintenance, to cover various tasks encompassed in Corrective Maintenance (CM) and Preventive Main- tenance (PM) that incorporate administrative and managerial actions, such as manpower management, spares sourcing and logistics. System reliability, influenced by deterioration, and maintenance strategies performed owing to equipment failure, are critical factors to the reali- zation of a plant's objectives, and overcoming various operational challenges (Jardine and Tsang, 2013). Stochastic models such as Markov models (MM) have proven more robust, in modelling dete- rioration and failure of equipment owing to their probabilistic nature (Nguyen et al., 2013). Semi-Markov Decision Process (SMDP), contrary to MM which is memoryless, calls for the memory of the process to be renewed each time it attains a state (Dehayem Nodem et al., 2011). Other Markov models, such as time-based Markov models are limited to dealing with time as a deterioration factor. Both the prior severity and the particular maintenance action carried out regarding its quality and harshness, can influence the deterioration of various equipment. An age reduction coefficient can be used to represent the actual influence of maintenance and deterioration on the equipment, (e.g., Duan et al., 2018), or a hazard rate adjustment factor (e.g., Xia et al., 2017). To abate the impact of deterioration on equipment, inspections, CM, PM and Overhaul actions are carried out (Bouslah et al., 2018; Rivera- Gómez et al., 2016). However, due to diverse factors, some organisa- tions outsource these maintenance actions, either, to focus on their competencies, or due to technological advances or lack of the required competencies (de Almeida et al., 2015). In an assessment of PM con- tract maintenance, Wu (2012) proposes two types of outsourcing, where type I, both CM and PM are outsourced and type II, only CM is outsourced.

Another significant aspect of maintenance is the often utilization of spares in both PM and CM actions hence the importance of joint or integrated maintenance and spare policies optimization. Integrated studies considering joint optimization of maintenance strategies and spares/inventory policies, predominantly have focused on specific as- pects, such as, evaluating optimal PM optimization (e.g., Lei et al., 2010), optimal production plan (e.g., Ba et al., 2016), optimal in- ventory holding (e.g., Cai et al., 2017), optimal maintenance policy (e.g., Nguyen et al., 2014). Nevertheless, some studies address diverse aspects, for instance, Rezg et al. (2005), presented integrated modelling and optimization for a randomly failing production unit. Similarly, Lei et al. (2010) presented a modularized Stochastic Timed Petri-Nets (STPNs) model, for system level PM optimization and dynamic main- tenance decision making. Gharbi and Kenné (2005) advanced simula- tion and experimental design to determine the optimal control policies and values of input factors while minimizing total cost of inventory, repair, and PM. Zohrul Kabir and Farrash (1996), presented a simula- tion model seeking for a joint determination of optimal age replacement and spare part provisioning policy, while Sarker and Haque (2000), developed a simulation model for a system operating with block re- placement and continuous review inventory policy. However, much of the research addressing PM (e.g., Roux et al., 2008; Van Horenbeek; Pintelon, 2013), disregard the effect of CM-related failure on the system, which undoubtedly impacts on the equipment reliability, hence affects PM actions and outcome. Moreover, failures addressed using CM, are considered to incorporate spare replacement and following two states “as good as new” (AGAN) and “as bad as old” (ABAO), (e.g.,

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Dijoux et al., 2016; Rivera-Gómez et al., 2016), which does not offer a comprehensive representation of CM actions that may have repairs with or without spare replacement, with random reliability outcome.

Another significant challenge found in considerable studies is the employment of one-factor-at-a-time (OFAT) analysis while analyzing the impact of various factors on the plant performance measures as previously indicated. Subsequently, these results are applied in main- tenance decision support, while disregarding their interactive char- acteristics. As Antony et al. (2003) alludes, despite its popularity, ease of use and precision on the effect of one variable, OFAT offers less precise estimates, it does not consider interrelationships (i.e. interac- tions) and cannot be used in optimization, challenges overcome by the design of experiments (DOE) technique. Similarly, Bouslah et al. (2018) suggest the interaction effects play an essential role to obtain an op- timal trade-off solution while considering an integrated control policy. While considering previous optimization studies in maintenance, it is becoming exceptionally challenging to overlook the interactive effects of various O&M aspects, on the plant's performance.

As regards evaluating the plant's performance, several factors, for instance, repair time taken, availability of manpower resources and logistical challenges involved in spare sourcing, and others, adversely affect the plant's availability (Nguyen et al., 2013). Due to the complex dynamic characteristics of these variables and their interrelationship, the use of classical analytical models in optimization is unsustainable. Hence, the use of simulation techniques, an approach which is also corroborated by various studies (Alrabghi and Tiwari, 2016; Nowakowski; Werbińka, 2009; Rezg et al., 2005), while, Sharma et al. (2011) accentuate that the use of simulation in maintenance optimi- zation has been increasing steadily. Several studies reviewed in this field employing simulation are highlighted in Table 1.

Surprisingly, the lack of carefully examining the effects of CM is noted, where most studies consider minimal repair towards bringing a component back to the previous operating state. This aspect is seen perhaps not a complete representation of both maintenance and spare policies, that potentially address component reliability and degradation challenges, both under PM and CM. Additionally, CM failures which are addressed by various maintenance and spare strategies consequently demonstrate an impact on the PM strategy, due to fundamental and observable reliability changes on the system impacted by the CM ac- tions.

Furthermore, the studies assumed perfect maintenance and con- sidered only one CM maintenance action, i.e. replacement of the failed item. This aspect may not offer a realistic maintenance analysis, be- cause repair actions may not always justify spare replacement, which restricts the research to perfect maintenance. Despite the importance of imperfect maintenance, which mimics real maintenance scenarios, there remains a paucity of evidence on the application of aspects im- plying imperfectness such as imperfect maintenance, imperfect re- placement, and failure diagnosis time, also alluded by Van Horenbeek et al. (2013).

While performing maintenance optimization, most of the studies lack a systematic framework for selecting variables that significantly affect the objective measure, which is subsequently considered as control variables in the optimization program. Such frameworks should

consider the interactive effects, where several statistical methods such as full factorial analysis and analysis of variance (ANOVA) offer the means to address this aspect. For instance, Bouslah et al. (2018) em- ployed ANOVA, to illustrate the interactions of variables, while estab- lishing variables that were significant in an integrated production, quality and maintenance control policy.

The first contribution of this paper is to fill the gap in the literature, by developing an integrated framework, derived from empirical data, for the joint optimization of maintenance and spares policy. Specifically, we consider maintenance on different engine subsystems, subject to imperfect maintenance and reliability degradation. The cri- teria used to select the subsystems, represent the impact to the system performance, in this case, downtime, an aspect corroborated by (Alrabghi and Tiwari, 2015). Moreover, most studies have dwelt on multiple systems, for example, several engines in a plant, whereas our study deals with subsystems within one single engine. The distinctive effect of respective subsystems, such as failure and deterioration, have been overlooked in such models, which may lead to generalized and uncomprehensive optimization solutions. In this case, subsystems are inter-linked to form a system, for instance, a power plant engine, has the cylinder, governor, fuel and turbocharger subsystems, which have unique operational and failure characteristics.

Secondly, this paper considers the reliability degradation of distinct subsystems, which typically require the prescription of clear CM stra- tegies. This distinction may not be forthcoming due to imperfect maintenance (imperfect diagnosis and repair) and alternative options available. Hence, the need to explore the value of several maintenance strategies simultaneously, that can be prescribed to the failed sub- systems, which is seldom done in research while modelling imperfect maintenance of deteriorating subsystems (Lei et al., 2010).

The third contribution of this paper aims to make the selection of significant variables affecting the maintenance performance measures more judicious, by involving expert assessment and employing statis- tical techniques to quantify their effects and interactions. Notably, this study will address the aspect of systematic selection of significant variables subsequently employed in a maintenance optimization pro- gram. Key plant performance indicators, such as, spares availability, maintenance strategy reliance, and others derived from the empirical data and agreed upon with the plant maintenance team, are subjected to this process.

Lastly, we employ the significant variables as decision variables in a simulation-based optimization with an objective of minimizing the total repair time. A case study approach is adopted to obtain in-depth in- formation and capture the complexities brought by the different vari- ables, derived from plant's empirical data.

3. Methodology

The methodology consists of several steps. Data collection, pre- processing and exploration represent the first and second step respec- tively. The third step incorporates identification of the model output parameters, while key input variables for the simulation model are extracted in the fourth step. The simulation model is developed and subsequent experiments performed in the fifth step. The simulation

Table 1 Sample summary of simulation-based articles-joint maintenance and spares optimization.

Article Variables investigated/affecting performance

Li et al. (2013) Manpower planning Alabdulkarim et al. (2011) Manpower availability, equipment usage, spares fill rate. Accurate fault diagnosis Savsar (2015) Maintenance policies - age-based (ABP) and block based (BBP) de Smidt-Destombes et al. (2007) Maintenance interval, the spare part inventory level and the repair capacity Scarf and Cavalcante (2012), Maintenance quality (inspection induced defects, quality of PM and replaced component) Duan et al. (2018) Maintenance quality Bouslah et al. (2018) Maintenance, quality, and Production-inventory policies

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experiment results are evaluated and interpreted in the sixth step. In this step, significant variables to be employed in the optimization are determined. Finally, the seventh step addresses the implementation of a simulation-based optimization.

3.1. Data collection

In this study, the analysis uses maintenance data describing failures recorded from thermal power plant engines, over a five-year period. Each equipment or engine (fuel oil-driven) consists of several inter- linked subsystems such as a governor, exhaust, cylinder and turbo- charger. The data contains, subsystem failure occurrences, separate maintenance actions carried out, and components details, such as the date and time of both the failure occurrence and repair finalization. To address inconsistencies, the International Standards Organization - ISO 14224 steps, were followed during pre-processing. In this step, various components were linked to their respective subsystem, while expert consultations were employed where clarity was needed.

3.2. Data exploration

Following the maintenance data exploration, several aspects are considered towards enabling modelling of the study.

3.2.1. Critical engine subsystems selection The power plant engine was decomposed into subsystems, from

which the four critical subsystems were selected based on failure fre- quency and the individual contribution to the power lost in megawatts- hours (MWhr) using Pareto analysis. The fifth critical subsystem item- ized as ‘others’ incorporated summation of all the remaining sub- systems.

3.2.2. Maintenance actions – Ri and subsystem state modelling Five maintenance actions employed in data exploration were clas-

sified following the ISO 14224:2016 classification and categorised on estimated time incurred by the action as corroborated by the main- tenance team. See Table 2.

The state of each subsystem is depicted by two variables, a discrete stochastic state FSj which take the values {1,2,3,4} denoting the op- erational state, in terms of severity at time t, and impact factor i (hazard rate adjustment factor) which takes a value between 0 and 1, and controls the changes of n at time t. In this case, we assume that the stochastic state of the subsystem is dependent on the stochastic prior state FSj and the maintenance action Ri carried out as discussed in the next section.

3.2.3. SMDP modelling of failure severity states Failure severity FSj, is the impact due to Ri on a subsystem, de-

picting the seriousness or harshness of a failure. This was used to de- termine the reliability measure attained by a subsystem following a respective Ri and subsequently used for diagnosis whilst selecting ap- propriate Ri by the maintenance team. While employing SMDP, FS1 is depicted as causing minor production stop, FS2, moderate, FS3, severe and FS4, an extensive stop in production/operation, as adopted from (ISO 14224:2016, 2016). Low FSj is assumed to have low Tri , while high FSj to have high Tri due to the intense maintenance action Ri required.

Fig. 1 illustrates an example where ideally a subsystem retaining FS2, should be diagnosed to undergo R2, but due to imperfect diagnosis, there is the possibility of undergoing one of the other Ri apart from R5 (mandatory for all subsystems during overhaul). For the purpose of analysis, the assumption is considered that due to imperfect main- tenance, FS2 undergoing R2, transitions to FS3, whereas, if perfect maintenance was considered (not in this case), it could transition to FS1. Following this process, a specific FSj stochastically transitions to a posterior state between low FS1 to high FS4. The scheduled overhaul maintenance reduces the failure severity to FS1 with some probability of FS2 which mimics a renewal state (near AGAN) with stochasticity. This process is modelled for all the FSj with possibilities of subjection to all the Ri.

The operating severities. =FS j; {1,2,3,4}j The finite maintenance actions. =R i; {1,2,3,4,5}i

3.3. Model output parameters

The model considers two performance measures of interest as the outputs. Firstly, the engine operational availability Ao, is the proportion of time the engine is running compared to total time including down- times due to failures and overhaul (PM). We use the running hours I against the total running length (includes running hours and down- time). Secondly, total repair time Tr , is the total value of the repair time, accrued by the engine (five subsystems) on purely CM repair processes. This time value excludes the spare sourcing lead-time Tl and diagnosis time Td delays incurred during the CM activities. The assumption of PM actions having pre-planning therefore, no lead times involved. Equations (3)–(5) provide an annualized average time value based on tn , which is more intuitive compared to the planning horizon of the plant.

= +

A I I DTo (1)

= + +T T T Tm d r l (2)

= =T T

tr k n

r

n

1 k

(3)

= =T T

td k n

d

n

1 k

(4)

= =T T

tl k n

l

n

1 k

(5)

3.4. Model parameter extraction

Several model parameters derived for the critical subsystem's ana- lysis include; the time to the initial failure generation tstn, which re- present the time the first failure of a respective nth subsystem occurred. The reliance factor/utilization probability i, for the different Ri, was computed from the subsystem failure frequency, while the mean time to repair Tri , was derived from the maintenance action time classifications using a uniform distribution (due to the classification entailing minimum and maximum time). A probability distribution was fitted for the better random forecast of maintenance interventions that utilized more than 13 h, to represent R4. The tbo and Tr5, that characterize R5,

Table 2 Maintenance actions classification based on ISO14224:2016.

Ri Maintenance action Description

i = 1 Do almost nothing Incorporate minor adjustments, may not cause a stoppage, e.g. tightening i = 2 Minor Incorporate spare replacement bringing the subsystem back to an operational state i = 3 Moderate Both moderate and major repair actions incorporate logistical lead times during spares sourcing and repair actions i = 4 Major i = 5 Overhaul PM action for whole engine overhaul as per the maintenance schedule

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were derived from the PM planning manual of the engine. The main- tenance team identified Tdn, the estimated time a failed subsystem will incur while being diagnosed to indicate the type of FSj, hence identify the appropriate intervention or Ri . The time to next failure n, for each subsystem, fitted to a probability distribution, was established by computing the time between repairing the subsystem to operable state up until its next failure. Spares availability f, also referred to as fill-rate or instantaneous reliability of spares (Louit et al., 2011), was provided by the plant supply chain, as the estimated probability of the plant holding spares stocks on hand to deal with the maintenance require- ment. Sourcing lead-time Tl for both local and imported spares, was derived similarly from the plant supply chain. In the instances requiring spare sourcing, the maintenance data included information on both actual repair and spare sourcing lead times amalgamated, without differentiating the two. Hence, to derive the actual repair time Tr in the model, we subtracted the estimated spare sourcing lead time Tl from the combined actual repair time plus spare parts sourcing lead times de- rived from empirical data. Therefore, due to the derivation and mod- elling of this aspect, it is expected that Tl will have an impact on Tr values. An outsourced contractor Oc, is partially involved in the PM (specialised activities), is constrained to working solely during the daytime shift.

3.5. Modelling

A discrete event simulation modelling framework is developed which mimics the system normal running I until failure occurrence and subsequent CM repair action undertaken, while PM is carried out after a time interval tbo. A i ranging from 0 to 1, was introduced for esti- mating the subsystem hazard rate adjustment factor (impact of the maintenance action on the n) in each Ri. The extreme values ρ = 0 depict ABAN, while ρ = 1 construe AGAN. SMDP was employed to model the stochastic deterioration process of the subsystems, based on the specific maintenance actions Ri, where initial FSj values were ran- domly assigned to the subsystems and posterior FSj generated as dis- cussed in Section 3.2.3. During the modelling step, the following as- sumptions are made:

1. Maintenance actions are imperfectly performed, hence, the equip- ment state does not attain “as good as new” (AGAN) state after maintenance intervention.

2. We consider that two or more subsystems cannot fail simulta- neously, because, a single subsystem failure, causes the engine stoppage.

3. Concerning the principle of FSj transition, we consider only the imperfect maintenance action and the stochastic failure severity of

the subsystem. 4. The availability of maintenance technicians is not a constraint. This

is because the expert analysis and interviews revealed that the technicians were shared from a pool, hence their availability was not viewed as a constraint.

5. PM incorporates a modularized design for the subsystem's main- tenance characterized by spare replacement. Thus, PM is assumed not to incur repair time.

3.6. Analysis, evaluation, and interpretation

This section encompasses two parts wherein the first part, considers the model results following a one-factor-at-a-time (OFAT) analysis, while in the second part, a set DOE, following a full 2k factorial design (k as the number of variables/controls to evaluate their effect to the engine Ao and Tr ) is conducted and computations of the controls' (here also termed as variables') average effects and interactions generated. The process will follow the 3-factor full factorial experiment with re- solution V, as described by NIST/SEMATECH (2012). This resolution or ability to separate main effects and low-order interactions from one another, has the capacity to estimate all main effects and two-way in- teractions (Sanchez et al., 2006). The significant variables selected during this step meet three conditions; firstly they have both main ef- fects and the corresponding interaction effects, an aspect corroborated by (Mccullagh, 2002). Secondly, they are statistically significant at a significant level of 0.5. Finally, using expert assessment, they are con- sidered significant based on the size and other techniques such as graphical methods.

3.7. Simulation-based optimization

This section outlines the 7-step simulation-based optimization ap- proach based on the conceptual framework proposed by Alrabghi and Tiwari (2016), further adapted for the optimization phase discussed in this study, as illustrated in Fig. 2.

The first step considers defining the scope of the optimization, which addresses the establishment of the maintenance policies to be employed in the process. The second step involves identifying the maintenance policies and the respective decision variables to be in- corporated in the optimization, while the third step, constitutes the formulation of the objective function. Depending on the outcome of the preceding step, the fourth step formulates the constraints. The selection of the optimization algorithm and setting up the required algorithm parameters is performed in the fifth and sixth steps respectively. Finally, the optimization results are evaluated and interpreted while considering the plant/asset's current context. To sum up, the 7-step

Fig. 1. Sample illustration of FS2 modelling using SMDP.

Fig. 2. Schematic framework for simulation-based optimization approach.

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process is scalable and will offer insights when followed step by step.

4. Results

This section presents the results, brief evaluation and discussion, while a wide-ranging discussion will be dealt with more extensively in Section 5.

4.1. Data collection and pre-processing

The maintenance data from the power plant, recorded in a free text structure was standardized to meet the analysis requirement following the ISO 14224:2016. The classification entailed the equipment class and types Combustion engine (CE) and Diesel engine (DE) respectively, while subsystem classification as illustrated in Table 3.

The data classification enabled the data to be categorised using the various subsystems utilized for the data exploration discussed in the next section.

4.2. Data exploration

Fig. 3 illustrates a Pareto chart prioritising the engine subsystems in the plant using the individual contribution to the power lost in mega- watt-hours (MWHrs). What stands out in the chart is the first four subsystems, i.e. cylinder, governor, turbocharger and lubrication system, which cumulatively contribute 86% of total power lost hence were selected as critical subsystems to be modelled. In this study, the four critical subsystems are modelled with an extra one “others” which is a summation of the remaining subsystems. As regards to maintenance decision support context, explicit strategic focus on the four critical subsystems would potentially improve and enhance the engine perfor- mance.

4.3. Model parameter extraction

Table 4 summarises the tstn and n for each of the critical subsystems selected, where the tstnwas computed based on the assumption of the analysis commencement of January 2011. It indicates the governor has the highest tstninferring its less susceptibility to failure during the early running hours, after commissioning compared to other subsystems. The Weibull distribution estimate represented as WEIB (α, β, γ) with the shape parameter β and scalar parameter α and exponential distribution (EXPO) has the mean i.e. EXPO (mean). The Weibull and Exponential distributions were characterized with a third parameter distribution (γ), also known as location parameter or failure free time, which indicates that failures start at a finite time and not at t = 0, for instance, turbo- charger failures (γ = 16). The governor, lubrication system, cylinder and others fit an exponential distribution with a random mean. This signifies failure occurrences that are independent of each other and randomly distributed and could be attributed to high replacement strategy hence tending to near constant or steady state as also corro- borated by (Louit et al., 2011).

The turbocharger subsystem fitted a Weibull distribution, exhibiting a shape parameter β < 1, which indicates that the failure rate de- creases over time. The components have their hazard rate decreasing due to less severing strategies for instance replacement that have a lower impact on the n. This is contrary to an intensive regenerative strategy which has a high negative impact on the n due to the strategy characteristics, where the component renewal is near ABAO, hence, lowering n depicts a shorter life experience for the subsystem.

Table 5 provides the different CM actions alongside extracted parameters like the probability of utilization i, repair time classes Tri and Tdi . Tri followed the Ri classification as discussed in Section 3.2. Mean time to preventive maintenance (overhaul)Tr5 for R5 had a uni- form distribution of minimum 192 h and maximum 224 h as depicted from the preventive maintenance schedule. The impact factor i , acts as a multiplier to the time to the next failure nof an individual sub- system. The i , was derived from proportionating the respective total

n following the approach utilized by Wakiru et al. (2018), which compares and aligns with major repair 4 as 0.80 under the assumption that attaining AGAN status is difficult in deteriorating systems, due to the introduction of errors such as diagnosis, tooling and human related errors. This is based on an empirical analysis of the estimated percen- tage changes in n of the various Ri , where 0.8 was seen as optimal for R4. Respective Tdi for the various CM actions were estimated by the plant maintenance team.

Table 6 presents the various parameters used while addressing the

Table 3 Sample data standardisation using ISO 14224.

Equipment class Equipment type Sub-units/Subsystems

Description Code Description Code Description Code

Combustion engines CE Diesel engine DE Cylinder CYL Turbocharger TC Fuel pumps FS Lubrication system LO Exhaust EXH

Fig. 3. Pareto analysis for subsystem/components using Power lost.

Table 4 Various subsystem time to next failure distributions.

Subsystem tstn (Hrs) n distribution Parameters Corresponding p-value

X2 Test K-S Test

Governor 2200 EXPO (2.82e+003) 0.341 > 0.15 Turbocharger 1998 16 + WEIB (3.55e+003,

0.854) 0.55 > 0.15

Others 640 2 + EXPO (723) 0.316 > 0.15 Lubrication 1260 13 + EXPO (1.28e+003) < 0.005 0.0753 Cylinder 1800 40 + EXPO (582) 0.477 > 0.15

Table 5 Repair time for various repair actions.

Repair Action Tdi (hrs.) Tri (hrs.) i (%) i ISO 14224:2016 classification

Do Nothing 0.15 0–1.0 16% = 0.651 Minor Minor Repair 0.50 1.0–7.0 57% = 0.752 Moderate Moderate Repair 0.7 7.0–13.0 15% = 0.853 Severe Major Repair 2.0 Over 13.0 12% 4 = 0.80 Catastrophic

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spare inventory and logistics. The percentage requirement of local and import sourcing, as well as the respective lead times, were provided by the experts from the plant maintenance and supply chain departments.

4.4. Model

The developed model mimics the operation of the engine, where the performance measurements were Aoand Tr . Fig. 4 illustrates the con- ceptual representation of the model.

The model was run with a replication length of 105,120 h equiva- lent of 12 years, reflecting the age and the first planning horizon based on the planned useful life. The industry average design engine lifespan is estimated to be 20–25years. Hence, this correlates to the lifetime of similar engines. For each simulation, 55 replications were made which allowed a large sample size to be considered, hence reducing the 95% confidence interval half width of the performance measures Tr (from ±45.00 to ±5.00) There was no significant variation in the percentage change of the half width beyond 55 replications.

4.5. Analysis of results

4.5.1. Model results The model generated Ao of 90.001%, and Tr of 1526 h per year re-

spectively. The achieved Ao and Tr using the model were close to the empirical values as analysed from the data of 92% and 1621 h respec- tively. This may be attributable to the stochasticity in the modelling parameters. However, the generated Ao is very close to the empirical value of 92%. Thus, we can assume that our model is a valid re- presentation of the modelled processes in the power plant. Further evaluating the individual contribution to Tr , the cylinder, turbocharger and governor subsystems, each contributed 23.2%, 19.9%, 18.1% re- spectively of the total as depicted in Table 7.

It should be noted; the values indicated are average values over the simulation time tn. The consolidative characteristic of “other” sub- systems as seen in Table 7 is attributed for the high Tr and Tl , hence not incorporated in the analysis for individual subsystems in this section. The turbocharger incurs the highest Tm compared to the other critical subsystems. Both the turbocharger and governor subsystem indicate high Tl , implying substantial failures characterized by spares sourcing requirement. This could offer a pointer towards, the need of a more plausible strategy, that could incorporate spares inventory, reuse, re- condition, or cannibalization strategies, if possible, to overcome the challenge. Cylinder subsystem has high Td, possibly attributed to the complexity of the assembly, that often require disassembly to diagnose internal components failure in the subsystem.

It can be seen from Table 8, obtained by carrying out an OFAT analysis, that increasing the tbo gradually decreases Tr in a non-linear manner. As a result of extended tbo, the frequency of R5 utilization (renewal instances) declines and more failures occur, requiring CM interventions, which are represented in the last column of Table 8. Additionally, this aspect is confirmed by the marked increase in the utilization of various Ri under CM, for instance, R2 (818–991), R3 (221–264) and R4 (152–187). The observed increase in Tl , can therefore be related to the increased utilization of both R3 (moderate repair) and R4 (major repair), which subsequently demand replacement of spares that incur high lead-times, an aspect demonstrated by the increase of Tl .

Hence, an objective and realistic analysis show the CM related repairs incur more time ( +T Tr l ) and more activity = Ri i1

4 , which is logical and corroborated by various studies, for instance, (Alrabghi and Tiwari, 2015). Further review demonstrates an inconsistent variation of Ao indicating the possible effect of other variables. However, a general increase is noted from 82.79% to 87.56%. A similar analysis indicates that increasing f improves Ao, while Tr increases and Tl decreases re- spectively. To explicitly understand the level of dependency between the variables while impacting the performance measures, a full factorial orthogonal design experiment is employed as discussed in the following section.

4.5.2. Full factorial effects and interactions experiment results A 3-factor complete factorial design experiment was carried out, to

determine significant variables. The respective variable ranges illu- strated in Table 9, were prepared after expert interviews and according to the procedure (save for t )bo used by (Sanchez et al., 2006; Zhu et al., 2017). An analysis of the effects and the respective p-value for different ranges was done in addition to expert consultation while assessing the appropriateness of the ranges as seen in Table 11. The ranges were computed using the model parameters derived as described in Section 4.3. We utilize the ranges adopted in both the full factorial experiment (in this Section 4.5.2) and the simulation-based optimization in Section 4.6.

The criteria employed to identify the significant variables, con- sidered, first, that the variable has both, the main effect and corre- sponding interaction effect, secondly, the P-Value confirms the variable (s) is statistically significant at the significance level of 0.05. Also, to visualise the error size of an effect, graphical methods were used, while, plots of residuals were used to check for model adequacy. The simu- lation was carried out using 55 replications, and results depict average values, using resolution V to estimate the average effects and interac- tions. Table 10 provides a sample of generated average main and in- teraction effects on the Ao and Tr from the designed experiment, while a detailed list is shown in Table A1, in the appendix.

As Table 10 indicates, an increase in tbo, will averagely increase the Ao by 5.87% while decrease theTr by 612.325 h. The improvement of Ao is because of compensated repair time by lengthened running or op- eration time I due to a decline of PM activities as also seen in Section 4.5.1 and Table 8. The availability of spares potentially reduces the subsystem downtime due to spares sourcing lead times Tl which posi- tively impact I, hence improve the Ao. An increase in 2 will averagely increase Ao (11.99%) and increase Tr (712.62 h). This indicates, that increased reliance of R2, offers a negative impact on Tr attributable to the fact that R2 incorporates solely repair without spares requirement, hence the modelled Tr retains a higher value.

Considering interaction effects, for instance, the interaction of tbo and f causes a significant change in Ao and a modest decrease of Tr by a factor of 12.52% and 92.07 h respectively. This infers that the effect on f by tbo positively affects the performance of the engine Ao and Tr . Similar interaction to some extent is seen between 2 and 3 with a modest improvement on Tr and a modest change on Ao. This implies that the tbo effect on Ao does not depend on the effect of f , signifying that tbo has a negative effect at high f but a positive effect at low f . While evaluating the impact on Tr , the effect of tbo, to some extent de- pends on the effect of f , where f has a negative effect at high tbo but a

Table 6 Spares availability and sourcing lead times.

Maintenance action Spares needed (%) f (%) Spares sourcing

Local (%) Lead-time (Hrs) Import (%) Lead-time (Hrs)

Moderate repair 80.19 90 10 1–5 90 36–120 Major repair 100.00 90 5 4–24 95 120–1080

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positive effect at low tbo. The main and interaction effects are presented in Table A1. To evaluate the variable ranges employed in this exercise along with expert interviews, we employed three sets of ranges and confirmed they gave same results in terms of significance of the

variables. A sample of the evaluation is shown in Table 11. In summary, it can be concluded from the DOE performed, that the

variables show a marked interaction impact on Tr compared to Ao, hence Tr is selected as the performance measurement to be employed in

Fig. 4. Conceptual representation of a discrete event simulation model.

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the optimization. Subsequently, the significant variables established include, tbo, 2, 3, and f. Due to the interactive characteristics of the significant variables, an optimization considering them jointly and several constraints, is advanced employing a simulation-based optimi- zation as discussed in the next section.

4.6. Simulation-based optimization

The simulation-based optimization framework described in Section 3.7 is followed here step by step:

1. Defining the scope of the optimization

The simulation-based optimization addresses the subsystems iden- tified and modelled as per Section 4.3. In this case study, the optimi- zation scope will include the total repair time and fill rate which ad- dresses the spares policy.

2. Applicable maintenance policies and decision variables for optimi- zation

The decision variables established as significant in Section 4.5.2 are considered for the maintenance optimization. The variables include the time between overhaul tbo addressing PM policy, fill rate f that deals with the inventory policy. Other variables addressing the CM policy in- clude the maintenance strategy reliance factors 2 and 3. However, Oc , the number of outsourced contractors will be included despite not being in the DOE performed in Section 4.5.2, because we view it as an essential aspect, that could influence downtime caused by PM strategy and sub- sequently influence CM policy in terms of reliability. Table 12 presents the summary of the decision variables (possible and revised choices), and the possible number of solutions in both cases. The simulation optimi- zation process utilises the revised choices to reduce the solution space.

3. Objective function formulation

The critical policies to consider based on the variables selected in Step 2 include the repair times, maintenance strategy reliance and spare parts availability. The effect of spares availability is incorporated in Tr , since it introduces lead time and affects the repair time due to multiple handling. In the same way, the maintenance strategy reliance effect would be noticed in generating Tr . Hence, minimizing the total repair time will be the only objective.

4. Constraints definition

Two constraints are defined, the first considers 2 and 3 , as illustrated in Table 5 in Section 4.3. Both constitute a combined 72% (57% and 15% respectively), hence we formulate the constraint as 2+ 3 = 72%. Secondly, to ensure the optimization considered a better scenario than the base, we define Ao to be more than the base value of 90%, as depicted in Section 4.5.1, hence, the problem can be formulated as follows:

= =T T

t Minimize: r k

n r

n

1 k

Subject to:

A 90%o

+ = 72%2 3

5. Optimization algorithm

We employ OptQuest for the optimization problem at hand, which offers the possibilities to optimize simulation experiments employing neural network filter and apply heuristics known as tabu search and scatter search (Kelton et al., 2010). Moreover, it offers both the option of setting up goals for explicit handling of bounds enforced on output values and the graphical output presentation that enhances inter- pretation. Furthermore, it is employed, to gain insights, while con- sidering the consistency the variable bounds, as previously employed in Section 4.5.2.

6. Simulation optimization set-up

The optimization using OptQuest was done with varying the number of replications from 5 to 55 for each simulation, allowing OptQuest to test for the statistical significance between the average objective function of our best previous and current simulation, whose intention is to rule out inferior solutions. The optimization process was only stopped and results retrieved when no change is noted on the optimal solution after 200 simulations. The Tr baseline before the op- timization is 1526.1 h as seen in Section 4.5.1.

Table 7 Summary of subsystem time variables.

Subsystem Trn Tln Tdn Tmn

Turbo charger 303.38 128.58 9.99 441.95 Governor 275.89 122.40 8.46 406.75 Cylinder 354.24 10.28 20.10 384.62 Lubrication 254.00 13.04 7.76 274.80 Others 338.61 520.64 34.30 893.55

Table 8 Annualized times and frequency of utilization for Ri while varying tbo.

tbo(hrs.) Ao (%) Annualized time over tn (hrs.) The frequency of utilization over tn

Tr Tl Td +T Tr l R1 R2 R3 R4 R5 = Ri i1

4

7000 82.79 1763.51 415.23 83.39 2178.74 236 818 221 152 18 1427 8000 91.60 1735.11 429.22 84.44 2164.33 280 824 225 154 17 1483 9000 90.01 1526.13 685.23 80.88 2211.36 256 833 232 165 15 1486 10000 87.00 1376.3 929.83 79.51 2306.13 230 857 246 165 13 1498 11000 87.60 1187.11 1222.13 70.57 2409.24 193 883 254 175 11 1505 12000 87.56 1175.89 1442.13 76.69 2618.02 205 991 264 187 11 1647

Table 9 Variables ranges used in the optimisations.

Variable Values Ranges

tbo 9000 7000 12000 2 57 45.60 68.40

3 15 12.00 18.00 Td1 0.15 0.07 0.23 Td2 0.5 0.25 0.75 Td3 0.7 0.35 1.05 Td4 2 1.00 3.00 f 90 72 99 Oc 1 1 2

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7. Results and discussion

Fig. 5 illustrates the optimization results, which indicates the best value being attained at the 186th simulation and no further change seen.

The optimization resulted in more than 30 solutions where the Tr is more than 1% below the base line value. Table 13 presents the top ten optimal solutions. From these results, we can see that optimality is at- tained while enhancing PM, spares availability, while, a modest change in the reliance of minor and moderate repair strategies. Scenario I generated the highest Ao and power generated in MWHrs as production output for the engine, while scenario A, returned the lowest Tr .

The values of 2 and 3 in the optimized scenarios, indicate more reliance on minor repair actions ( 2). This was expected, because of the inherent characteristics of the minor repair actions, which exhibit lower repair times and no spare sourcing lead time. Oc in this case depicts a higher value of 2, which can be attributed to the fact that the out- sourced capacity is only available during the daytime shift, hence the increase by 1 to ensure availability of the resource.

As far as reviewing the optimization results is concerned, there is strong concurrence that enhancement of tbo, f , leads to optimization of the plant's performance measures. An implication of this is, firstly, the possibility of re-evaluating the tbo to optimize the planned maintenance effectively, based on the lifecycle of the subsystems. Secondly, spares inventory challenge if overcome, shows a potential positive optimiza- tion solution, an outcome also corroborated by Kennedy et al. (2002). In this case, an introduction of different inventory policies such as consignment stocking, employing other recovery actions such as re- conditioning and adoption of industrial symbiosis, would probably ensure spares are available throughout and could positively impact on the optimization. A caution here would involve carrying out a cost- benefit analysis to balance the cost and improvement on either Ao or Tr

as also corroborated by Alabdulkarim et al. (2011). Furthermore, due consideration should be taken on probable risks that accompany en- hanced f such as increased risk due to spare costs, insurance costs, pilferages and storage space requirement.

5. Discussion

The initial model analysis results are significant in at least two significant respects. In the first place, they guide the practitioner while selecting the critical subsystem, where in our case, the turbocharger is picked based on total maintenance time. In the second place, they offer insights on the bottlenecks suffered by the plant using various main- tenance policies. Among the subsystems' identified through the ap- proach as critical regarding portended time characteristics, such as repair time, lead-time to procure spare parts and diagnosis includes the turbocharger, cylinder and governor. Hence, such subsystems necessi- tate further investigations with a view of identifying robust main- tenance strategies, which seeks to optimize operational availability. The proposed simulation is demonstrated as useful for decision support as observed from the results illustrated in Section 4. As an example, as described in Section 4.5.1 (Table 7), the turbocharger and governor, exhibit lengthier lead-time delays based on the modelled stochastic spare part sourcing lead times. An implication of this is the need to investigate further the specific spare part inventory that frequently requires to be sourced, either locally or imported from the original equipment manufacturer (OEM). In real-life, determining the stocking policy is not straightforward in the absence of a decision support fra- mework, owing to the stochasticity of time characteristics like repair, diagnosis, and sourcing lead times. Moreover, the interaction effects between the stochastic spare part availability and other variables, in- fluence the stocking strategy, yet modelling this aspect and evaluating its influence on system availability is somewhat challenging. However,

Table 10 A sample of significant main and interaction effects.

tbo f 2 3 +t fbo +2 3 +tbo 2 +f 2 +tbo 3

Δ Ao (%) 5.87 19.4 11.99 5.59 1.52 1.5 −1.95 −0.66 −1.89 Prob > |t| < 0.0001 < 0.0001 < 0.0001 0.0004 < 0.0001 0.0446 0.0225 0.0134 0.0267 Δ Tr (hrs.) −612.33 548.14 716.62 −209.83 −92.07 −42.38 −94.96 −379.9 78.58 Prob > |t| < 0.0001 < 0.0001 < 0.0001 0.0001 0.01850 0.0038 0.0160 < 0.0001 < 0.0001

Table 11 Evaluation of different variable ranges scenarios.

Variable 50%:100%:150% 80%:100%:120% 90%; 100%:110% Significant

Effect p-value Effect p-value Effect p-value

f 1464.18 0.0000 548.14 0.0000 718.52 0.0000 Yes 3 708.7 0.0007 −209.83 0.0001 88.79 0.0000 Yes

t fbo −421.5 0.0000 −92.07 0.0185 −68.72 0.0003 Yes f 3 −282.18 0.0002 −112.27 0.0350 −31.9 0.0244 Yes Td2 70.10 0.8840 160.22 0.6092 26.26 0.7426 No f Td2 −25.20 0.9581 −18.20 0.9534 −2.52 0.9748 No

Table 12 Variable ranges and the possible number of solutions.

Variable Ranges Possible choices Revised choices Remarks

tbo 7000 12,000 5000 5000 No change 2 45 68 230 23 Changed from step 0.1 to step 1.0

3 12 18 60 6 Changed from step 0.1 to step 1.0 f 72 99 27 27 No change Oc 1 2 2 2 No change Possible solutions 3,726,000,000 37,260,000

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from the simulation model, it is observed that it is possible to derive insights on such interaction effects through the simulation modelling approach. For instance, the turbocharger and governor which exhibit longer sourcing delays could benefit through initiatives like prioritised stocking, Just-in-Time (JIT) or consignment stocking from the OEM/ local agent.

Moreover, for the above, utilization of condition monitoring tech- niques such as oil analysis or vibration analysis on such subsystems, potentially can provide early warnings that assist the plant in advanced planning of spare parts sourcing, a strategy similarly suggested by Eruguz et al. (2018). While addressing the diagnosis delay and accuracy for critical subsystems such as the cylinder and turbocharger, the plant could re-train the technicians and bring in better diagnostic technolo- gies, which could enhance better detection of failure severities as this aspect in most cases is influenced by technician knowledge and ex- perience, an observation also corroborated by Wang (2012). This im- provement would also yield better repair strategies, for instance, a component replacement for high severity failures.

Importantly, modelling stochastic failure diagnosis Tdi times, despite its insignificant impact on Tr in this case, illustrate the significance of this seldom utilized maintenance downtime constituent, as a modelling variable which influences the quality of the maintenance action, an aspect also corroborated by Van Horenbeek et al. (2013). Further in- vestigations concerning Td would lead to unearthing aspects such as the suitability of a technician skills, their response time, maintenance quality, availability of tools, and could further examine automation of decisions as concerns the use of sensor or historical data, aspects also corroborated by Bousdekis et al. (2015). This aspect could be addressed by employing appropriate fault diagnostic systems, for example uti- lizing thresholds such as RUL and hazard rates to trigger decisions of appropriate interventions under CBM, an area the authors view for future work.

While reviewing the second phase where main and interaction ef- fects are determined, the results doubtlessly, despite dependent on the case study characteristics, has some reliable conclusions. The sys- tematic determination of significant variables, employing various techniques, based on the main and interaction effects demonstrates a

plausible framework. It lays emphasis that the analysts must explore factor effects concurrently to understand how their simulation model behaves when its factors are changed. Despite the use of p-values, in- formation about the size of an effect and its possible error must be al- lowed to interact with expert knowledge. Graphical methods, ad- ditionally provide a valuable means of allowing information in the data and the mind of the expert to interact appropriately, an aspect also corroborated by (Kleijnen et al., 2005).

Taken collectively, these results suggest it is essential to optimize variables jointly since the decision variables or controls can interact with each other and yield a sub-optimal solution. For instance, as seen in the results in Table 10, variable such as 2 and f negatively affected Tr individually, based on their individual main effects on Tr . However, when their interactions were considered, their combined beneficial influence on Tr was positive. As an example, the combined effects of 2 and f generated a decrease in Tr despite both having negative effects individually. Hence, this suggests that performing optimization based on a single variable (or the OFAT approach) could eventually lead to sub-optimal maintenance optimization, and by extension, considerable modelling time owing to repetitive OFAT experiments. This observation corroborates to a greater extent the findings by (Sarker and Haque, 2000) who suggested that this type of model using interactions is ap- plicable in maintenance strategies of multiple components in max- imizing service levels, similarly considered in this study.

With regard to the optimization results in Section 4.6, the results indicate that the total repair time would be optimized by considering firstly, the CM related factors (i.e., the maintenance strategies to rely on and the spares availability), and secondly the PM-related factors (TBO and Outsourced maintenance). Concerning the reliance on different maintenance strategies, the results show that a slight increase in minor repair with a small decrease in reliance on moderate repair actions would contribute to an optimal solution. This result may be explained by the fact that minor repair retains a lower repair time strategy with no spare requirement. As for the spares availability, the results are as ex- pected, where to reduce repair time, spares availability should be guaranteed. However, this aspect requires further investigation con- sidering the operational context of different plants, where a trade-off

Fig. 5. Graphical representation of the optimization results.

Table 13 Optimization parameters while minimizing Tr .

Scenario A B C D E F G H I J

Tr 1432.30 1432.74 1437.65 1437.70 1438.48 1440.06 1440.44 1441.84 1442.37 1444.35 tbo 12000 12000 12000 12000 11976 11976 12000 12000 12000 12000

2 58 58 58 58 58 58 58 58 58 58

3 14 14 14 14 14 14 14 14 14 14 f 99 99 99 99 99 99 99 99 99 99 Oc 2 2 2 2 2 2 2 2 2 2 Ao 91.21 91.01 91.43 91.29 91.42 91.32 91.14 91.47 91.44 91.23 Power Generated 87135 86940 87340 87203 87336 87232 87061 87382 87348 87149

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may be required between stocks level, holding costs, pilferage and spares shelf-life. Concerning TBO, the results indicate that for this case, the increased interval would offer lower repair time. The observed decrease in Tr could be attributed to the modelling approach of the time variants T T,r d and Tl as indicated in Section 4.5.1. Moreover, the possible interference of protracted Tl , thereby reducing respective Trn cannot be ruled out. However, an introduction of other performance measure such as total maintenance cost or time that amalgamate the time incurred (T T and T,d r l ), will undoubtedly cause this observation to change.

From the optimization results, contract or outsourced maintenance during equipment overhaul as currently implemented at the power plant negatively influenced the total repair time for the power plant. This influence was due to limitations such as availability timelines of the outsourced resource (often only during one shift), or the type of outsourced maintenance service. For the latter, two types of main- tenance services are outsourced, wherein the type I, both corrective and preventive maintenance services are outsourced, and in type II, only, CM is outsourced. The availability limitation is observed as negatively impacting the overhaul time since repairs would otherwise have been performed during both the day and night shifts. Secondly, outsourcing only PM services limits the maintenance repair processes, since the outsourced resource are deprived of valuable insights which could be derived from performing CM actions. As an example, root causes of chronic subsystem failures which are correctively repaired could be missed during PM actions, yet such root causes could be appropriately addressed during the CM actions by the outsourced resource, who are more specialised in maintaining the critical subsystems. This finding is also demonstrated by Wu (2012), where he suggests that attention should be given while selecting the type of outsourced resource for plant maintenance. He argues that for better maintenance processes, organisations should outsource type I services (CM and PM). Further, the ageing process of the subsystem could be a factor to consider during outsourcing, where a balance between in-house and outsourced main- tenance should be considered. As an example, ageing components may require more outsourced maintenance services. This observation cor- roborates findings by Bazargan (2016), who recommended a combi- nation of in-house and outsourced in such circumstances.

The proposed methodology is generalizable and can be scaled to fit different applications that constitute multiple subsystems. Table 14 il- lustrates several potential applications, indicating the respective sector, system, and possible subsystems. It is essential to bear in mind that the application of this proposed methodology to various applications, for instance, the manufacturing sector would require some adaptations to suit the operational context. Firstly, the identification of the system to be investigated, for instance, the cement mill/grinder in a cement plant. Secondly, for the identified system, a precise segmentation of the sub- systems constituting it (indicated in the “sample subsystems” column in Table 14). The third aspect will involve the adoption of the metho- dology as highlighted in Section 3, where maintenance data is collected, preprocessed and explored. From the data exploration, plants exhibiting numerous subsystems, prioritisation based on the performance mea- sures employed, for instance, downtime, may be employed to establish critical subsystems. For the identified subsystems, the different model parameters are extracted from empirical data and expert assessment while the performance measures and objective functions are formulated

for the simulation model. Expected differences would emanate while modelling due to the differences in the operational context. For in- stance, some plant set-ups constitute redundant or buffer subsystems to guarantee continuous operations, an aspect that should be considered (Rezg et al., 2005).

6. Conclusion

The present study was designed to develop a methodology that commences with empirical data, to analyse the effects and interactions of various maintenance and operational factors and their impact on the optimization of the engine total repair time using a simulation model. The case study of a thermal power plant was advanced with con- sideration of repairable subsystems with both PM and CM actions. The subsystem deterioration problem was formulated stochastically in- tegrating the previous subsystem severity influenced by maintenance actions. Further to identifying the turbocharger as critical among the subsystems using total maintenance and repair time, the study has shown that the different subsystems have different repair, diagnosis and lead time's characteristics offering different impacts to their life cycle times. Spares availability, reliance on minor and moderate repair stra- tegies and TBO were demonstrated to have the most potent effect on total repair time. The analysis results while evaluating the model, conceivably support the hypothesis that interactions of the variables play a role in influencing the performance measures. The optimization exercise which openly supports the relevance of interactions, indicates that tbo, spares availability and maintenance strategies reliance as es- sential ingredients. These findings have a significant implication in understanding parameters that require further investigation while car- rying out maintenance decision making, whereby, if enhanced, would greatly improve the maintenance strategies, resource allocations and ensure priorities are set right to improve the availability of the engine and eventually the plant economics. This combination of findings pro- vides some support for the conceptual premise that while carrying out maintenance optimization, a balance of decision variables used, need to be struck by considering their effects, interactions and expert knowl- edge. The research lays a groundwork for future studies into other maintenance strategies with their possible interactions towards an in- depth optimization model. Moreover, the simulation-based experiments and optimization on real power plant data verify the validity and ro- bustness of the developed technique.

Several limitations of the present study should be acknowledged, which should be dealt with in detail in future studies. For example, modelling shared resources like technicians amongst several systems, which could offer decision support concerning the same. Another lim- itation of the study is based on the fact that it considered only PM and CM policies, whereas additional maintenance and restorative strategies identified like condition monitoring, spares reconditioning, and reuse of spares could be incorporated. An optimization extension utilizing the failure diagnosis remains a possible aspect interesting to be investigated about the human factor effect on maintenance. Other studies will be needed to investigate the impact and balancing of in-house and out- sourced maintenance, to develop a full picture of outsourced main- tenance.

Table 14 A sample of different possible applications of the proposed methodology.

Sector/Industry Sample System Sample subsystems

Manufacturing Cement mill Weigh feeder, conveyor system, mill/grinder, elevator, water system, air, and blower system Exploration A drilling rig (fossil/geothermal/

offshore) Air system, a hoisting system, power supply, top-drive/rotary table, well monitoring system.

Aviation Turbofan engine Air intake/compressor, combustion chamber, Turbine, exhaust system, ignition system, engine fuel system, lubrication, exhaust system

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Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Appendix A. Design of Experiment full factorial analysis

Table A1 Main and interaction effects considering Tr .

Effect Estimate D.f Sum of Squares F Ratio p-value Significant

tbo −612.325 1 1499767.6 384.4216 0.00000 Yes f 548.138 1 1201818.9 308.0512 0.00000 Yes 2 716.62 1 2054176.9 526.5282 0.00000 Yes

f 2 −379.9 1 577303.6 147.9749 0.00000 Yes tbo 3 78.58 1 49404 31.1416 0.00000 Yes

3 −209.828 1 176110.32 46.3816 0.00010 Yes

2* 3 −42.38 1 3591.71 36.6776 0.00380 Yes tbo 2 −94.96 1 36069.6 9.2454 0.01600 Yes t fbo −92.073 1 33909.4 8.6917 0.01850 Yes f * 3 −112.273 1 25210.2 9.8302 0.03500 Yes t Tbo d2 54.12 1 11715.9 3.0856 0.11710 No

Td3 2 35.02 1 4907.7 1.2925 0.28850 No Td2 70.10 1 2543.4 0.0222 0.8840 No Td3 37.35 1 5580.09 0.0478 0.83250 No Td4 12.62 1 2549 0.0062 0.9373 No f Td4 8.39 1 1128.00 0.0035 0.9530 No T Td d2 3 −29.24 1 3418.74 0.0293 0.86840 No

Td3 3 15.71 1 987.22 0.0085 0.92900 No t Tbo d3 28.3 1 3204.13 0.1784 0.68020 No

Table A1, illustrates the main and interaction effects of the decision variables, where D.f is the degrees of freedom. Main and Interaction effects that are significant, means that the variables are statistically significant (P-Value 5%), in relation to Tr . The significant interaction effects indicate the validity of determining a balanced trade-off solution while integrating the decision variables.

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