machines

Review
Condition-Based Maintenance—An Extensive
Literature Review
Elena Quatrini * , Francesco Costantino , Giulio Di Gravio and Riccardo Patriarca
Department of Mechanical and Aerospace Engineering, University of Rome “La Sapienza,” Via Eudossiana, 18,
00184 Rome, Italy; francesco.costantino@uniroma1.it (F.C.); giulio.digravio@uniroma1.it (G.D.G.);
riccardo.patriarca@uniroma1.it (R.P.)
* Correspondence: elena.quatrini@uniroma1.it; Tel.: +39-0644585260




Received: 8 May 2020; Accepted: 5 June 2020; Published: 8 June 2020


Abstract: This paper presents an extensive literature review on the field of condition-based
maintenance (CBM). The paper encompasses over 4000 contributions, analysed through bibliometric
indicators and meta-analysis techniques. The review adopts Factor Analysis as a dimensionality
reduction, concerning the metric of the co-citations of the papers. Four main research areas have been
identified, able to delineate the research field synthetically, from theoretical foundations of CBM;
(i) towards more specific implementation strategies (ii) and then specifically focusing on operational
aspects related to (iii) inspection and replacement and (iv) prognosis. The data-driven bibliometric
results have been combined with an interpretative research to extract both core and detailed concepts
related to CBM. This combined analysis allows a critical reflection on the field and the extraction of
potential future research directions.

Keywords: condition-based maintenance; factor analysis; bibliometric analysis

1. Introduction
The complicated nature of modern engineering systems and manufacturing processes is increasing
rapidly. Consequently, managing the reliability of the systems becomes challenging in modern
dynamic operational settings [1]. In this context, condition-based maintenance (CBM) is a leading
strategy for the scheduling of maintenance interventions, in contrast to more traditional solutions
relying on time-based maintenance (TBM) [2]. Reflections on CBM implementation can be found
since the 1970s [3–5]. Since its early implementations, the need for collecting information when
the system is in operating conditions has been recognized (i.e., Condition Monitoring, CM) [6].
Such information generally ensures a reduced number of interventions, if compared to TBM. CM is
defined as the monitoring of one or more meaningful parameters to model the performance of
the considered systems and to identify changes potentially linked to future failures. This is a crucial
step for ensuring proactive monitoring and resource optimization of repair interventions, to limit
performance losses. CBM is considered as the optimal maintenance strategy to be adopted when a
failure or the degradation process can cause important economic losses [7].
An optimal CBM strategy has the potential to generate important benefits for the competitiveness
of industrial companies, even in the modern industrial systems (e.g., increasing system availability
and consequent benefits for safety management [8], reducing maintenance costs [9], increasing product
quality [10]).
Since CBM is a well-established research field, the presence of previous literature reviews is not
surprising. One of them reviews worldwide CBM industrial practices, introducing basic concepts
such as the necessity for planned maintenance, the role of CM and the difference between prediction
and diagnosis up to 1994 [11]. Other papers review the techniques commonly adopted to monitor

Machines 2020, 8, 31; doi:10.3390/machines8020031 www.mdpi.com/journal/machines

Machines 2020, 8, 31 2 of 28

the condition of mechanical systems and the decision models up to 1993 [12] as well as a more
modern state-of-the-art about data integration for CBM [13] or the statistical data-driven approaches
for the prediction of remaining useful life (RUL) [14], respectively dated 2009 and 2011. Further papers
review a specific area of CBM implementation, such as prognostics and health management [15–18],
aircraft engine health management [19], vehicle health management [18], punching/blanking of
sheet metal [20], CBM strategies for multi-component systems [21] or the prognostics of the rotating
machines [22].
Nowadays, there is a lack of a global analytical review that analyses the field of CBM in its entirety
from a thematical and temporal perspective. As far as the authors know, this manuscript proposes
the first meta-analysis in the context of CBM.
This article investigates available research on CBM, by an extensive review of the literature
published over more than 40 years (first considered contribution dated back to 1976 [3]).
The meta-analytic perspective adopted in this study allows reducing the number of subjective choices
to those requested just for pragmatical reasons—restriction to Scopus database, the largest available
academic repository; the definition of parameters for bibliometric analyses; and the interpretative
labelling of the research areas.
In summary, this paper aims to explore literature in the field to provide an overview of the most
relevant research themes and potential future research directions.
For clarity purposes, a homogenous terminology has been adopted throughout the document.
Main terms and respective definitions are as follows:

• MAINTENANCE POLICY—all management activities that set requirements, objectives, strategies

and responsibilities for maintenance and implement them using management approach
(i.e., planning, control, supervision and improvement). Policies refer to a set of rules made
by the organization to ensure rational decision making.
• MAINTENANCE STRATEGY—management direction used to achieve maintenance objectives,
achieving a competitive and effective position in the market.
• MAINTENANCE PLAN—structured and documented set of commitments including activities,
procedures, resources and time required to perform maintenance activities.

These definitions are based on the UNI EN 13306:2018 [23]. Specifically, maintenance policy
follows the definition of maintenance management but maintenance strategy and maintenance plan
refer to the same concepts in the standard.

Structure of the Paper

Before getting to the core of the paper, to make it easier to read and understand the review,
the authors consider it appropriate to explain in detail the structure of the paper. The rationale behind
the structure given to the paper can be ascribed to two macro-motivations:

• the overall structure of the paper reflects the actual path followed by the authors for
the implementation of the presented literature review
• the presentation of the extracted research factors (RFs) follows what the authors consider to be
the logical path within CBM.

Detailing the sections of the paper, Section 2, that is, methodology, firstly describes in detail how
the papers were searched, as well as the database from which the papers were extracted. Secondly,
it describes the technique used to circumscribe the areas of interest within the CBM field and the reasons
for this choice.
In Section 3 instead, that is, findings from a systematic literature search and factor analysis,
the authors can primarily explain to readers the path taken for the selection and screening of the papers.
According to the selected papers, in this section the extracted factors and therefore the sub-areas in
the context of CBM reality, are stated.
Machines 2020, 8, 31 3 of 28

Section 4, that is, research factors, retraces the logical flow of thematic areas covered by
the identified RFs.
Finally, Sections 5 and 6 present the discussion of the conclusions drawn from the analysis
of the main areas of CBM. Based on these considerations, possible and desirable future research
developments on the topic are presented.
To summarize, the remainder of the paper is organized as follows. Section 2 details the bibliometric
approach adopted in this study; Section 3 presents a brief descriptive summary of the results, which
are extensively discussed in Section 4. Section 5 proposes critical reflections on the field and proposes
potential future research directions. Lastly, the conclusions summarize the outcome of the study.

2. Methodology
The literature search of this study considered the Scopus database, the largest abstract and citation
database of peer-reviewed literature [24]. The selected key-search was set to include all the documents
proposing “condition-based maintenance” in the title, abstract or keywords, that is, TITLE-ABS-KEY
(“condition based maintenance”). The query has been run-up in July 2019.
The query results 4292 documents, that refer to different subject areas, mainly “Engineering,”
“Computer Science,” “Energy,” “Mathematics,” “Material Science,” “Physics and Astronomy,”
“Business, Management and Accounting” and “Decisions Sciences.”
Due to the multiplicity and the large number of contributions on CBM, it remains challenging
to understand and delineate the main areas of this research field by a priori choice. For this reason,
the authors decided to implement a meta-analysis approach based on bibliometric indicators.
The analysis of the co-citations of the papers is a common approach in this context since it enables
the comprehension of the connections between two or more papers [25]. Its main assumption is that if
two contributions are often co-cited, the same contributions most likely share a thematic concept [26].
This analysis is developed through an explorative Principal Component Analysis (PCA), that is,
a multivariate technique used for dimensionality reduction and the metric used for analytical proximity
is the count of the co-citations. The output of PCA is a set of factors or even “research factors” (RF)—a
set of documents that explore a shared thematic value. PCA is used to define the sub-fields of research
on CBM.

3. Findings from a Systematic Literature Search and Factor Analysis

Among the starting 4292 contributions, 465 contributions (10.83%) are never cited by other papers,
while 2619 of the cited contributions (61.02%) are never co-cited with other papers of the dataset.
Therefore, just 1208 papers in the dataset have been co-cited at least once.
The authors have decided to further refine the dataset, inserting a threshold of co-citations
for inclusion in text analysis. The threshold has been calculated based on the ratio between
the papers considered and the percentage of citations preserved. The 1208 considered papers
share 66,130 co-citations. Considering only the documents with at least 3 co-citations (i.e., using a
threshold of 2), the dataset can be reduced up to 386 hits. In this scenario, the obtained dataset contains
31.2% of the 1208 documents but keeping about 86% of total co-citations. Documents in the final
dataset have 69.92 average citations, which confirm the significance of the filtered contributions across
the research field.
In operational terms, a 386 × 386 co-citation matrix has been defined. This matrix constitutes
the input for a PCA with VariMax rotation to extract the minimum number of factors. Analytically,
a factor represents a linear combination of optimally weighted observed variables that account for a
maximal amount of variance in the observed variables, not accounted for by the preceding components
and uncorrelated with all of the preceding components [27]. The first ten factors include 378 papers
and explain 86.4% of the total variance (see Table 1), while the first four factors economically describe
the same phenomenon (75%).
Machines 2020, 8, 31 4 of 28

Table 1. Results of the Principal Component Analysis (PCA) for the first ten factors.

Factor Value Percent Cum% Ratio

1 138.902 36.0 36.0 1.403
2 98.884 25.6 61.6 2.991
3 34.007 8.8 70.4 1.889
4 18.004 4.7 75.1 1.495
5 12.043 3.1 78.2 1.275
6 9.443 2.4 80.7 1.181
7 7.9955 2.1 82.7 1.441
8 547 1.4 84.2 1.182
9 4.694 1.2 85.4 1.162
10 4.040 1.0 86.4 1.093

Based on previous research [27], the authors have chosen 0.3 as a threshold for significant
factor loading.
At this step, it is necessary to assign each document to the highest loaded factor (factor with
the highest value of factor loading, above the threshold). Subsequently, the authors read independently
the title, abstract and full text of the records to identify common themes of papers, as grouped in
factors. This step allows re-assigning some papers with multiple loadings to the more suitable factor
and shifting to the notion of research factors (cf. Section 2). Assessing thematical aspects, the authors
isolated 4 research factors covering different and complementary areas of CBM (cf. Section 5):

• Research factor 1: The fundamentals of CBM and its implementation

• Research factor 2: CBM strategies
• Research factor 3: Replacement and inspections management and plan and actual machinery
health state
• Research factor 4: Prognosis management and plan

The reduction of the number of research factors compared to the starting 10 PCA factor is justified
considering the reduced number of documents (as well as the minor explained variance, see Table 1).
The structure of the factors excluded from an in-depth thematical analysis has been kept summarizing
minor research contributions, where relevant (cf. Other, Section 4.5).
For the sake of completeness, it is necessary to better explain the management of the factors not
included in the 4 RFs presented:

• Factor 5, factor 7 and factor 9 are presented in Section 4.5 respectively as CBM for electrical
components, Maintenance scheduling for wind farms and Lot-sizing optimization for maintenance
• Factor 8 and factor 10 were relocated within one of the four RFs presented in the paper, that is, RF1,
RF2, RF3 and RF4. Factor 6 has been excluded due to the lack of articles attributed to this factor.

Figure 1 summarizes the proposed research methodology.

The temporal distribution of RFs clearly explains the trend of interest in the CBM field, providing
some observations. To simplify this analysis, Figure 2 shows the trend of contributions attributable to
each RF over the years. One can observe that the first included year is 1994 and the last is 2018.

• Besides the initial interest on standard themes about CBM (RF1 and RF3), there is a common
ground interest on these topics over the years
• RF2 is one of the most examined research themes, with a significant increase around 2008 and 2015
and opposite tendency over more recent years
• RF3 can be considered a saturated RF, as for only three contributions belong to it over the last
three years
• After 2008, RF4 raised significantly, becoming one of the most investigated CBM research areas in
terms of number of contributions
Machines 2020, 8, 31 5 of 28

• “Other” research topics seem to be attracting increasing interest in recent years

Machines 2020, 8, x FOR PEER REVIEW 5 of 28

Machines 2020, 8, x FOR PEER REVIEWFigure 1. Research methodology. 6 of 28

Figure 1. Research methodology.

The temporal distribution of RFs clearly explains the trend of interest in the CBM field, providing
some observations. To simplify this analysis, Figure 2 shows the trend of contributions attributable
to each RF over the years. One can observe that the first included year is 1994 and the last is 2018.
• Besides the initial interest on standard themes about CBM (RF1 and RF3), there is a common
ground interest on these topics over the years
• RF2 is one of the most examined research themes, with a significant increase around 2008 and
2015 and opposite tendency over more recent years
• RF3 can be considered a saturated RF, as for only three contributions belong to it over the last
three years
• After 2008, RF4 raised significantly, becoming one of the most investigated CBM research areas
in terms of number of contributions
• “Other” research topics seem to be attracting increasing interest in recent years

Figure 2. Temporal
Figure distribution
2. Temporal distributionof
ofresearch factors
research factors (RF)(RF) using
using a histogram.
a histogram.

Table 2 summarizes
Table 2 summarizes some some bibliometric
bibliometric aspects of
aspects of each
eachresearch factor.
research factor.
Table 2. Analysis of the citations trend by RF.

Minimum Number of Maximum Number of Average Number of

Rf
Citations Citations Citations
1 3 543 56.75
2 3 253 51.50
3 3 307 48.41
Machines 2020, 8, 31 6 of 28

Table 2. Analysis of the citations trend by RF.

Rf Minimum Number of Citations Maximum Number of Citations Average Number of Citations

1 3 543 56.75
2 3 253 51.50
3 3 307 48.41
4* 5 772 85.57
other 7 99 24.75
* Note that the value referred to RF4 does not consider an outlier document presenting 2271 citations [2].

4. Research Factors
Figure 3 represents the logical flow of thematic areas covered by the 4 identified RFs. RF1 introduces
CBM, its theoretical fundamentals and main differences with other policies, as a support for policy
selection. Moreover, it defines the main steps to be carried out for its implementation, discussing all of
them except for prognosis,
Machines presented
2020, 8, x FOR PEER REVIEW in RF4. 7 of 28

Figure Figure
3. Main3. Main research
research areainincondition-based
area condition-based maintenance (CBM).(CBM).
maintenance
RF2 further explores CBM at a more strategic level. Once CBM has been chosen as the
RF2 further explores CBM at a more strategic level. Once CBM has been chosen as the organization
organization maintenance policy, it is necessary to select the best strategy which ensures its proper
maintenance policy, it is necessary
implementation. to select
Based on these the bestthe
considerations, strategy whichinensures
contributions RF2 deal its proper
with implementation.
such an issue,
Based on these considerations,
dividing the contributions
substantially between single-unit and in RF2 deal with
multi-component such RF3
systems. an issue,
and RF4 dividing
deal with substantially
the
planning phase of maintenance. RF3 deals with maintenance strategies based
between single-unit and multi-component systems. RF3 and RF4 deal with the planning phase only on the actual
health state of the machinery and related activities of replacement and inspections. RF4 deals with
strategies where future state and useful life of the machinery are also modeled, that is, prognosis.
The following Sections 4.1–4.5 present each RF, specifying its contributions, outcomes and
limitations.

4.1. The Fundamentals of CBM and Its Implementation

Machines 2020, 8, 31 7 of 28

of maintenance. RF3 deals with maintenance strategies based only on the actual health state of
the machinery and related activities of replacement and inspections. RF4 deals with strategies where
future state and useful life of the machinery are also modeled, that is, prognosis.
The following Sections 4.1–4.5 present each RF, specifying its contributions, outcomes
and limitations.

4.1. The Fundamentals of CBM and Its Implementation

This research factor includes 96 (of 386) contributions. Most contributions in this RF discuss
the fundamentals of CBM and its implementation, following either a theoretical or an operational
approach. The RF includes comparison studies between CBM and other maintenance strategies.
The contributions in this RF span over more than 20 years of research—1994 [11]–2016 [28–30].
The oldest one [11] reviews worldwide industrial practices on CBM, introducing basic concepts such
as the necessity of planned maintenance, the role of CM and the difference between prediction
and diagnosis. It also introduces the state of the art on automatic monitoring devices for
industrial machines.
A temporal evolution remains relevant within this factor. This latter starts with more general
contributions about performance indicators to be considered for building a maintenance strategy [31] or
the main techniques used for item monitoring [12]. Early research focused on general industrial settings,
without a specific machine-oriented contextualization. Later on, research interest in the construction
industry emerged [32,33].

4.1.1. Domain-Based CBM Fundamentals

The interest of the field enlarged in recent years including mainly but not limited to, (i) railway,
(ii) naval operations, (iii) nuclear plants, (iv) aviation.
The interest in railway maintenance is recently increasing due to the necessity to guarantee
both safety and availability of lines [28,34]. It is possible to differentiate between railway vehicle,
that is made up of several components and the identification of a failure root is neither obvious nor
unique [34] and railway infrastructure, that is difficult to maintain, due to the number of stakeholders
involved, the effects of weather or the designed for previous operating conditions [28]. The recent
increment in rail traffic causes more rapid degradation of railway tracks, that have a crucial role in
railway maintenance [28,34,35]. Railway tracks can affect maintenance costs, comfort, safety and overall
performance [28]. Despite the high costs of investment, the return in terms of reliability and maintenance
costs justifies the application of CBM in the railway area [36].
CBM in the naval field has to consider the impossibility of causing failures and considerable
difficulty in data collection [37]. Nowadays, interest for CBM in naval settings is primarily about
very expensive equipment such as propulsion systems [30] or more specifically on gas turbines or
coolers, compressors and fuel injection systems [37–39]. In this context, machine learning is reaching
valuable results for condition monitoring [30], especially through neural networks [37]. The main
areas of intervention for gas turbines, which can affect fuel consumption and pollution emissions [39],
are internal crank wash, fuel nozzles and lube oil filter replacement.
An outdated nuclear power plant has a higher cost for maintenance if compared to modern
generation ones because their decommission at the end of the licensing lives is cherished and the high
costs to satisfy energy demand and generate the required capacity [40]. Considering their characteristics,
the natural degradation phenomena of materials inside them and their correlation with the specific
driving stressors, that are the root cause of the degradation process [40,41], must be monitored
and controlled. Monitoring vibration signals may be helpful, for example, for the management of
motor position indication, the accelerator response and the dynamic force loading on the bearings [41].
CBM has been widely applied within the aviation domain. The first challenge is the integration
of data, distinguishing between onboard and offboard data sources [42]. In general, aviation health
monitoring systems are separated, generating costs and complexity [42]. Based on this, the integration
Machines 2020, 8, 31 8 of 28

between model-based diagnosis and prognosis could be useful, to synthesize them within the system
design [43]. Gas turbines are important components of the aviation systems, composed by a large
number of items and various levels of subsystems, that can be affected by hostile environments
and that show promising responses with artificial neural networks [44]. The relationships between
prognostics and health management technologies and servitization for aviation components should be
considered [18] because it can deeply reduce the risk connected with the latter [45].
Besides the previously mentioned contributions on CBM for turbines, further contributions
refer to their application for thermal plants as a response to the expansion of renewable energy
market [46], also for offshore wind farms [47]. Traditional CBM models developed for steady-state
situations should be revisited to consider the intermittence of the respective parameters [46], caused by
the necessity to compensate intermittent renewable energy sources. Over the years, these settings
proofed the superiority of data-driven approaches rather than physical-based ones [47,48], considering,
for example, neural networks for the diagnosis, especially when designed individually for specific
failure modes [44].

4.1.2. Meta-Dimensions of CBM Fundamentals

In addition to the proposed domain-based perspective, this RF encompasses contributions ranging
from pure theoretical papers towards more practical models for diagnosis implementation, besides
reviews that consider only specific sub-topic related to CBM, as mentioned in Section 1.
CBM implementation relies on four main steps, that is, physical description, functional description,
components prioritization, data handling, diagnosis and prognosis. Regarding data handling,
it is relevant to consider data collection, data analysis, decision-making and implementation, as collected
through eight relevant postulates [49]. The first steps refer to the comprehension of information
sources, subordinated to physical structure and functional aspects [29]. These latter constitute necessary
outputs for analyzing the symptoms and making interpretative sense out of them. The selection of
the most important systems and the most critical components precede the description of maintenance
tasks and general actions, that is, diagnosis and prognosis [50], which require periodic updates
for optimal setting [50,51]. The analysis of critical components connects CBM with the concept of
Reliability Centered Maintenance (RCM), which enhances CBM with a specific focus on failure modes
analysis [29,52]. Based on these considerations, data fusion levels remain relevant [51]—starting from
signal-level fusion, including feature-level fusion up to decision-level fusion. Decision-making refers to
the prioritization of maintenance activities [53]. Every equipment has different reliability requirements,
safety levels and failure effects and needs different maintenance policies and strategies [54]. The decision
making process is a multi-criteria problem, acknowledging costs, safety, added-value, feasibility [54]
and risk [55]. The literature proposes the Analytic Hierarchy Process (AHP) for decision-making [54,56],
sometimes combined with different algorithms [55]. A fuzzy version of the AHP has been proposed as
well to include uncertainty analysis [54]. About diagnosis, some papers present practical suggestions
for its implementation concerning data mining and data processing. Four main areas can be identified,
that is, Bayesian models [57], Logical Analysis of Data (LAD) [58–60], Fuzzy model [61,62] and Neural
Networks [44,63–65]. The Hierarchical Bayesian approach helps with the uncertainty of degradation
data and maintenance activities, providing its quantification. Moreover, the Bayesian theory is the basis
for the particle filtering, that can powerfully process sequential signals, facilitating the prognosis [57].
LAD is a supervised learning data mining technique, based on combinatory and Boolean theory, to
find patterns in a binary database and generate decision functions without any statistical theory [59].
LAD affects the process of handling missing data and noise since it provides structured approaches
for the replacement of missing values by the Min-Max method [59]. LAD has been successfully
applied for the diagnosis of rotor bearings [58], as well as for the systemic identification of rogue
components [60]. Finally, LAD is completely transparent [59,60], with the possibility to find the root
causes for the categorization of each observation. Fuzzy models have been adopted for both diagnosis
and prognosis. Starting from traditional fuzzy inference systems based on if-then rules requiring
Machines 2020, 8, 31 9 of 28

manual tuning of parameters [61], more advanced approaches including fuzzy inference systems
and neural networks can enhance performance, simplifying the interaction with other business
functions [61]. The neuro-fuzzy approach overcomes the non-transparency of neural networks, which
involves a difficult interpretation of the resulting control law [62], as proved for CBM applications
in bearings management. Neural networks have been largely applied in CBM, even in terms of
decentralized artificial neural networks. These latter involve the use of a hierarchical approach based
on multiple neural networks, each of them specialized for a specific task [44]. The digression in
Fuzzy models can be improved with a neuro-fuzzy approach, also including self-organizing map
techniques. These latter are able to learn without having the corresponding class labels for the input
pattern and with unknown conditions can be activated where the previous neural classifier lose its
validity [64].
An interest in data gathering and data management, with associated data quality problems, can
be observed [66]. Poor raw data management can affect CBM implementation, as proved by a set of
wide reviews about data-driven approaches (from data preparation to sensitivity analysis) [47,66].
CM is central for ensuring correct data management [67] and relates to ICT (Information Communication
Technology) application, specifically of web and agent technologies [13]. After the data integration,
a correspondent technological support development is required, especially in contexts where assets are
geographically dislocated [13,68]. Even considering the publishing years of [13,67], respectively 2009
and 2008, one can assert that data management and its correlation with technologies is still an open
challenge. Sensor technologies have an important role for CM and they have been developed widely in
response to the monitoring of specific parameters (particularly for vibration, a largely used parameter
for CBM) and usability challenges (portability, non-contact and reduced size) [69]. The evolution
in sensor technologies is tightly linked to prognostics and health management, facilitating a more
powerful and cheaper data acquisition [67]. Prognostics and health management are defined as
methods and technologies to analyze the reliability of a product and understand potential failures,
mitigating risks. They represent a complex research area on CBM, affecting CBM effectiveness from
raw data gathering to item behavior forecasts [15,70]. Recently, they have been enhanced by artificial
intelligence [17]. One can observe that implementing maintenance correctly implies integrating three
policies, that is, corrective, preventive and CBM, depending on the role of items and associated
cost-effectiveness [32]. Focusing on CBM, it is essential to understand that it involves—and requires
integrated management of—various disciplines like data mining, artificial intelligence and statistics [71].
Production contexts must be considered for the effectiveness of CBM since they are differently affected
by CBM implementation [72]. The main areas of CBM are diagnosis and prognosis and the systematic
explorative integration of different data sources is the most challenging task [70].

4.2. CBM Strategies

This research factor includes 121 (of 386) contributions, which discuss CBM strategies through
practical examples, explaining the ones previously available or proposing variations of them.
As a complementary perspective to RF1, RF2 defines more details for CBM policy implementation,
with a distinction between single-unit systems and multi-component systems. The term single-unit is
used to depict a system with a unique unit or even a system with a unique critical component able to
sufficiently represent the entire system [73]. Multi-component systems refer to either a system with more
than one unit or a unit with multiple sub-components to be analyzed jointly [74]. Literature is mainly
focused on single-unit systems [75–79], even if recently multi-component systems are increasingly
investigated since they represent a more realistic setting [80–83]. Multi-component system analysis is
usually more demanding since it involves dependencies analysis between the various components
and even environmental settings [21,84–87]. Reproducing the strategy for a single-component system to
a multi-component system does not usually represent an optimal solution [88], that is, the superposition
property does not remain valid [80,89]—a single-unit strategy can be applied to a multi-unit system
only if there are no dependencies inside it.
Machines 2020, 8, 31 10 of 28

4.2.1. Single-Unit Systems

For single-unit systems, parameters are usually optimized as a primary function of maintenance
costs. This latter should be precisely assessed since production rate and capacity or availability could be
aspects to be prioritized under specific circumstances [90–92]. For this purpose, a dynamic maintenance
structure can be preferred to reduce uncertainty on measurements [93]. The most applied strategy
for single-unit systems refers to opportunistic maintenance, in which maintenance decisions usually
follow control-limit rules [90,94]. The presented strategy ensures that inspection time is optimized to
guarantee that the failure probability before the next inspection remains lower than an imposed limit
Q (0 < Q < 1), also considering environmental conditions [95].

4.2.2. Multi-Component Systems

This subsection refers to those components which require more sophisticated approaches, in light
of their numerosity and respective functionally intertwined properties [96].
Multi-component systems can be analyzed either at the system—or at a component-level. In the first
case, the predictive reliability of the system is determined as a function of the reliability of its components
and it drives preventive maintenance interventions. On the other hand, the component-level analysis
drives the identification of an optimal components grouping to ensure the optimal implementation of
the triggered systemic preventive intervention [86]. An intertwined perspective on these two levels
should encompass multi-level decision-making [97]. In this context, a two-stages approach has been
proposed as well—the first stage determines the maintenance strategy for each component, based on
the nature and the urgency of the problem; the second stage considers pre-determined maintenance
strategies for the individual components and aggregates them at the system level to minimize total costs
in light of risk tolerance of degradation behavior [98]. CBM is often compared with the ABR (Age-Based
Replacement), usually in terms of cost-savings [99]. A comparison of the difference for these strategies
in serial and parallel configuration reported how CBM outperforms ABR in parallel configurations
and vice versa for serial configurations, due to starving and blocking effects [100]. Further observations
remain relevant when comparing CBM and ABR, (e.g.,) maintenance worker constraints, external
maintenance workers with response time and a limited number of internal maintenance workers [100].
Such aspects pave the way to human-oriented analyses focused on human error during maintenance
interventions [101]. A proper CBM strategy development for multi-component systems profits in
prognostics and RUL information analysis [84,85,97,102–104]. In this context, the degradation level
of any component may affect the RUL of any other component in the system [85]. More specifically,
a relevant property of the RUL (i.e., monotonicity) allows converting the events of RUL associated
with quantity in degradation levels [103]. As such, RUL represents a valuable condition index to
make the maintenance actions more reliable [97], also ensuring dynamic information update [102].
Degradation processes acquire a central role for CBM implementation—required planning time,
imprecise conditional information and uncertainty of failure levels have a strong influence on
the strategy cost-benefit [105]. In this way, CBM optimization can be modeled either as a Markov [80,106]
or a semi-Markov decision process [96]. It can also refer to the proportional hazards model [75].
Alternatively, Monte Carlo simulation represents a valuable approach since it enables modeling a large
set of realistic scenarios [107,108]. In large multi-component systems, analytical models are indeed less
effective than simulation models, as proven by Markov models [109,110], continuous-time Markov,
time hidden-Markov chains [111,112], gamma processes [113,114] or competition/cooperative heuristic
hybrid games [115]. The genetic algorithm has been used as well in combination with Monte Carlo
simulation [107] or for risk management associated with strategy selection [116]. The computation of
relevant thresholds is a central issue for CBM, especially in multi-component settings. Their calculation
is usually based on costs [108] or failure probability [84]. In practical terms, one can imagine that there
is no single optimum strategy, especially considering imperfect maintenance actions and short-run
availability constraints [113]. In this context, CBM should be linked to inventory, as for the (s, S) strategy
(i.e., variable spare part order quantity to reach the maximum stock level S to be scheduled only below a
Machines 2020, 8, 31 11 of 28

certain level of the inventory s) [80]. Such inventory strategy can be further improved if combined with
the condition-based replacement strategy, named as the (T, S, s, Lp) strategy, where T is the inspection
interval, S is the maximum stock level, s is the reorder level and Lp is the preventive replacement
threshold [117]. For multi-component systems, multiple competing failure modes should be considered
to correctly design a CBM strategy [118]. A preliminary distinction refers to internal degradation
and external shocks [119–121], which can include human-induced ones [101]. Another distinction is
on failure type—hard (i.e., abrupt) and soft failures (i.e., gradual) [122]. One advantage of CBM is its
capability of being independent from the failure mode, that is, being able to consider jointly multiple
failures modes (at least expect abrupt failure, where there is no evidence of a detectable precursor
signal) [123]. An example is represented by wind turbines, which can be affected by types of failure
even in relation to external operating conditions [109].

4.2.3. About Dependencies

A multi-component system involves some dependencies that cannot be neglected between
different components as well as with the environment. These dependencies are the main difference
between a single-unit strategy and a multi-component strategy. Based on this, in multi-component
systems the optimal maintenance and inventory decisions depend on the complete system. As asserted
before, these dependencies are the reason why reproducing the strategy for a single-component system
to a multi-component system could not be optimal [80,89] and a single-unit strategy can be applied to
a multi-unit system only if there are no dependencies inside it.
Based on this assumption, an important amount of contributions focuses on these dependencies,
their role and their management.
The most considered dependencies in literature are economical-oriented or structure-based,
with research also referring to stochastic dependencies [21]. The biggest part of the analyzed papers
agrees about the importance of the economical dependencies [21,75,84–86,89,94,97,98,102,116,124–127].
This kind of dependence can be approached in two main ways, that is, grouping maintenance
and opportunistic maintenance. The former is suitable in those settings when reliability is less
important than economic requirements or when the multi-component system has a high level
of structural dependencies. The latter is more suitable when there are several stochastically
failing parts or high-reliability requirements [85]. Structural dependencies represent the structural
and static relationships between different components, mainly represented by technical dependencies
or performance dependencies [98,124]. Considering structural dependencies, component repair
or replacement may require or inhibit additional components to be maintained. The literature
presents rather limited contributions referred to the investigation of this dependency [97,125],
with some attempts aimed at interfacing economical and structural dependencies, modeling the latter
based on the former [102]. Stochastic dependencies entail the deterioration or failure processes
of components that are partially or totally dependent, for failure-induced damage, load sharing
or common-mode deterioration [89,102,116]. Further types of dependencies include resources
management, that is, maintenance activities can be performed only if the required resources are
available (i.e., maintenance worker restrictions, tool restrictions, spares restrictions, transport restrictions
and budget restrictions) [128]. In this context, spare parts acquire a central role, since they have to be
available for the actual CBM implementation [128].
Different approaches have been proposed for the definition and the management of dependencies
in a system, required for a full comprehension of their influence on CBM implementation. Risk-attitude
becomes relevant for the optimization of the parameters—when a subject is risk-neutral, the optimal
strategy should consider the minimization of the cost rate; when a subject is risk-adverse or risk-seeking,
the strategy should consider the stochastic dominant rules [129]. For economic dependencies, the most
frequent strategies are complete clustering [130], inspection-driven clustering [99], opportunistic
clustering and optimal clustering [124]. For structural dependencies, thresholds for opportunistic
replacement and preventive replacement or threshold for preventive replacement and probability
Machines 2020, 8, 31 12 of 28

thresholds for grouping replacements [89]. Finally, for what concern the stochastic dependencies,
the most applied strategies are the threshold for preventive replacement and the thresholds for
preventive imperfect repair and preventive replacement [131], as well as copulas, motivated by their
particular flexibility and simplicity in modeling multi-dimensional variables [129,132].

4.3. Replacement and Inspections Management and Plan and Actual Machinery Health State
This research factor includes 42 (of 386) contributions. It explores maintenance strategies that rely
only on the actual state of the machinery, discussing specific inspection and replacement strategies
and respective maintenance plans. As a premise, it is worth separating the two ways state information
can be collected from a machine, that is, directly (the measured parameter that directly determines a
failure process) or indirectly (provides associated information, which is influenced by the component
condition but is not a direct measure of the failure process) [133,134].

4.3.1. About Inspection

Common practices for inspection management start from the development of a model for machine
reliability based on its historical failure data [135]. Nowadays, it has been recognized the need to
integrate such static data with real-time ones, as proved (e.g.,) by the adoption of the Kalman filter
where even a shorter increment time for every step can improve model accuracy [136]. The evidence
of the condition of one or more components can be correlated both with efficiency and inspection
intervals [137]. Nevertheless, considering the computational efforts of the method, it should be used
only for those elements in a minimum cut set as obtained from a fault tree analysis or a Petri net
model failure [136]. The inspection interval is strictly correlated with the typology of deterioration to
consider [138].
For Markovian or semi-Markovian deterioration models, the effectiveness of a multi-variate
process capability index supports the integration of equipment multiple parameters into a synthetic
equipment health index [135]. The LAD ensures reasonable performance to evaluate the health state
and consequently to predict the survivability of a machine [139]. Risk factors should be considered
and integrated through proportional hazards models to extract information from the signals obtained
during CM [134]. A correct signal estimation is essential to the proper implementation of replacement
and inspection policies [140,141]. Nevertheless, since the validity of the results can be compromised
by an excessive number of variables compared to available instances, it becomes necessary to reduce,
if possible, their number (e.g., through PCA, principal components analysis) [142]. PCA has been
combined with the proportional hazards model for time-dependent stochastic covariates in real
settings [143]. Parameter estimation can be implemented online and offline, with an increasing interest
in real-time online settings [141].

4.3.2. About Replacement

Replacement strategy should refer to a precise machinery health state assessment and aim at
minimizing the expected total discounted cost, especially in partially observable systems [140,141,144–146].
Costs minimization can be modelled as a Markov decision process whose state contains the probability
distribution of system deterioration levels [144]. In theoretical terms, a component can be preventively
replaced if its associated risk of failure exceeds a pre-determined threshold, as for the data obtained from
inspections, which have a non-negligible cost [133,147]. The role of the interval for an inspection is linked
even with the development of a significant critical level about an objective function for replacement, (e.g.,)
expected cost per unit time, the expected downtime per unit time or other reliability measures [148].
In simpler approaches, the maintenance threshold is usually fixed, while it could be of interest to
link it to other parameters related to costs, downtime and reliability [149,150]. On these assumptions,
replacement becomes tightly related to inspections to trade-off the cost associated with inspection
frequency and potential induced failure costs due to non-replaced components [147,151,152]. More frequent
inspections provide detailed information about the system conditions and avoid unnecessary replacements.
Machines 2020, 8, 31 13 of 28

A two stages approach can be applied to model this trade-off—the first stage assumes inspections costs as
negligible in a partial replacement strategy; the second stage relaxes the assumption through an A * heuristic
algorithm to refine the replacement strategy [133]. The application of the Weibull proportional-hazards
model for determining the optimal replacement strategy provided relevant results [143,153]. It has been
used as a Weibull baseline hazard combined with a Markov process for modeling equipment lifetime [153]
and in combination with time-dependent stochastic covariates to describe the system failure rate [143].

4.4. Prognosis Management and Plan

This RF includes 103 (of 386) contributions that discuss RUL or future health state prediction for
a machine. RF4 is complementary to RF3 because it is integrated with maintenance strategies that
consider both the actual and the future health state, integrating prognostics both at a management
and at a plan level.
From a theoretical perspective, four main steps constitute a prognostics process—data acquisition,
health indicator construction, health stage division and RUL prediction [154]. A major challenge in
predicting RUL is the uncovering of the relationships between quantitative measures and damage
states [155], exploring direct or indirect state variables. Direct state variables are usually analyzed
via regression-based models, Brownian motion with drift (Wiener processes [156]), gamma processes
and Markovian-based models; indirect ones via stochastic filtering-based models, covariate based
hazard models and Hidden Markov model (HMM) and hidden semi-Markov model (HSMM)
based methods [14]. Another distinction consists of model-based approaches and data-driven
approaches [157]. The former relies on developing physics models of failure or degradation, while
the latter is based on data transformation directly from sensor outputs into models, especially valuable
if adopting artificial intelligence [2,155]. Experience-based prognostics (or reliability-based prognostics)
can be considered as a hybrid approach based on using knowledge from experience feedbacks
gathered during a significant period (maintenance data, operating data, failure times, etc.) to adjust
the parameters of some predefined reliability models [158].
From a methodological point of view, some methods have been largely used within prognostics,
that is, fuzzy logic, Monte Carlo simulation, neural networks, Kalman filters, Wavelet methods,
Bayesian models, Support Vector Machines, Markov and semi-Markov models. All these techniques
are rarely used standalone since their integration usually provides more advantageous results [159].
The fuzzy process has been investigated especially on bearings [160–163]. In combination with
the Weibull distribution and neural networks, fuzzy logic can manage nonlinear time series [160].
Similarly, it is possible to mix fuzzy c-means (a user-friendly method for pattern recognition) with
the lifting wavelet packet decomposition, that is, the most used time-frequency analysis method [161].
This composed method assures the user a simplified set of parameters and it has been further expanded
including a support vector data description to increase robustness to outliers and degradation
assessment [162]. Adaptive neuro-fuzzy inference systems can also be mixed with high-order particle
filtering [163]. Monte Carlo simulation is particularly relevant for modern applications since it
remains valid in nonlinear systems [164]. It can be effectively combined with Hidden Markov
models [159] or Bayesian networks [165–167]. Kalman filter has been used to increase prediction
accuracy, even if it requires a large amount of data to be implemented [168]. Some extensions of
Kalman filter have been tested to relax the assumption on the linear system dynamics model with
Gaussian noise [169,170]. The wavelet packet–empirical mode decomposition has been applied
for feature extraction in combination with the self-organization mapping to evaluate performance
degradation [171]. To extract system features, the wavelet transform has been combined with
support vector regression [172,173]. The wavelet decomposition has been also used as a basis for
the development of health indexes [174]. In this regard, it is important to note that the decomposition
level of the wavelet has generally an impact on prediction accuracy [173]. The effectiveness of support
vector machines for RUL prediction has been confirmed standalone [175] or even if applied in a Cox
proportional hazard model for the estimation of the survival function of a system [176]. Bayesian
Machines 2020, 8, 31 14 of 28

logic guarantees correct uncertainty management, especially in light of parameter estimation dynamic
updates [177]. A dynamic Bayesian approach enables more flexible Hidden Markov models [178]
and remains effective even if combined with a particle filter algorithm [179]. A Bayesian model
can be used to iteratively evaluate the probability of failure of a component, mainly in the case of
individual failure modes [180]. Neural networks and especially deep neural networks, are applicable
for dimensionality reduction problems [181,182] In data management context, self-organizing map
neural networks can be applied as a feature-level fusion algorithm [183]. Additional neural network
based approaches include a Weibull failure rate function to reduce the noise effect [184,185] or
the adoption of a recurrent two layers structure, that is, the Elman context layer and the Jordan
context layer [186]. Interesting considerations can be done even about the use of wavelet neural
networks in prognostics [187]. They can also be combined with wavelets to produce a joint approach
particularly flexible for non-linear failure modes analyses [187]. Markov and semi-Markov models have
been largely adopted due to their flexibility for both diagnosis and prognosis which counterbalances
their challenging design and training [188–196]. Hidden Markov models ensure effective results
even without data pre-processing and remain valuable to reduce the computational complexity
in multi-sensor systems [189], especially in case of no knowledge on previous failure states [190]
or to include environmental factors via belief rule-based methodologies [191]. In general, hidden
semi-Markov models are preferable since they guarantee more realistic applicability if compared to
Markov chains [193].
The performance of any prognosis model should be assessed based on different metrics referring
to three major categories—algorithm performance metrics, computational performance metrics
and cost-benefit metrics [197]. The most frequent metrics are accuracy, precision, mean square
error and mean absolute percentage error [198]. When human experts are involved, it becomes
necessary to provide a measure of the consistency of the judgments and their influence on the entire
process [199]. Similar observations remain valid for the reliability of the sensors networks [200]. In this
context, the 5S methodology can be used to convert raw data in prognostics information [201] via 5
steps, that is, streamline, smart processing, synchronize & see, standardize and sustain.

4.5. Other
Besides the major factors previously discussed, it is possible to isolate some minor sub-factors
referred to very specific domains, inductively identified after full-text reading—(i) maintenance
scheduling for wind farms, (ii) lot-sizing optimization for maintenance, (iii) CBM for
electrical components.

4.5.1. Maintenance Scheduling for Wind Farms

The 6 papers in this area deal with scheduling of maintenance tasks, evolving traditional time-based
maintenance [202], as discussed (e.g.,) through a risk-based model for offshore wind turbines [203].
The approach relies on the pre-posterior Bayesian decision theory to quantify indirect information about
the damage state of critical components [203]. Alternative approaches for wind turbines rely on Markov
decision process models to develop an optimal cost-effective maintenance strategy [204] or discrete
event simulation to include stochastic hourly and seasonal loading [205]. An innovative mixed-integer
optimization model for maintenance scheduling is proposed to rely on sensor-driven interventions,
via a Bayesian prognostic model [206]. The approach has been further extended considering the effects
of maintenance on network operation [207].

4.5.2. Lot-Sizing Optimization for Maintenance

This minor sub-factor including just 3 documents refers to contributions dealing with
the integration of maintenance with production aspects linked to lot-sizing.
Sampling models do not consider interactions with production, inventory and maintenance
aspects [208].
Machines 2020, 8, 31 15 of 28

One of these models suggests the minimization of an objective function defined by costs constrained
on production quality. Through the proposed numerical examples, several functional inter-connections
are defined between maintenance, production, inventory and quality.
A similar contribution adopting a slightly different objective function in this context is the long-run
expected average cost per unit time, acknowledging multiple costs such as shortage, set-up, maintenance,
inventory holding and lost production costs [209]. Relying on the same costs, another research presents
a joint optimization model of production lot-sizing and CBM for a multi-component production system
to meet in a finite time horizon demand schedule [210].

4.5.3. CBM for Electrical Components

This sub-factor includes 15 contributions which deal with CBM for electrical components, as
investigated by Chinese scholars. These contributions encompass maintenance decision-making aspects
and risk-based strategies [211–213], mostly concerning very specific technical issues, (e.g.,) electrical
transmission equipment and the power transmission system [214,215] or electrical substation [216].
In this case, the minimization of an integrated risk cost function including equipment failure risk
and grid operation risk factors has been solved via a Tabu search algorithm [215]. Another document
adopts the Marquardt method in combination with Weibull distribution fitting and refers to how
Machines 2020, 8, x FOR PEER REVIEW 16 of 28
post-failure statistical analysis has low significance for electrical failure rate estimation [217]. The same
method hasand
fitting been combined
refers with a fuzzy
to how post-failure analytic
statistical hierarchy
analysis process
has low to prioritize
significance eventsfailure
for electrical and reliability
rate
levelsestimation
for life cycle
[217].failure ratesmethod
The same of electrical power
has been transformers
combined [218].analytic hierarchy process to
with a fuzzy
prioritize events and reliability levels for life cycle failure rates of electrical power transformers [218].
5. Discussion
5. Discussion
This section aims to discuss and critically reflect on the results of the literature review. Firstly,
This section
a bibliometric aims toisdiscuss
discussion and critically
proposed, reflect on the results
as a complementary of the literature
explorative review.
dimension toFirstly, a
the detailed
bibliometric discussion is proposed, as a complementary explorative dimension to the detailed
analysis of RFs proposed in Section 4. Then, the topics of each RFs are critically re-discussed to give a
analysis of RFs proposed in Section 4. Then, the topics of each RFs are critically re-discussed to give
synthetic overview of the current status of the literature.
a synthetic overview of the current status of the literature.
5.1. Bibliometric-Driven Discussion
5.1. Bibliometric-Driven Discussion
An analysis of the citations of each RF offers some tangible measures on the topic being investigated
An analysis of the citations of each RF offers some tangible measures on the topic being
(see Figure 4). Note
investigated that Figure
(see Figure 4). Note4 that
excludes
Figurea4 highly
excludescited paper
a highly ascribed
cited to RF4to([2],
paper ascribed RF42271 citations,
([2], 2271
whilecitations,
averagewhile
citations
averageare 85.57)are
citations which
85.57)reviews both both
which reviews diagnosis andand
diagnosis prognosis,
prognosis,with
with aafocus
focus on
RUL onprediction.
RUL prediction.

Figure4.4.Temporal
Figure Temporal analysis ofRFs,
analysis of RFs,excluding
excluding[2].[2].

Figure 4 clarifies that the most relevant RFs in recent years are RF2 and RF4. Such results can be
explained by two main reasons—the increasing interest in multi-component systems as for RF2
[21,98,124]; the evolution of sensors technologies as well as the evolution of machine learning and
data management techniques as for RF4 [154,160,169,219].
A peak in the citations graph referred to RF2 can be easily observed (1997), followed by a
substantial decrease in citations for the following papers. 1997 includes a contribution dealing with
Machines 2020, 8, 31 16 of 28

Figure 4 clarifies that the most relevant RFs in recent years are RF2 and RF4. Such results
can be explained by two main reasons—the increasing interest in multi-component systems as for
RF2 [21,98,124]; the evolution of sensors technologies as well as the evolution of machine learning
and data management techniques as for RF4 [154,160,169,219].
A peak in the citations graph referred to RF2 can be easily observed (1997), followed by a substantial
decrease in citations for the following papers. 1997 includes a contribution dealing with the application
of multiple mathematical models in maintenance [220]. This latter represents a milestone for CBM
since it emphasizes topics that remain largely relevant even today, that is, inspection maintenance,
maintenance for multi-component systems and maintenance management information systems.
Analysing RF4, one can note that there is a peak of citations and published contributions from
2005 to 2012, which is reflected also by an increase in the number of contributions—11 documents
per year (2009–2012), 2 contributions per year (2005–2009), 4 contributions per year (2012 onwards).
Contributions over these years are highly cited since they refer to important reviews on topics
considerably debated in the CBM field, (e.g., prognostics and rotating machines [14,132]). Specifically,
the peak in 2005 can be ascribed to References [188,221]—the former suggests the application of a
large-scale hidden Markov model for both diagnosis and prognosis, demonstrating how it can improve
RUL prediction; the latter critically reflects on diagnosis and prognosis. In 2007, two further highly-cited
contributions present the applicability of hidden semi-Markov models in prognostics and confirm
their effectiveness [193,222]. The most relevant document in 2009 is the review of prognostics for
rotating machines, which remains a topic of large interest in industrial settings [22]. This review is
then integrated by the paper published in 2011 including data-driven approaches, which have been
progressively investigated over recent years [14].
The analysis of contributions in RF3 reveals how its early contributions have received considerable
research interest over the years, with a decreasing trend for more recent contributions. Documents
published until 2002 collect about 40% of the total citations of this RF, proving its recent saturation.
Most recognized research in RF3 spans over replacement policy management [153], actual machinery
health state assessment [136] and inspections interval management [137].
Citations analysis of RF1 reveals three peaks, that is, 1995, 2000 and 2007, respectively due
to References [12,54,56]. The first document [12] is a milestone document summarizing different
maintenance settings, including CBM, while the other ones [54,56] discuss optimization of maintenance
policy selection using the analytic hierarchy process, a well-known and consolidated technique.
In conclusion, one can observe how RF4 and RF2 appear as the RFs with the largest overall
number of citations, with a higher trend for RF4 over recent years, proving its attractiveness for
contemporary scholars.

5.2. Future Research

For what concerns RF1, 50% of its contributions have been published by 2010. It is, therefore, a RF
including essential contributions used as references (and thus highly co-cited) for many aspects of
CBM, such as its theoretical fundamentals and its main steps. This observation implies that RF1 is
the most various RF, dealing mostly with abstract topics. The importance of CBM for cost management
has been clearly underlined and specified in all papers analysed in this review. Cost-effectiveness
is one of the basic criteria for proper maintenance and the reduction of maintenance costs can
help increasing enterprise profit [51], to compete in the modern global business landscape [223].
Nevertheless, the equipment is becoming more complicated and sophisticated, with a consequent
growth of maintenance costs [63], starting from the decision-making process [53]. In conclusion,
the continuous pressure on companies to reduce costs and improve customer satisfaction motivated
increasingly detailed examinations of maintenance practices and strategies [224]. Such observations
become considerably relevant for equipment or plants with a higher cost and high availability
constraints, such as marine propulsion plants. A typical example is represented by propulsion systems,
Machines 2020, 8, 31 17 of 28

because several propulsion components are periodically subjected to expensive maintenance works to
restore, as far as possible, their original design characteristics [39].
The relationship between CBM and the evolution of technologies has been widely discussed.
The correct choice about technologies can be fundamental for the implementation of a suitable
prognosis, nowadays recognized as a key feature for any successful maintenance strategy [17].
This area relies on sensor and information system technologies [225,226], whose technical progress
enabled significant evolution in CBM, mainly linked to remote dynamic data collection [99,227,228].
The use of machine learning is still an open topic concerning such advancements especially for RUL
and future health state prediction. Examples in this sense are represented by the application of support
vector machine [175,176] or neural networks [62,65] and their derived self-organizing maps [64,171].
A large number of papers suggests the application of hidden semi-Markov model [159,189,196] or
hidden Markov model [112,190,229] for diagnosis or prognosis.
Data management for CBM appears still as an immature research area, with several open
challenges at different levels. Several CBM approaches are data-driven [47,230] and as such scarcity,
incompleteness or miss of data require a dedicated approach for its compensation [231]. The handling
of missing data is a crucial aspect for modern CBM implementation and in general for the management
of asset-related maintenance, to support CBM decision analysis [66]. Due to the different properties of
processed CBM data [42], the conversion and integration of multiple data from sensors are usually
challenging [201,232]. Due to the growth of new technologies [67] and the widespread application of
machine learning in the field of CBM, a deeper investigation in this direction seems necessary.
Another promising research area, not deeply investigated, refers to the effects of human factors for
CBM. Research should analyze human-induced failure scenarios emergent from erroneous functional
dependencies, including human reliability and functional characteristics of human error, as well as its
main performance influencing factors [101]. It is important to clarify the need for integrating technical,
human and organizational aspects of maintenance activities [21,100,101].
RUL prediction is another largely discussed research area, which involves aspects of
the degradation processes that affect a system—different degradation processes need different RUL
prediction approaches [85,167,168,184]. As such, a proper comprehension of the degradation processes
is a cornerstone for this research area, with even more research desirable to develop more accurate
models for several of their effects [124,233].
When referring to real operating settings, research on multi-component systems become
fundamental, forcing to model both economic, stochastic, structural and resource dependencies [97,125].
Future research should encompass mainly the resource dependencies, which are less investigated so
far [21].
Finally, more systemic approaches linked to CBM should be investigated within industrial settings,
such as the integration of lot-sizing and maintenance actions [208–210] or the optimization of a
maintenance strategy considering economic manufacturing quantity [234].

6. Conclusions
CBM is a wide research area. Its effectiveness and impact on industrial settings have been largely
recognized and proved via multiple empirical research projects in a variety of contexts. This research
aimed at uncovering the structure of the field, epitomizing its main streams of research. The proposed
bibliometric approach defined 4 main research areas, able to capture synthetically the domain.
The field has been investigated in terms of policy, strategies and implementation plans, compared
with traditional ones. In this regard, research contributions have been differentiated between simpler
single-unit systems and more realistic multi-component ones. This distinction presents different
perspectives both at theoretical and operational levels for inspection, replacement and prognosis.
A large set of methods have been used standalone or integrated for CBM different steps, with a
promising tendency over recent years towards artificial intelligence and machine learning. Nevertheless,
new challenges are already open in front of contemporary and future technological developments—more
Machines 2020, 8, 31 18 of 28

specific component degradation models, the integration of CBM in multi-component multi-sensor

systems, in light of global optimization functions and the analysis of humans and machine interactions
in a progressively more digitalized era.

Funding: This research received no external funding.

Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations
In this section are summarized all the abbreviations encountered in the various sections of the paper. Abbreviations
are presented in alphabetical order.

Abbreviation Meaning
ABR Age-Based Replacement
AHP Analytic Hierarchy Process
CBM Condition-Based Maintenance
CM Condition Monitoring
HMM Hidden Markov Model
HSMM Hidden Semi-Markov Model
ICT Information And Communication Technology
LAD Logical Analysis Of Data
PCA Principal Component Analysis
RCM Reliability-Centered Maintenance
RF Research Factor
RUL Remaining Useful Life
TBM Time-Based Maintenance

References
1. Lee, J.; Ghaffari, M.; Elmeligy, S. Self-maintenance and engineering immune systems: Towards smarter
machines and manufacturing systems. Annu. Rev. Control 2011, 35, 111–122. [CrossRef]
2. Jardine, A.K.S.; Lin, D.; Banjevic, D. A review on machinery diagnostics and prognostics implementing
condition-based maintenance. Mech. Syst. Signal Process. 2006, 20, 1483–1510. [CrossRef]
3. Baldin, A.E. Global approach to plant maintenance. In Proceedings of the AIPE Conference, Montreal, QC,
Cananda, 1 June 1976.
4. Baldin, A.E. Condition based maintenance: A powerful tool for modern plant management. Terotechnica
1979, 1, 119–129.
5. Hirani, J.A.; Varadrajan, R. Condition-Based Maintenance. Indian Text. J. 1985, 95, 43–50.
6. Henry, T.A. The simple approach to condition monitoring. Terotechnical 1979, 1, 131.
7. Baldin, A.E. Condition-based maintenance. Chem. Eng. 1981, 88, 89–95.
8. Harrou, F.; Sun, Y.; Madakyaru, M. Kullback-Leibler distance-based enhanced detection of incipient anomalies.
J. Loss Prev. Process Ind. 2016, 44, 73–87. [CrossRef]
9. Wiboonrat, M. Developing diagnostics and prognostics of data center systems implementing with
condition-based maintenance. In Proceedings of the IECON 2018—44th Annual Conference of the IEEE
Industrial Electronics Society, Washington, DC, USA, 21–23 October 2018; pp. 4901–4906.
10. Harrou, F.; Sun, Y.; Khadraoui, S. Amalgamation of anomaly-detection indices for enhanced process
monitoring. J. Loss Prev. Process Ind. 2016, 40, 365–377. [CrossRef]
11. Martin, K.F. A review by discussion of condition monitoring and fault diagnosis in machine tools. Int. J.
Mach. Tools Manuf. 1994, 34, 527–551. [CrossRef]
12. Tsang, A.H.C. Condition-based maintenance: Tools and decision making. J. Qual. Maint. Eng. 1995, 1, 3–17.
[CrossRef]
13. Campos, J. Development in the application of ICT in condition monitoring and maintenance. Comput. Ind.
2009, 60, 1–20. [CrossRef]
14. Si, X.-S.; Wang, W.; Hu, C.-H.; Zhou, D.-H. Remaining useful life estimation—A review on the statistical data
driven approaches. Eur. J. Oper. Res. 2011, 213, 1–14. [CrossRef]
Machines 2020, 8, 31 19 of 28

15. Guillén, A.J.; Crespo, A.; Macchi, M.; Gómez, J. On the role of Prognostics and Health Management in
advanced maintenance systems. Prod. Plan. Control 2016, 27, 991–1004. [CrossRef]
16. Kothamasu, R.; Huang, S.H.; Verduin, W.H. System health monitoring and prognostics—A review of current
paradigms and practices. Int. J. Adv. Manuf. Technol. 2006, 28, 1012–1024. [CrossRef]
17. Dragomir, O.E.; Gouriveau, R.; Dragomir, F.; Minca, E.; Zerhouni, N. Review of prognostic problem in
condition-based maintenance. In Proceedings of the 2009 European Control Conference, ECC 2009, Budapest,
Hungary, 23–26 August 2009; pp. 1587–1592.
18. Benedettini, O.; Baines, T.S.; Lightfoot, H.W.; Greenough, R.M. State-of-the-art in integrated vehicle health
management. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 2009, 223, 157–170. [CrossRef]
19. Jaw, L.C. Recent advancements in aircraft Engine Health Management (EHM) technologies
and recommendations for the next step. In Proceedings of the ASME Turbo Expo, Reno-Tahoe, NV,
USA, 6–9 June 2005; Volume 1, pp. 683–695.
20. Klingenberg, W.; de Boer, T.W. Condition-based maintenance in punching/blanking of sheet metal. Int. J.
Mach. Tools Manuf. 2008, 48, 589–598. [CrossRef]
21. Olde Keizer, M.C.A.; Flapper, S.D.P.; Teunter, R.H. Condition-based maintenance policies for systems with
multiple dependent components: A review. Eur. J. Oper. Res. 2017, 261, 405–420. [CrossRef]
22. Heng, A.; Zhang, S.; Tan, A.C.C.; Mathew, J. Rotating machinery prognostics: State of the art, challenges
and opportunities. Mech. Syst. Signal Process. 2009, 23, 724–739. [CrossRef]
23. UNI EN 13306:2018 - Maintenance—Maintenance Terminology. 2018. Available online:
http://store.uni.com/catalogo/uni-en-13306-2018?josso_back_to=http://store.uni.com/josso-security-
check.php&josso_cmd=login_optional&josso_partnerapp_host=store.uni.com (accessed on 7 June 2020).
24. Elsevier, Scopus, An Eye on Global Research. 2018. Available online: https://www.elsevier.com/solutions/
scopus (accessed on 7 June 2020).
25. Shafique, M. Thinking inside the box? Intellectual structure of the knowledge base of innovation research
(1988–2008). Strateg. Manag. J. 2013, 34, 62–93. [CrossRef]
26. Di Stefano, G.; Gambardella, A.; Verona, G. Technology push and demand pull perspectives in innovation
studies: Current findings and future research directions. Res. Policy 2012, 41, 1283–1295. [CrossRef]
27. Patriarca, R.; Bergström, J.; Di Gravio, G.; Costantino, F. Resilience engineering: Current status of the research
and future challenges. Saf. Sci. 2018, 102, 79–100. [CrossRef]
28. Al-Douri, Y.K.; Tretten, P.; Karim, R. Improvement of railway performance: A study of Swedish railway
infrastructure. J. Mod. Transp. 2016, 24, 22–37. [CrossRef]
29. Guillén, A.J.; Crespo, A.; Gómez, J.F.; Sanz, M.D. A framework for effective management of condition based
maintenance programs in the context of industrial development of E-Maintenance strategies. Comput. Ind.
2016, 82, 170–185. [CrossRef]
30. Coraddu, A.; Oneto, L.; Ghio, A.; Savio, S.; Anguita, D.; Figari, M. Machine learning approaches for improving
condition-based maintenance of naval propulsion plants. Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ.
2016, 230, 136–153. [CrossRef]
31. Arts, R.H.P.M.; Knapp, G.M.; Mann, L. Some aspects of measuring maintenance performance in the process
industry. J. Qual. Maint. Eng. 1998, 4, 6–11. [CrossRef]
32. Horner, R.M.W.; El-Haram, M.A.; Munns, A.K. Building maintenance strategy: A new management approach.
J. Qual. Maint. Eng. 1997, 3, 273–280. [CrossRef]
33. Edwards, D.J.; Holt, G.D.; Harris, F.C. Predictive maintenance techniques and their relevance to construction
plant. J. Qual. Maint. Eng. 1998, 4, 25–37. [CrossRef]
34. Galar, D.; Kumar, U.; Villarejo, R.; Johansson, C.-A. Hybrid prognosis for railway health assessment:
An information fusion approach for PHM deployment. Chem. Eng. Trans. 2013, 33, 769–774.
35. Su, Z.; Núñez, A.; Jamshidi, A.; Baldi, S.; Li, Z.; Dollevoet, R.; De Schutter, B. Model Predictive Control for
Maintenance Operations Planning of Railway Infrastructures. In Proceedings of the 6th International
Conference on Computational Logistics, ICCL 2015, Delft, The Netherlands, 23–25 September 2015;
Volume 9335, ISBN 9783319242637.
36. Berdinyazov, A.; Camci, F.; Baskan, S.; Sevkli, M.; Eldemir, F. Economic analysis of condition based
maintenance. Int. J. Ind. Eng. Theory Appl. Pract. 2011, 18, 386–403.
37. Basurko, O.C.; Uriondo, Z. Condition-based maintenance for medium speed diesel engines used in vessels
in operation. Appl. Therm. Eng. 2015, 80, 404–412. [CrossRef]
Machines 2020, 8, 31 20 of 28

38. Kacprzynski, G.J.; Gumina, M.; Roemer, M.J.; Caguiat, D.E.; Galie, T.R.; McGroarty, J.J. A prognostic
modeling approach for predicting recurring maintenance for shipboard propulsion systems. In Proceedings
of the ASME Turbo Expo, New Orleans, LA, USA, 4–7 June 2001; Volume 1.
39. Altosole, M.; Campora, U.; Martelli, M.; Figari, M. Performance decay analysis of a marine gas turbine
propulsion system. J. Ship Res. 2014, 58, 117–129. [CrossRef]
40. Bond, L.J.; Doctor, S.R.; Griffin, J.W.; Hull, A.B.; Malik, S.N. Damage assessment technologies for prognostics
and proactive management of materials degradation. Nucl. Technol. 2011, 173, 46–55. [CrossRef]
41. Jarrell, D.B.; Sisk, D.R.; Bond, L.J. Prognostics and condition-based maintenance: A new approach to
precursive metrics. Nucl. Technol. 2004, 145, 275–286. [CrossRef]
42. Dunsdon, J.; Harrington, M. The application of Open system architecture for condition based maintenance
to complete IVHM. In Proceedings of the IEEE Aerospace Conference Proceedings, Big Sky, MT, USA,
1–8 March 2008.
43. Luo, J.; Namburu, M.; Pattipati, K.; Qiao, L.; Kawamoto, M.; Chigusa, S. Model-based Prognostic Techniques.
In Proceedings of the AUTOTESTCON (Proceedings), Anaheim, CA, USA, 22–25 September 2003; pp. 330–340.
44. Ogaji, S.O.T.; Singh, R. Advanced engine diagnostics using artificial neural networks. Appl. Soft Comput. J.
2003, 3, 259–271. [CrossRef]
45. Greenough, R.M.; Grubic, T. Modelling condition-based maintenance to deliver a service to machine tool
users. Int. J. Adv. Manuf. Technol. 2011, 52, 1117–1132. [CrossRef]
46. Tsoutsanis, E.; Meskin, N.; Benammar, M.; Khorasani, K. A dynamic prognosis scheme for flexible operation
of gas turbines. Appl. Energy 2016, 164, 686–701. [CrossRef]
47. Wiggelinkhuizen, E.; Verbruggen, T.; Braam, H.; Rademakers, L.; Xiang, J.; Watson, S. Assessment of condition
monitoring techniques for offshore wind farms. J. Sol. Energy Eng. Trans. ASME 2008, 130, 0310041–0310049.
[CrossRef]
48. Zhou, D.; Zhang, H.; Weng, S. A novel prognostic model of performance degradation trend for power
machinery maintenance. Energy 2014, 78, 740–746. [CrossRef]
49. Veldman, J.; Klingenberg, W.; Wortmann, H. Managing condition-based maintenance technology: A multiple
case study in the process industry. J. Qual. Maint. Eng. 2011, 17, 40–62. [CrossRef]
50. Waeyenbergh, G.; Pintelon, L. Maintenance concept development: A case study. Int. J. Prod. Econ. 2004, 89,
395–405. [CrossRef]
51. Niu, G.; Yang, B.-S.; Pecht, M. Development of an optimized condition-based maintenance system by data
fusion and reliability-centered maintenance. Reliab. Eng. Syst. Saf. 2010, 95, 786–796. [CrossRef]
52. Lehtonen, M. On the optimal strategies of condition monitoring and maintenance allocation in distribution
systems. In Proceedings of the 2006 9th International Conference on Probabilistic Methods Applied to Power
Systems, PMAPS, Stockholm, Sweden, 11–15 June 2006.
53. Moore, W.J.; Starr, A.G. An intelligent maintenance system for continuous cost-based prioritisation of
maintenance activities. Comput. Ind. 2006, 57, 595–606. [CrossRef]
54. Wang, L.; Chu, J.; Wu, J. Selection of optimum maintenance strategies based on a fuzzy analytic hierarchy
process. Int. J. Prod. Econ. 2007, 107, 151–163. [CrossRef]
55. Arunraj, N.S.; Maiti, J. Risk-based maintenance policy selection using AHP and goal programming. Saf. Sci.
2010, 48, 238–247. [CrossRef]
56. Bevilacqua, M.; Braglia, M. Analytic hierarchy process applied to maintenance strategy selection. Reliab. Eng.
Syst. Saf. 2000, 70, 71–83. [CrossRef]
57. Ly, C.; Tom, K.; Byington, C.S.; Patrick, R.; Vachtsevanos, G.J. Fault diagnosis and failure prognosis for
engineering systems: A global perspective. In Proceedings of the 2009 IEEE International Conference on
Automation Science and Engineering, CASE 2009, Bangalore, India, 22–25 August 2009; pp. 108–115.
58. Mortada, M.-A.; Yacout, S.; Lakis, A. Diagnosis of rotor bearings using logical analysis of data. J. Qual. Maint.
Eng. 2011, 17, 371–397. [CrossRef]
59. Bennane, A.; Yacout, S. LAD-CBM; New data processing tool for diagnosis and prognosis in condition-based
maintenance. J. Intell. Manuf. 2012, 23, 265–275. [CrossRef]
60. Mortada, M.-A.; Carroll III, T.; Yacout, S.; Lakis, A. Rogue components: Their effect and control using logical
analysis of data. J. Intell. Manuf. 2012, 23, 289–302. [CrossRef]
61. Kothamasu, R.; Huang, S.H. Adaptive Mamdani fuzzy model for condition-based maintenance. Fuzzy Sets
Syst. 2007, 158, 2715–2733. [CrossRef]
Machines 2020, 8, 31 21 of 28

62. Ciarapica, F.E.; Giacchetta, G. Managing the condition-based maintenance of a combined-cycle power plant:
An approach using soft computing techniques. J. Loss Prev. Process Ind. 2006, 19, 316–325. [CrossRef]
63. Yam, R.C.M.; Tse, P.W.; Li, L.; Tu, P. Intelligent predictive decision support system for condition-based
maintenance. Int. J. Adv. Manuf. Technol. 2001, 17, 383–391. [CrossRef]
64. Wu, F.; Wang, T.; Lee, J. An online adaptive condition-based maintenance method for mechanical systems.
Mech. Syst. Signal Process. 2010, 24, 2985–2995. [CrossRef]
65. Garga, A.K.; McClintic, K.T.; Campbell, R.L.; Yang, C.-C.; Lebold, M.S.; Hay, T.A.; Byington, C.S. Hybrid
reasoning for prognostic learning in CBM systems. IEEE Aerosp. Conf. Proc. 2001, 6, 62957–62969.
66. Tsang, A.H.C.; Yeung, W.K.; Jardine, A.K.S.; Leung, B.P.K. Data management for CBM optimization. J. Qual.
Maint. Eng. 2006, 12, 37–51. [CrossRef]
67. Fumagalli, L.; Macchi, M.; Rapaccini, M. Computerized maintenance management systems in SMEs:
A survey in Italy and some remarks for the implementation of Condition Based Maintenance. IFAC Proc. Vol.
(IFAC-PapersOnline) 2009, 13, 1615–1619. [CrossRef]
68. Campos, J.; Jantunen, E.; Prakash, O. A web and mobile device architecture for mobile e-maintenance. Int. J.
Adv. Manuf. Technol. 2009, 45, 71–80. [CrossRef]
69. Goyal, D.; Pabla, B.S. Condition based maintenance of machine tools–A review. CIRP J. Manuf. Sci. Technol.
2015, 10, 24–35. [CrossRef]
70. Galar, D.; Palo, M.; Van Horenbeek, A.; Pintelon, L. Integration of disparate data sources to perform
maintenance prognosis and optimal decision making. Insight Non-Destr. Test. Cond. Monit. 2012, 54, 440–445.
[CrossRef]
71. Prajapati, A.; Bechtel, J.; Ganesan, S. Condition based maintenance: A survey. J. Qual. Maint. Eng. 2012, 18,
384–400. [CrossRef]
72. Koochaki, J.; Bokhorst, J.; Wortmann, H.; Klingenberg, W. Evaluating condition based maintenance
effectiveness for two processes in series. J. Qual. Maint. Eng. 2011, 17, 398–414. [CrossRef]
73. Do, P.; Voisin, A.; Levrat, E.; Iung, B. A proactive condition-based maintenance strategy with both perfect
and imperfect maintenance actions. Reliab. Eng. Syst. Saf. 2015, 133, 22–32. [CrossRef]
74. Rasmekomen, N.; Parlikad, A.K. Condition-based maintenance of multi-component systems with degradation
state-rate interactions. Reliab. Eng. Syst. Saf. 2016, 148, 1–10. [CrossRef]
75. Tian, Z.; Liao, H. Condition based maintenance optimization for multi-component systems using proportional
hazards model. Reliab. Eng. Syst. Saf. 2011, 96, 581–589. [CrossRef]
76. Huynh, K.T.; Barros, A.; Bérenguer, C.; Castro, I.T. A periodic inspection and replacement policy for systems
subject to competing failure modes due to degradation and traumatic events. Reliab. Eng. Syst. Saf. 2011, 96,
497–508. [CrossRef]
77. Deloux, E.; Castanier, B.; Bérenguer, C. Predictive maintenance policy for a gradually deteriorating system
subject to stress. Reliab. Eng. Syst. Saf. 2009, 94, 418–431. [CrossRef]
78. Berrade, M.D.; Scarf, P.A.; Cavalcante, C.A.V.; Dwight, R.A. Imperfect inspection and replacement of a system
with a defective state: A cost and reliability analysis. Reliab. Eng. Syst. Saf. 2013, 120, 80–87. [CrossRef]
79. Liu, B.; Liang, Z.; Parlikad, A.K.; Xie, M.; Kuo, W. Condition-based maintenance for systems with aging
and cumulative damage based on proportional hazards model. Reliab. Eng. Syst. Saf. 2017, 168, 200–209.
[CrossRef]
80. Olde Keizer, M.C.A.; Teunter, R.H.; Veldman, J. Joint condition-based maintenance and inventory optimization
for systems with multiple components. Eur. J. Oper. Res. 2017, 257, 209–222. [CrossRef]
81. Bouvard, K.; Artus, S.; Bérenguer, C.; Cocquempot, V. Condition-based dynamic maintenance operations
planning & grouping. Application to commercial heavy vehicles. Reliab. Eng. Syst. Saf. 2011, 96, 601–610.
82. Alaswad, S.; Xiang, Y. A review on condition-based maintenance optimization models for stochastically
deteriorating system. Reliab. Eng. Syst. Saf. 2017, 157, 54–63. [CrossRef]
83. Flage, R.; Coit, D.W.; Luxhøj, J.T.; Aven, T. Safety constraints applied to an adaptive Bayesian condition-based
maintenance optimization model. Reliab. Eng. Syst. Saf. 2012, 102, 16–26. [CrossRef]
84. Tian, Z.; Jin, T.; Wu, B.; Ding, F. Condition based maintenance optimization for wind power generation
systems under continuous monitoring. Renew. Energy 2011, 36, 1502–1509. [CrossRef]
85. Shi, H.; Zeng, J. Real-time prediction of remaining useful life and preventive opportunistic maintenance
strategy for multi-component systems considering stochastic dependence. Comput. Ind. Eng. 2016, 93,
192–204. [CrossRef]
Machines 2020, 8, 31 22 of 28

86. Nguyen, K.-A.; Do, P.; Grall, A. Multi-level predictive maintenance for multi-component systems. Reliab. Eng.
Syst. Saf. 2015, 144, 83–94. [CrossRef]
87. Shafiee, M.; Finkelstein, M.; Bérenguer, C. An opportunistic condition-based maintenance policy for offshore
wind turbine blades subjected to degradation and environmental shocks. Reliab. Eng. Syst. Saf. 2015, 142,
463–471. [CrossRef]
88. Castanier, B.; Grall, A.; Bérenguer, C. A condition-based maintenance policy with non-periodic inspections
for a two-unit series system. Reliab. Eng. Syst. Saf. 2005, 87, 109–120. [CrossRef]
89. Li, H.; Deloux, E.; Dieulle, L. A condition-based maintenance policy for multi-component systems with Lévy
copulas dependence. Reliab. Eng. Syst. Saf. 2016, 149, 44–55. [CrossRef]
90. Van, P.D.; Bérenguer, C. Condition based maintenance model for a production deteriorating system.
In Proceedings of the Conference on Control and Fault-Tolerant Systems, SysTol’10—Final Program and Book
of Abstracts, Nice, France, 6–8 October 2010; pp. 424–429.
91. Van, P.D.; Bérenguer, C. Condition-based maintenance with imperfect preventive repairs for a deteriorating
production system. Qual. Reliab. Eng. Int. 2012, 28, 624–633. [CrossRef]
92. Wang, L.; Chu, J.; Mao, W. A condition-based order-replacement policy for a single-unit system. Appl. Math.
Model. 2008, 32, 2274–2289. [CrossRef]
93. Huynh, K.T.; Barros, A.; Bérenguer, C. Maintenance decision-making for systems operating under indirect
condition monitoring: Value of online information and impact of measurement uncertainty. IEEE Trans.
Reliab. 2012, 61, 410–425. [CrossRef]
94. Huynh, T.K.; Barros, A.; Bérenguer, C. A reliability-based opportunistic predictive maintenance model for
k-out-of-n deteriorating systems. Chem. Eng. Trans. 2013, 33, 493–498.
95. Chouikhi, H.; Khatab, A.; Rezg, N. A condition-based maintenance policy for a production system under
excessive environmental degradation. J. Intell. Manuf. 2014, 25, 727–737. [CrossRef]
96. Zhang, Z.; Zhou, Y.; Sun, Y.; Ma, L. Condition-based maintenance optimisation without a predetermined
strategy structure for a two-component series system | Optymalizacja zależnego od stanu technicznego
utrzymania urza{ogonek}dzeń dla dwuskładnikowego systemu szeregowego nie wymagaja{ogonek}.
Eksploat. Niezawodn. 2012, 14, 120–129.
97. Huynh, K.T.; Barros, A.; Bérenguer, C. Multi-level decision-making for the predictive maintenance of
k-out-of-n:F deteriorating systems. IEEE Trans. Reliab. 2015, 64, 94–117. [CrossRef]
98. Verbert, K.; De Schutter, B.; Babuška, R. Timely condition-based maintenance planning for multi-component
systems. Reliab. Eng. Syst. Saf. 2017, 159, 310–321. [CrossRef]
99. Zhu, Q.; Peng, H.; van Houtum, G.-J. A condition-based maintenance policy for multi-component systems
with a high maintenance setup cost. OR Spectr. 2015, 37, 1007–1035. [CrossRef]
100. Koochaki, J.; Bokhorst, J.A.C.; Wortmann, H.; Klingenberg, W. The influence of condition-based maintenance
on workforce planning and maintenance scheduling. Int. J. Prod. Res. 2013, 51, 2339–2351. [CrossRef]
101. Asadzadeh, S.M.; Azadeh, A. An integrated systemic model for optimization of condition-based maintenance
with human error. Reliab. Eng. Syst. Saf. 2014, 124, 117–131. [CrossRef]
102. Van Horenbeek, A.; Pintelon, L. A dynamic predictive maintenance policy for complex multi-component
systems. Reliab. Eng. Syst. Saf. 2013, 120, 39–50. [CrossRef]
103. Huynh, K.T.; Castro, I.T.; Barros, A.; Berenguer, C. On the use of mean residual life as a condition index
for condition-based maintenance decision-making. IEEE Trans. Syst. Man Cybern. Syst. 2014, 44, 877–893.
[CrossRef]
104. Huynh, K.T.; Grall, A.; Bérenguer, C. Assessment of diagnostic and prognostic condition indices for efficient
and robust maintenance decision-making of systems subject to stress corrosion cracking. Reliab. Eng. Syst.
Saf. 2017, 159, 237–254. [CrossRef]
105. de Jonge, B.; Teunter, R.; Tinga, T. The influence of practical factors on the benefits of condition-based
maintenance over time-based maintenance. Reliab. Eng. Syst. Saf. 2017, 158, 21–30. [CrossRef]
106. Kim, M.J.; Makis, V. Joint optimization of sampling and control of partially observable failing systems.
Oper. Res. 2013, 61, 777–790. [CrossRef]
107. Marseguerra, M.; Zio, E.; Podofillini, L. Condition-based maintenance optimization by means of genetic
algorithms and Monte Carlo simulation. Reliab. Eng. Syst. Saf. 2002, 77, 151–165. [CrossRef]
Machines 2020, 8, 31 23 of 28

108. Barata, J.; Soares, C.G.; Marseguerra, M.; Zio, E. Simulation modelling of repairable multi-component
deteriorating systems for “on condition” maintenance optimisation. Reliab. Eng. Syst. Saf. 2002, 76, 255–264.
[CrossRef]
109. Byon, E.; Ding, Y. Season-dependent condition-based maintenance for a wind turbine using a partially
observed markov decision process. IEEE Trans. Power Syst. 2010, 25, 1823–1834. [CrossRef]
110. Zhao, X.; Fouladirad, M.; Bérenguer, C.; Bordes, L. Condition-based inspection/replacement policies for
non-monotone deteriorating systems with environmental covariates. Reliab. Eng. Syst. Saf. 2010, 95, 921–934.
[CrossRef]
111. Wang, L.; Zheng, E.; Li, Y.; Wang, B.; Wu, J. Maintenance optimization of generating equipment based on a
condition-based maintenance policy for multi-unit systems. In Proceedings of the 2009 Chinese Control
and Decision Conference, CCDC 2009, Guilin, China, 17–19 June 2009; pp. 2440–2445.
112. Naderkhani, Z.G.F.; Makis, V. Optimal condition-based maintenance policy for a partially observable system
with two sampling intervals. Int. J. Adv. Manuf. Technol. 2015, 78, 795–805. [CrossRef]
113. Liao, H.; Elsayed, E.A.; Chan, L.-Y. Maintenance of continuously monitored degrading systems. Eur. J. Oper.
Res. 2006, 175, 821–835. [CrossRef]
114. Tan, L.; Cheng, Z.; Guo, B.; Gong, S. Condition-based maintenance policy for gamma deteriorating systems.
J. Syst. Eng. Electron. 2010, 21, 57–61. [CrossRef]
115. Feng, Q.; Bi, X.; Zhao, X.; Chen, Y.; Sun, B. Heuristic hybrid game approach for fleet condition-based
maintenance planning. Reliab. Eng. Syst. Saf. 2017, 157, 166–176. [CrossRef]
116. Camci, F. System maintenance scheduling with prognostics information using genetic algorithm. IEEE Trans.
Reliab. 2009, 58, 539–552. [CrossRef]
117. Wang, L.; Chu, J.; Mao, W. A condition-based replacement and spare provisioning policy for deteriorating
systems with uncertain deterioration to failure. Eur. J. Oper. Res. 2009, 194, 184–205. [CrossRef]
118. El-Thalji, I.; Jantunen, E. On the development of condition based maintenance strategy for offshore wind
farm: Requirement elicitation process. Energy Procedia 2012, 24, 328–339. [CrossRef]
119. Caballé, N.C.; Castro, I.T.; Pérez, C.J.; Lanza-Gutiérrez, J.M. A condition-based maintenance of a dependent
degradation-threshold-shock model in a system with multiple degradation processes. Reliab. Eng. Syst. Saf.
2015, 134, 98–109. [CrossRef]
120. Castro, I.T.; Caballé, N.C.; Pérez, C.J. A condition-based maintenance for a system subject to multiple
degradation processes and external shocks. Int. J. Syst. Sci. 2015, 46, 1692–1704. [CrossRef]
121. Li, W.; Pham, H. An inspection-maintenance model for systems with multiple competing processes.
IEEE Trans. Reliab. 2005, 54, 318–327. [CrossRef]
122. Chen, D.; Trivedi, K.S. Closed-form analytical results for condition-based maintenance. Reliab. Eng. Syst. Saf.
2002, 76, 43–51. [CrossRef]
123. Liu, X.; Li, J.; Al-Khalifa, K.N.; Hamouda, A.S.; Coit, D.W.; Elsayed, E.A. Condition-based maintenance
for continuously monitored degrading systems with multiple failure modes. IIE Trans. 2013, 45, 422–435.
[CrossRef]
124. Olde Keizer, M.C.A.; Teunter, R.H.; Veldman, J. Clustering condition-based maintenance for systems with
redundancy and economic dependencies. Eur. J. Oper. Res. 2016, 251, 531–540. [CrossRef]
125. Do, P.; Scarf, P.; Lung, B. Condition-based maintenance for a two-component system with dependencies.
IFAC-PapersOnLine 2015, 28, 946–951. [CrossRef]
126. Nguyen, K.-A.; Do, P.; Grall, A. Condition-based maintenance for multi-component systems using importance
measure and predictive information. Int. J. Syst. Sci. Oper. Logist. 2014, 1, 228–245. [CrossRef]
127. Qian, X.; Wu, Y. Dynamic control-limit policy of condition based maintenance for the hydroelectricity
generating unit. Int. J. Secur. Appl. 2014, 8, 95–106. [CrossRef]
128. De Smidt-Destombes, K.S.; Van der Heijden, M.C.; Van Harten, A. On the availability of a k-out-of-N system
given limited spares and repair capacity under a condition based maintenance strategy. Reliab. Eng. Syst.
Saf. 2004, 83, 287–300. [CrossRef]
129. Hong, H.P.; Zhou, W.; Zhang, S.; Ye, W. Optimal condition-based maintenance decisions for systems with
dependent stochastic degradation of components. Reliab. Eng. Syst. Saf. 2014, 121, 276–288. [CrossRef]
130. Shafiee, M.; Finkelstein, M. A proactive group maintenance policy for continuously monitored deteriorating
systems: Application to offshore wind turbines. Proc. Inst. Mech. Eng. Part O J. Risk Reliab. 2015, 229,
373–384. [CrossRef]
Machines 2020, 8, 31 24 of 28

131. Liang, Z.; Parlikad, A.K. A tiered modelling approach for condition-based maintenance of industrial assets
with load sharing interaction and fault propagation. IMA J. Manag. Math. 2015, 26, 125–144. [CrossRef]
132. Zhang, Z.; Wu, S.; Lee, S.; Ni, J. Modified iterative aggregation procedure for maintenance optimisation of
multi-component systems with failure interaction. Int. J. Syst. Sci. 2014, 45, 2480–2489. [CrossRef]
133. Golmakani, H.R. Optimal age-based inspection scheme for condition-based maintenance using A* search
algorithm. Int. J. Prod. Res. 2012, 50, 7068–7080. [CrossRef]
134. Jardine, A.K.S. Optimizing condition based maintenance decisions. In Proceedings of the Annual Reliability
and Maintainability Symposium, Seattle, WA, USA, 28–31 January 2002; pp. 90–97.
135. Chen, A.; Wu, G.S. Real-time health prognosis and dynamic preventive maintenance policy for equipment
under aging Markovian deterioration. Int. J. Prod. Res. 2007, 45, 3351–3379. [CrossRef]
136. Yang, S.K. An experiment of state estimation for predictive maintenance using Kalman filter on a DC motor.
Reliab. Eng. Syst. Saf. 2002, 75, 103–111. [CrossRef]
137. Saranga, H.; Knezevic, J. Reliability prediction for condition-based maintained systems. Reliab. Eng. Syst.
Saf. 2001, 71, 219–224. [CrossRef]
138. Hontelez, J.A.M.; Burger, H.H.; Wijnmalen, D.J.D. Optimum condition-based maintenance policies for
deteriorating systems with partial information. Reliab. Eng. Syst. Saf. 1996, 51, 267–274. [CrossRef]
139. Ghasemi, A.; Esmaeili, S.; Yacout, S. Development of equipment failure prognostics model based on Logical
Analysis of Data (LAD). Eng. Lett. 2013, 21, 256–263.
140. Lin, D.; Makis, V. Filters and parameter estimation for a partially observable system subject to random failure
with continuous-range observations. Adv. Appl. Probab. 2004, 36, 1212–1230. [CrossRef]
141. Lin, D.; Makis, V. On-line parameter estimation for a failure-prone system subject to condition monitoring.
J. Appl. Probab. 2004, 41, 211–220. [CrossRef]
142. Lin, D.; Banjevic, D.; Jardine, A.K.S. Using principal components in a proportional hazards model with
applications in condition-based maintenance. J. Oper. Res. Soc. 2006, 57, 910–919. [CrossRef]
143. Banjevic, D.; Jardine, A.K.S.; Makis, V.; Ennis, M. A control-limit policy and software for condition-based
maintenance optimization. INFOR 2001, 39, 32–50. [CrossRef]
144. Ohnishi, M.; Morioka, T.; Ibaraki, T. Optimal minimal-repair and replacement problem of discrete-time
Markovian deterioration system under incomplete state information. Comput. Ind. Eng. 1994, 27, 409–412.
[CrossRef]
145. Makis, V.; Jiang, X. Optimal replacement under partial observations. Math. Oper. Res. 2003, 28, 382–394.
[CrossRef]
146. Grall, A.; Bérenguer, C.; Dieulle, L. A condition-based maintenance policy for stochastically deteriorating
systems. Reliab. Eng. Syst. Saf. 2002, 76, 167–180. [CrossRef]
147. Golmakani, H.R.; Pouresmaeeli, M. Optimal replacement policy for condition-based maintenance with
non-decreasing failure cost and costly inspection. J. Qual. Maint. Eng. 2014, 20, 51–64. [CrossRef]
148. Wang, W. A model to determine the optimal critical level and the monitoring intervals in condition-based
maintenance. Int. J. Prod. Res. 2000, 38, 1425–1436. [CrossRef]
149. Li, L.; You, M.; Ni, J. Reliability-based dynamic maintenance threshold for failure prevention of continuously
monitored degrading systems. J. Manuf. Sci. Eng. Trans. ASME 2009, 131, 0310101–0310109. [CrossRef]
150. Castanier, B.; Bérenguer, C.; Grall, A. A sequential condition-based repair/replacement policy with
non-periodic inspections for a system subject to continuous wear. Appl. Stoch. Model. Bus. Ind. 2003, 19,
327–347. [CrossRef]
151. Golmakani, H.R. Condition-based inspection scheme for condition-based maintenance. Int. J. Prod. Res.
2012, 50, 3920–3935. [CrossRef]
152. Golmakani, H.R.; Fattahipour, F. Age-based inspection scheme for condition-based maintenance. J. Qual.
Maint. Eng. 2011, 17, 93–110. [CrossRef]
153. Vlok, P.J.; Coetzee, J.L.; Banjevic, D.; Jardine, A.K.S.; Makis, V. Optimal component replacement decisions
using vibration monitoring and the proportional-hazards model. J. Oper. Res. Soc. 2002, 53, 193–202.
[CrossRef]
154. Lei, Y.; Li, N.; Guo, L.; Li, N.; Yan, T.; Lin, J. Machinery health prognostics: A systematic review from data
acquisition to RUL prediction. Mech. Syst. Signal Process. 2018, 104, 799–834. [CrossRef]
155. Ray, A.; Tangirala, S. Stochastic modeling of fatigue crack dynamics for on-line failure prognostics. IEEE Trans.
Control Syst. Technol. 1996, 4, 443–451. [CrossRef]
Machines 2020, 8, 31 25 of 28

156. Le Son, K.; Fouladirad, M.; Barros, A.; Levrat, E.; Lung, B. Remaining useful life estimation based on
stochastic deterioration models: A comparative study. Reliab. Eng. Syst. Saf. 2013, 112, 165–175. [CrossRef]
157. Medjaher, K.; Tobon-Mejia, D.A.; Zerhouni, N. Remaining useful life estimation of critical components with
application to bearings. IEEE Trans. Reliab. 2012, 61, 292–302. [CrossRef]
158. Tobon-Mejia, D.A.; Medjaher, K.; Zerhouni, N.; Tripot, G. A data-driven failure prognostics method based on
mixture of gaussians hidden markov models. IEEE Trans. Reliab. 2012, 61, 491–503. [CrossRef]
159. Liu, Q.; Dong, M.; Peng, Y. A novel method for online health prognosis of equipment based on hidden
semi-Markov model using sequential Monte Carlo methods. Mech. Syst. Signal Process. 2012, 32, 331–348.
[CrossRef]
160. Ben Ali, J.; Chebel-Morello, B.; Saidi, L.; Malinowski, S.; Fnaiech, F. Accurate bearing remaining useful life
prediction based on Weibull distribution and artificial neural network. Mech. Syst. Signal Process. 2015, 56,
150–172. [CrossRef]
161. Pan, Y.; Chen, J.; Li, X. Bearing performance degradation assessment based on lifting wavelet packet
decomposition and fuzzy c-means. Mech. Syst. Signal Process. 2010, 24, 559–566. [CrossRef]
162. Pan, Y.N.; Chen, J.; Dong, G.M. A hybrid model for bearing performance degradation assessment based on
support vector data description and fuzzy c-means. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2009, 223,
2687–2695. [CrossRef]
163. Chen, C.; Zhang, B.; Vachtsevanos, G.; Orchard, M. Machine condition prediction based on adaptive
neuro-fuzzy and high-order particle filtering. IEEE Trans. Ind. Electron. 2011, 58, 4353–4364. [CrossRef]
164. Caesarendra, W.; Niu, G.; Yang, B.-S. Machine condition prognosis based on sequential Monte Carlo method.
Expert Syst. Appl. 2010, 37, 2412–2420. [CrossRef]
165. Barraza-Barraza, D.; Tercero-Gómez, V.G.; Beruvides, M.G.; Limón-Robles, J. An adaptive ARX model to
estimate the RUL of aluminum plates based on its crack growth. Mech. Syst. Signal Process. 2017, 82, 519–536.
[CrossRef]
166. Camci, F.; Chinnam, R.B. Health-state estimation and prognostics in machining processes. IEEE Trans. Autom.
Sci. Eng. 2010, 7, 581–597. [CrossRef]
167. Sun, J.; Zuo, H.; Wang, W.; Pecht, M.G. Application of a state space modeling technique to system prognostics
based on a health index for condition-based maintenance. Mech. Syst. Signal Process. 2012, 28, 585–596.
[CrossRef]
168. Lei, Y.; Li, N.; Lin, J. A New Method Based on Stochastic Process Models for Machine Remaining Useful Life
Prediction. IEEE Trans. Instrum. Meas. 2016, 65, 2671–2684. [CrossRef]
169. Singleton, R.K.; Strangas, E.G.; Aviyente, S. Extended kalman filtering for remaining-useful-life estimation of
bearings. IEEE Trans. Ind. Electron. 2015, 62, 1781–1790. [CrossRef]
170. Carr, M.J.; Wang, W. An approximate algorithm for prognostic modelling using condition monitoring
information. Eur. J. Oper. Res. 2011, 211, 90–96. [CrossRef]
171. Hong, S.; Zhou, Z.; Zio, E.; Hong, K. Condition assessment for the performance degradation of bearing based
on a combinatorial feature extraction method. Digit. Signal Process. A Rev. J. 2014, 27, 159–166. [CrossRef]
172. Loutas, T.H.; Roulias, D.; Georgoulas, G. Remaining useful life estimation in rolling bearings utilizing
data-driven probabilistic E-support vectors regression. IEEE Trans. Reliab. 2013, 62, 821–832. [CrossRef]
173. Yaqub, M.F.; Gondal, I.; Kamruzzaman, J. Multi-step support vector regression and optimally parameterized
wavelet packet transform for machine residual life prediction. JVC/J. Vib. Control 2013, 19, 963–974. [CrossRef]
174. Wang, D.; Miao, Q.; Kang, R. Robust health evaluation of gearbox subject to tooth failure with wavelet
decomposition. J. Sound Vib. 2009, 324, 1141–1157. [CrossRef]
175. Kim, H.-E.; Tan, A.C.C.; Mathew, J.; Choi, B.-K. Bearing fault prognosis based on health state probability
estimation. Expert Syst. Appl. 2012, 39, 5200–5213. [CrossRef]
176. Tran, V.T.; Thom Pham, H.; Yang, B.-S.; Tien Nguyen, T. Machine performance degradation assessment
and remaining useful life prediction using proportional hazard model and support vector machine. Mech. Syst.
Signal Process. 2012, 32, 320–330. [CrossRef]
177. Tang, S.-J.; Guo, X.-S.; Yu, C.-Q.; Zhou, Z.-J.; Zhou, Z.-F.; Zhang, B.-C. Real time remaining useful life
prediction based on nonlinear Wiener based degradation processes with measurement errors. J. Cent. South
Univ. 2014, 21, 4509–4517. [CrossRef]
Machines 2020, 8, 31 26 of 28

178. Camci, F.; Chinnam, R.B. Hierarchical HMMs for autonomous diagnostics and prognostics. In Proceedings of
the IEEE International Conference on Neural Networks—Conference Proceedings, Vancouver, BC, Canada,
16–21 July 2006; pp. 2445–2452.
179. Dong, M.; Yang, Z.-B. Dynamic Bayesian network based prognosis in machining processes. J. Shanghai
Jiaotong Univ. 2008, 13E, 318–322. [CrossRef]
180. Carr, M.J.; Wang, W. Modeling failure modes for residual life prediction using stochastic filtering theory.
IEEE Trans. Reliab. 2010, 59, 346–355. [CrossRef]
181. Heng, A.; Tan, A.C.C.; Mathew, J.; Montgomery, N.; Banjevic, D.; Jardine, A.K.S. Intelligent condition-based
prediction of machinery reliability. Mech. Syst. Signal Process. 2009, 23, 1600–1614. [CrossRef]
182. Guo, L.; Gao, H.; Huang, H.; He, X.; Li, S. Multifeatures Fusion and Nonlinear Dimension Reduction for
Intelligent Bearing Condition Monitoring. Shock Vib. 2016, 2016, 1–10. [CrossRef]
183. Niu, G.; Yang, B.-S. Intelligent condition monitoring and prognostics system based on data-fusion strategy.
Expert Syst. Appl. 2010, 37, 8831–8840. [CrossRef]
184. Tian, Z. An artificial neural network method for remaining useful life prediction of equipment subject to
condition monitoring. J. Intell. Manuf. 2012, 23, 227–237. [CrossRef]
185. Mahamad, A.K.; Saon, S.; Hiyama, T. Predicting remaining useful life of rotating machinery based artificial
neural network. Comput. Math. Appl. 2010, 60, 1078–1087. [CrossRef]
186. Tian, Z.; Zuo, M.J. Health condition prediction of gears using a recurrent neural network approach. IEEE Trans.
Reliab. 2010, 59, 700–705. [CrossRef]
187. Wang, P.; Vachtsevanos, G. Fault prognostics using dynamic wavelet neural networks. Artif. Intell. Eng. Des.
Anal. Manuf. AIEDAM 2001, 15, 349–365. [CrossRef]
188. Baruah, P.; Chinnam, R.B. HMMs for diagnostics and prognostics in machining processes. Int. J. Prod. Res.
2005, 43, 1275–1293. [CrossRef]
189. Liu, Q.; Dong, M.; Lv, W.; Geng, X.; Li, Y. A novel method using adaptive hidden semi-Markov model for
multi-sensor monitoring equipment health prognosis. Mech. Syst. Signal Process. 2015, 64–65, 217–232.
[CrossRef]
190. Yu, J. Health condition monitoring of machines based on hidden markov model and contribution analysis.
IEEE Trans. Instrum. Meas. 2012, 61, 2200–2211. [CrossRef]
191. Zhou, Z.-J.; Hu, C.-H.; Xu, D.-L.; Chen, M.-Y.; Zhou, D.-H. A model for real-time failure prognosis based on
hidden Markov model and belief rule base. Eur. J. Oper. Res. 2010, 207, 269–283. [CrossRef]
192. Chinnam, R.B.; Baruah, P. Autonomous diagnostics and prognostics in machining processes through
competitive learning-driven HMM-based clustering. Int. J. Prod. Res. 2009, 47, 6739–6758. [CrossRef]
193. Dong, M.; He, D. A segmental hidden semi-Markov model (HSMM)-based diagnostics and prognostics
framework and methodology. Mech. Syst. Signal Process. 2007, 21, 2248–2266. [CrossRef]
194. Dong, M.; He, D. Hidden semi-markov models for machinery health diagnosis and prognosis. Trans. N. Am.
Manuf. Res. Inst. SME 2004, 32, 199–206.
195. Jiang, R.; Kim, M.J.; Makis, V. Maximum likelihood estimation for a hidden semi-markov model with
multivariate observations. Qual. Reliab. Eng. Int. 2012, 28, 783–791. [CrossRef]
196. Dong, M.; Peng, Y. Equipment PHM using non-stationary segmental hidden semi-Markov model.
Robot. Comput. Integr. Manuf. 2011, 27, 581–590. [CrossRef]
197. Saxena, A.; Celaya, J.; Balaban, E.; Goebel, K.; Saha, B.; Saha, S.; Schwabacher, M. Metrics for evaluating
performance of prognostic techniques. In Proceedings of the 2008 International Conference on Prognostics
and Health Management, PHM 2008, Denver, CO, USA, 6–9 October 2008.
198. Saxena, A.; Celaya, J.; Saha, B.; Saha, S.; Goebel, K. Evaluating algorithm performance metrics tailored
for prognostics. In Proceedings of the IEEE Aerospace Conference Proceedings, Big Sky, MT, USA,
7–14 March 2009.
199. Wang, W.; Zhang, W. An asset residual life prediction model based on expert judgments. Eur. J. Oper. Res.
2008, 188, 496–505. [CrossRef]
200. Elghazel, W.; Bahi, J.; Guyeux, C.; Hakem, M.; Medjaher, K.; Zerhouni, N. Dependability of wireless sensor
networks for industrial prognostics and health management. Comput. Ind. 2015, 68, 1–15. [CrossRef]
201. Lee, J.; Wu, F.; Zhao, W.; Ghaffari, M.; Liao, L.; Siegel, D. Prognostics and health management design for
rotary machinery systems—Reviews, methodology and applications. Mech. Syst. Signal Process. 2014, 42,
314–334. [CrossRef]
Machines 2020, 8, 31 27 of 28

202. Andrawus, J.A.; Watson, J.F.; Kishk, M.; Adam, A. The selection of a suitable maintenance strategy for wind
turbines. Wind Eng. 2006, 30, 471–486. [CrossRef]
203. Sørensen, J.D. Framework for risk-based planning of operation and maintenance for offshore wind turbines.
Wind Energy 2009, 12, 493–506. [CrossRef]
204. Wu, Y.-R.; Zhao, H.-S. Optimization maintenance of wind turbines using Markov decision processes.
In Proceedings of the 2010 International Conference on Power System Technology: Technological Innovations
Making Power Grid Smarter, POWERCON2010, Hangzhou, China, 24–28 October 2010.
205. Byon, E.; Pérez, E.; Ding, Y.; Ntaimo, L. Simulation of wind farm operations and maintenance using discrete
event system specification. Simulation 2011, 87, 1093–1117. [CrossRef]
206. Yildirim, M.; Sun, X.A.; Gebraeel, N.Z. Sensor-Driven Condition-Based Generator Maintenance
Scheduling—Part I: Maintenance Problem. IEEE Trans. Power Syst. 2016, 31, 4253–4262. [CrossRef]
207. Yildirim, M.; Sun, X.A.; Gebraeel, N.Z. Sensor-Driven Condition-Based Generator Maintenance
Scheduling—Part II: Incorporating Operations. IEEE Trans. Power Syst. 2016, 31, 4263–4271. [CrossRef]
208. Bouslah, B.; Gharbi, A.; Pellerin, R. Joint economic design of production, continuous sampling inspection
and preventive maintenance of a deteriorating production system. Int. J. Prod. Econ. 2016, 173, 184–198.
[CrossRef]
209. Jafari, L.; Makis, V. Optimal lot-sizing and maintenance policy for a partially observable production system.
Comput. Ind. Eng. 2016, 93, 88–98. [CrossRef]
210. Cheng, G.Q.; Zhou, B.H.; Li, L. Joint optimization of lot sizing and condition-based maintenance for
multi-component production systems. Comput. Ind. Eng. 2017, 110, 538–549. [CrossRef]
211. Xu, B.; Han, X.; Li, Y.; Zhang, Y.; Li, M.; Huang, H. Opportunistic maintenance decision-making model for
power equipment. Zhongguo Dianji Gongcheng Xuebao/Proc. Chin. Soc. Electr. Eng. 2016, 36, 6379–6388.
212. Yuan, Z.; Sun, C.; Li, J.; Du, L.; Liao, R. Study on condition-based maintenance policy of transformer based
on fuzzy multiple expert and multiple attribute group decision making. Dianli Xitong Zidonghua/Autom.
Electr. Power Syst. 2004, 28, 66–70.
213. Tian, L.; Xing, J.-G. Discussion on making decision about electric equipment for condition based maintenance.
Power Syst. Technol. 2004, 28, 60–63.
214. Li, M.; Han, X.; Yang, M.; Guo, Z. Basic concept and theoretical study of condition-based maintenance for
power transmission system. Zhongguo Dianji Gongcheng Xuebao/Proc. Chin. Soc. Electr. Eng. 2011, 31, 43–52.
215. Pan, L.; Lu, G.; Zhang, Y.; Yu, G.; Zhu, D. Decision-making optimization of equipment condition-based
maintenance according to risk comprehensive evaluation. Dianli Xitong Zidonghua/Autom. Electr. Power Syst.
2010, 34, 28–32.
216. Li, M.; Han, X.; Wang, Y.; Guo, Z.; Liu, G. Decision-making model and solution of condition-based
maintenance for substation. Zhongguo Dianji Gongcheng Xuebao/Proc. Chin. Soc. Electr. Eng. 2012, 32, 196–202.
217. Pan, L.; Zhang, Y.; Yu, G.; Du, C. Prediction of electrical equipment failure rate for condition-based
maintenance decision-making. Dianli Zidonghua Shebei/Electr. Power Autom. Equip. 2010, 30, 91–94.
218. Sun, P.; Chen, S.-H.; Zhang, C.-Q. Assessment of failure rate for substation equipment life cycle based on
Marquardt parameter estimation method. Dianli Xitong Baohu yu Kongzhi/Power Syst. Prot. Control 2012, 40,
85–90.
219. Meeker, W.Q.; Hong, Y. Reliability meets big data: Opportunities and challenges. Qual. Eng. 2014, 26,
102–116. [CrossRef]
220. Scarf, P.A. On the application of mathematical models in maintenance. Eur. J. Oper. Res. 1997, 99, 493–506.
[CrossRef]
221. Katipamula, S.; Brambley, M.R. Review article: Methods for fault detection, diagnostics, and prognostics for
building systems—A review, part I. HVAC R Res. 2005, 11, 3–25. [CrossRef]
222. Wang, W. A two-stage prognosis model in condition based maintenance. Eur. J. Oper. Res. 2007, 182,
1177–1187. [CrossRef]
223. Goh, K.M.; Tjahjono, B.; Baines, T.; Subramaniam, S. A review of research in manufacturing prognostics.
In Proceedings of the 2006 IEEE International Conference on Industrial Informatics, INDIN’06, Singapore,
16–18 August 2006; pp. 417–422.
224. Mechefske, C.K.; Wang, Z. Using fuzzy linguistics to select optimum maintenance and condition monitoring
strategies. Mech. Syst. Signal Process. 2001, 15, 1129–1140. [CrossRef]
Machines 2020, 8, 31 28 of 28

225. De Jonge, B.; Klingenberg, W.; Teunter, R.; Tinga, T. Reducing costs by clustering maintenance activities for
multiple critical units. Reliab. Eng. Syst. Saf. 2016, 145, 93–103. [CrossRef]
226. Peng, H.; Van Houtum, G.-J. Joint optimization of condition-based maintenance and production lot-sizing.
Eur. J. Oper. Res. 2016, 253, 94–107. [CrossRef]
227. Shin, J.-H.; Jun, H.-B. On condition based maintenance policy. J. Comput. Des. Eng. 2015, 2, 119–127.
[CrossRef]
228. Wang, W. Condition-Based Maintenance Modelling. Springer Ser. Reliab. Eng. 2008, 8, 111–131.
229. Neves, M.L.; Santiago, L.P.; Maia, C.A. A condition-based maintenance policy and input parameters
estimation for deteriorating systems under periodic inspection. Comput. Ind. Eng. 2011, 61, 503–511.
[CrossRef]
230. Ji, G.; Wu, W.; Zhang, B.; Liu, S.; Jiang, W. A time-varying component outage model for power system
condition-based maintenance. Zhongguo Dianji Gongcheng Xuebao/Proc. Chin. Soc. Electr. Eng. 2013, 33,
139–146.
231. Zuashkiani, A.; Banjevic, D.; Jardine, A.K.S. Estimating parameters of proportional hazards model based on
expert knowledge and statistical data. J. Oper. Res. Soc. 2009, 60, 1621–1636. [CrossRef]
232. Galar, D.; Gustafson, A.; Tormos, B.; Berges, L. Maintenance decision making based on different types of
data fusion | Podejmowanie decyzji eksploatacyjnych w oparciu o fuzje{ogonek} różnego typu danych.
Eksploat. Niezawodn. 2012, 14, 135–144.
233. Creveling, C.J. Increasing the Reliability of Electronic Equipment by the Use of Redundant Circuits. Proc. IRE
1956, 44, 509–515. [CrossRef]
234. Jafari, L.; Makis, V. Joint optimal lot sizing and preventive maintenance policy for a production facility
subject to condition monitoring. Int. J. Prod. Econ. 2015, 169, 156–168. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).