Condition-Based Maintenance in Complex Degradation Systems: A Review of Modeling Evolution, Multi-Component Systems, and Maintenance Strategies

Abstract

This review systematically examines the evolution of maintenance strategies for complex systems, with a focus on the advancements in condition-based maintenance (CBM) decision-making methodologies. Traditional approaches, such as post-failure maintenance and time-based maintenance, are increasingly supplanted by CBM due to challenges like high costs or inefficiency in resource allocation. CBM leverages system reliability models in conjunction with component degradation data to dynamically establish maintenance thresholds, optimizing resource utilization while minimizing operational risks and repair costs. Research has expanded from single-component degradation systems to multi-component systems, leveraging degradation models and optimization algorithms to propose strategies addressing multi-level control limits, economic dependencies, and task constraints. Recent studies emphasize multi-component interactions, incorporating structural influences, imperfect repairs, and economic correlations into maintenance planning. Despite progress, challenges persist in modeling coupled degradation mechanisms and coordinating maintenance decisions for interdependent components. Future research directions should encompass adaptive learning strategies for dynamic degradation processes, such as those employed in intelligent agents for real-time environmental adaptation, and the incorporation of intelligent predictive technologies to enhance system performance and resource utilization.

1. Introduction

As the complexity of modern engineering systems escalates, the optimization of maintenance strategies has emerged as a pivotal area of research within the field of reliability engineering, with a particular emphasis on predictive maintenance and intelligent system integration. Traditional maintenance strategies, including post-failure and time-based maintenance, are fraught with limitations such as high repair costs, economic inefficiency, and the risk of over- or under-maintenance. Driven by the increasing demands of sectors like aerospace, energy, and manufacturing for enhanced operational availability and safety, while reducing the significant downtime costs and inefficient resource utilization inherent in traditional approaches. Predictive maintenance systems, however, offer a more efficient and cost-effective approach by leveraging real-time data and advanced analytics to preemptively address potential equipment failures. These challenges have spurred the development of condition-based maintenance (CBM) strategies, which integrate system reliability with predictive analytics and real-time monitoring to enhance equipment availability and reduce maintenance costs. Recent studies underscore the importance of predictive maintenance frameworks, which integrate stochastic degradation modeling with maintenance decision optimization, leveraging advanced technologies to enhance operational efficiency and safety across industries. While significant progress has been achieved in single-component systems through Gamma process modeling, adaptive imperfect repair strategies, and multi-level control limit methods, the growing sophistication of modern equipment demands a paradigm shift toward multi-component system analysis. This review, therefore, explicitly aims to synthesize this progression by examining recent advancements that integrate degradation modelling, system reliability analysis, and optimal maintenance strategies for complex systems.

This work specifically targets the synthesis of methodological advancements in integrating degradation modeling, system reliability analysis, and optimal maintenance strategies for complex multi-component systems, with a focus on degradation propagation, imperfect maintenance effects, structural interdependencies among components, economic and interrelations, multiple tasks, and resource constraints in maintenance actions. Moreover, this review systematically examines the progression from single-component CBM strategies to sophisticated maintenance frameworks for multi-state complex systems, analyzing the integration of various degradation models with system reliability models and maintenance strategies. Special attention is given to emerging approaches handling system-structure-influenced degradation propagation, imperfect maintenance effects, and resource-constrained maintenance scheduling in complex engineering systems. The interrelationships among the degradation model, system reliability, and maintenance strategy are shown in Figure 1.

This review employed a systematic literature search across Web of Science, Scopus, and IEEE Xplore databases. Keywords included condition-based maintenance, multi-component system, imperfect maintenance optimization, single-component model, and degradation systems. Inclusion criteria mainly focused on peer-reviewed articles (2015–2025) in the past ten years. The literature selection followed three stages: (1) initial screening of titles/abstracts, (2) full-text review for relevance, and (3) synthesis of key findings. Data extraction focused on degradation modeling techniques, system reliability metrics, and maintenance strategy. Therefore, this work was categorized based on: (1) component degradation modeling, (2) Reliability Modeling of Complex degradation Systems, and (3) maintenance strategies for complex degradation systems. It mainly serves both researchers in reliability engineering seeking the latest methodological developments and practitioners in maintenance management requiring insights into implementing advanced, cost-effective CBM frameworks.

2. Component Degradation Modeling

Complex equipment systems are characterized by complex manufacturing processes, harsh operating conditions, stringent control demands, and challenging maintenance procedures [1]. These factors contribute to continuous performance degradation during operation, which is a critical concern in system reliability assessment. The degradation levels vary across components due to differences in operational stress and material properties, as reflected in reliability indicators such as confidence levels and testing conditions. Moreover, the reliability evaluation of such systems becomes particularly challenging because of their structural complexity—comprising numerous interdependent components whose degradation states collectively influence overall system performance. In this context, the degradation state of each component serves as a direct measure of its reliability. Furthermore, since component degradation evolves over time, it dynamically affects their structural importance within the system. Consequently, maintenance decisions must account for both the immediate reliability of individual components and their changing roles in system functionality. Specifically, components exhibiting more severe degradation (i.e., lower reliability) should be prioritized in maintenance planning, as their failure would disproportionately impact system performance. The degradation paths of system components are illustrated in Figure 2, providing a quantitative basis for reliability-based maintenance optimization.

As shown in Figure 2, the system reliability of each component decreases with mission execution time. At time t1, path B exhibits a higher maintenance priority compared to the other path due to its more degraded state.

Besides, the degradation states of components, their inter-dependencies, and repair priorities significantly influence maintenance strategies. Moreover, since these systems must perform diverse tasks, their operational requirements vary, further complicating maintenance planning. To address these challenges, it is essential to consider both the conditions of components and their operational context task demands when developing optimal maintenance strategies. Generally speaking, there are two maintenance approaches for system performance-degraded components: replacement maintenance and preventive maintenance. In practical engineering applications, these two maintenance methods can describe the majority of maintenance activities.

Therefore, effective failure models that describe the degradation process of system components are established as a fundamental aspect of evaluating system reliability and play a critical role in formulating maintenance strategies for degrading systems. Reliability is traditionally predicted and assessed based on statistical analyses of failure times [2]. These methods require large datasets of failure observations to statistically infer failure time distributions.

However, when sample sizes are limited or low, long-term testing is necessary, as the absence of adequate failure data and extended assessment durations directly affects the precision and applicability of reliability evaluation outcomes. ystem performance is characterized by key component features, whose degradation over time contains valuable reliability information. For instance, this encompasses a range of degradations such as the deterioration of electronic packaging [3], the rise in hardness of closed rubber [4], the relaxation of spring stress [5], and the fatigue damage of rolling bearings [6]. Degradation information can be fully utilized for statistical analysis to derive patterns of equipment reliability changes. Various types of degradation reliability models have been developed based on different degradation mechanisms. Among these, the most commonly used are degradation path models and stochastic process models, and relevant methodologies for reliability assessment and maintenance optimization in complex degrading systems.

2.1. The Degradation Path Model

The degradation path (DP) model, initially studied and applied in the early stages, has evolved into a sophisticated framework for describing degradation processes, as evidenced by its extensive use in materials science. It focuses on modeling changes in degradation quantities or performance parameters over time, often expressing these as functions of time. Typical DP models include random slope-intercept models, Paris models, power-law models, and damage theory models. The comparative summary of typical degradation path models is shown in

Table 1. Comparative summary of typical degradation path models.

Model	Mathematical Formulation	Key Parameters	Typical Applications
Random Slope-Intercept	$Y(t)={\beta }_0+{\beta }_1+\epsilon (t)$	β0: Random initial degradation β1: Degradation rate ε(t): White noise	Bearings, linear degradation systems
Paris’ Law	${\displaystyle \frac{dN}{da}}=C{(\mathrm{\Delta }K)}^m$	C, m: Material constants ΔK: Stress intensity factor range	Metal fatigue crack propagation
Power-Law	$Y(t)=\alpha t^{\beta }+\epsilon (t)$	α: Scale parameter β: Shape parameter ε(t): Error term	Electronics aging, nonlinear degradation
Damage Theory	$D(t)={\displaystyle \sum _{i=1}^k\frac{n_i}{N_i}}$	D(t): Cumulative damage ni/Ni: Cycle ratio	Mechanical systems under multi-stress

.

2.1.1. Random Slope-Intercept Model

This statistical model describes degradation as a linear function of time with random effects:

$$Y(t)={\beta }_0+{\beta }_1+\epsilon (t)$$

(1)

where, ${\beta }_0~\phi ({\mu }_0,{\sigma }_0^2)$ and ${\beta }_1~\phi ({\mu }_1,{\sigma }_1^2)$ represent the stochastic initial degradation level and degradation rate, respectively. The error term $\epsilon (t)~\phi (0,{\sigma }_{\epsilon }^2)$ accounts for measurement noise. The model is widely adopted for components exhibiting approximately linear degradation trends. Gopikrishnan et al. [7] extensively discussed the modeling and statistical inference methods for random slope-intercept models, which are also known as random coefficient models or mixed-effect models, as highlighted in the literature in their book, addressing practical applications of such models. Furthermore, Freitas et al. [8] applied random slope-intercept models to establish a degradation model for train wheel diameters and assessed predicted service life using analytical and numerical methods. Yuan and Pandey [9] extended the random slope-intercept model by incorporating process randomness and correlations during measurements and applied it to predict corrosion degradation of nuclear pipe components. Gebraeel et al. [10] The study modeled bearing vibration signal degradation data using a hybrid approach that combines CNN-GRU deep learning models with Bayesian updating techniques for real-time prediction of remaining bearing life.

2.1.2. Paris Law

A physics-based model for fatigue crack growth, expressed as:

$${\displaystyle \frac{dN}{da}}=C{(\mathrm{\Delta }K)}^m$$

(2)

where $\mathrm{\Delta }K$ denoting the stress intensity factor range. The material-specific constants C and m are determined experimentally. This model is fundamental in predicting the remaining useful life of metallic structures subjected to cyclic loading. Chen et al. [11] used proportional-type Paris models to describe average crack propagation paths and established single-sample fatigue crack extension stochastic models using inverse Gaussian processes. Ma et al. [12] applied the Paris equation to establish state space models for different degradation stages of rolling bearings, successfully predicting bearing operational trends in later stages. Luo et al. [13] used Paris models to describe fatigue crack propagation in aircraft fuselage skin structures and combined Kalman filtering techniques to predict structural service life.

2.1.3. Power-Law Model

A flexible empirical model capturing nonlinear degradation dynamics:

$$Y(t)=\alpha t^{\beta }+\epsilon (t)$$

(3)

where scale parameter α (>0) and shape parameter β govern the degradation trajectory magnitude and curvature. It effectively characterizes accelerated or decelerated degradation processes, such as semiconductor device aging. Chun et al. [14] employed power-law models to characterize the degradation of thin-film resistors and constructed reliability assessment models based on these insights. Song et al. [15] applied power-law models to fit low-temperature viscoelastic parameters and studied a method for predicting rubberized asphalt stress relaxation modulus based on low-temperature bending creep tests.

2.1.4. Damage Theory Model

A generalized framework for cumulative damage assessment. The Miner’s rule variant provides a linear damage summation:

$$D(t)={\displaystyle \sum _{i=1}^k\frac{n_i}{N_i}}$$

(4)

where n_i and N_i are the actual and failure cycles under the ith stress level, respectively. D(t) accommodates continuous damage evolution driven by stress damage evolution driven by stress, temperature, or other covariates. This model is critical for reliability analysis of mechanical systems exposed to variable operational conditions. Carey and Koenig [16] created models to predict how subsea cables break down, using damage theory and aging data. This matches an earlier way of checking insulation. A monitoring system makes things more reliable by watching them in real time. Research backs up the reliability and life predictions that these models handle.

2.2. The Random Process Model

Research has shown that the degradation of system components is a result of both internal and external factors, with internal factors characterized by irreversible changes in material performance states, while external factors include comprehensive effects of environmental stresses such as temperature, pressure, and strong vibrations. The degradation process exhibits random fluctuation characteristics. Degradation trajectory models represent the randomness of degradation quantity through random parameters; however, they face difficulties in elucidating the influence of the environment on the system’s degradation. In this context, modeling the degradation process using stochastic processes aligns more closely with engineering practices. Wiener processes, Gamma processes, and inverse Gaussian processes are among the most frequently employed stochastic process models. The comparative summary of the random process models is shown in

Table 2. Comparative summary of the random process models.

Model	Mathematical Formulation	Key Parameters	Increment Properties	Typical Applications
Wiener Process	$Y(t)=\mu (t)+\sigma B(t)$	μ: Drift coefficient σ: Diffusion coefficient B(t): Standard Brownian motion	Independent Gaussian increments (can be positive/negative)	LED light decay, Capacitor wear,
Gamma Process	$Y(t)~\mathrm{\Gamma }(\alpha t,\beta )$	αt: Shape parameter β: Scale parameter	Non-negative, Strictly increasing increments	Rubber aging, bearing wear
Inverse Gaussian (IG) Process	$Y(t)~IG(\mu t,\lambda t^2)$	μt: Mean degradation at time t λt2: Shape parameter	Non-negative, flexible-distributed increments	tool wear

.

The Wiener process, which is based on the physical description of Brownian motion diffusion, is especially renowned for its characteristic independent increments that follow a Gaussian distribution, making it suitable for characterizing non-monotonic degradation processes. For instance, Tseng and Colleagues [17] employed the Wiener process to model the degradation process of LED lamps. Hu et al. [18] utilized a linear-drift Wiener process to model online degradation data for metalized film pulsed capacitors, achieving online reliability assessments. Dong et al. [19] adopted a two-stage Wiener random process to model rail degradation and provided expressions for system reliability and availability. Ye et al. [20] proposed a stochastic effect Wiener process model considering the correlation between diffusion coefficients and drift coefficients, effectively modeling random fluctuations in degradation processes such as hard disk fatigue crack propagation and head wear. Si et al. [21], using 2017-T4 aluminum alloy fatigue crack growth data, described the degradation evolution process as a Wiener process and derived an analytical form of the remaining life distribution. The simplicity of the Wiener process structure and its extensive research outcomes make it one of the most commonly used degradation models in reliability studies. Literature [22] provides a comprehensive review of research progress in degradation data modeling and reliability assessment methods based on the Wiener process, as well as their applications in life prediction and condition health management.

The Gamma process is also widely studied and applied as a degradation model, differing from the Wiener process in that it describes non-decreasing performance degradation increments. It is primarily used to model external random impacts leading to slow degradation and irreversible minor damage accumulation. The Gamma process can be viewed as a composite Poisson process where damage converges to zero at a constant rate [23]. Sun et al. [24] established a degradation process model for annular rubber using the Gamma random process, deriving its reliability and storage life. Zhang et al. [25] utilized the Gamma process to model the monotonic degradation of alloy products, determining the wear reliability of spherical sliding bearings under long-term use. Lu et al. [26] applied the Gamma process to model the degraded performance of vertical-cavity surface-emitting lasers, analyzing their reliability and remaining life distribution.

Similar to the Gamma process, the inverse Gaussian process is also used to describe cumulative damage processes under random impacts; however, it features different distributions for impact damage. Compared to the Gamma process, the inverse Gaussian process offers greater flexibility in modeling performance degradation data with random effects [27]. In recent years, degradation reliability modeling techniques based on the inverse Gaussian process have garnered increasing attention from researchers. For example, Huang et al. [28] employed the inverse Gaussian model to simulate the surface wear degradation process of cutting tools, enabling real-time prediction of their remaining useful life. Sun et al. [29] proposed an improved inverse Gaussian process model incorporating random effects and measurement errors, which they used to model wear degradation processes in order to predict system reliability for components such as bearings.

2.3. The Intelligence Model (PINN)

The integration of Physics-Informed Neural Networks (PINN) into degradation trend prediction has emerged as a powerful approach, combining the strengths of data-driven learning and physical laws. This hybrid methodology leverages the underlying physical principles governing degradation processes, embedding them directly into neural network architectures. By doing so, PINN can provide more accurate and robust predictions of system degradation, especially in scenarios where data are limited or the degradation mechanisms are highly complex [30].

The rise of Physical Information Neural Networks (PINN) in the prediction of degradation trends is both an innovation in earlier maintenance modeling approaches and a natural consequence of the development of intelligent maintenance. Grall et al. laid the foundation for degradation modeling through a continuous time frame [31], and E. Barlow et al. [32] and Bérenguer et al. [33] emphasized the criticality of predictive modeling and the advantage of physical models for capturing dynamics, respectively. However, these approaches are limited by the rigidity of mathematical optimization, computational complexity, and insufficient data, and there are significant difficulties in adapting to complex nonlinear degradation mechanisms as noted by Zhang [34] and Marseguerra et al. [35]. With the development of intelligent maintenance, Kang and Subramaniam [36] attempt to integrate production control with data-driven forecasting, and with the joint optimization of maintenance and inventory by Keizer et al. [37], there is an increasing demand for highly accurate, data-driven forecasting models that can effectively integrate physical knowledge, and scholars such as Wang et al. [38] have proposed the need to incorporate physical constraints into intelligent models to improve accuracy, which provides an opportunity for the application of PINN. In this context, PINN has become a powerful tool to solve the problem of unstable State-of-Health (SOH) estimation under variable battery chemistries and user-specific charging protocols, achieving <1% mean absolute percentage error (MAPE) across 387 batteries from four independent datasets. In recent years, PINN has significantly improved the prediction of complex nonlinear degradation mechanisms by embedding physical laws (e.g., fatigue crack growth equation, Wiener process) into the neural network architecture. Derived from the pioneering work of Raissi et al. [39], the core of PINN is to embed partial differential equations (PDE) or physical laws (e.g., fatigue crack growth law, electrochemical reaction equations, and Wiener processes describing stochastic degradation) describing the physical processes directly into the neural network architectures, which effectively overcomes the limitations of the traditional methods. In the field of degradation prediction, the application of PINN has demonstrated significant advantages [40]: for example, Qing et al. [41] used it for the prediction of remaining life (RUL) of integrating the physical mechanism of fatigue crack growth with vibration monitoring data; Meng et al. [42] further developed a hybrid framework integrating Physics-Informed Neural Networks (PINN) with the First-Order Reliability Method (FORM) to solve reliability analysis problems governed by implicit partial differential equations (PDEs), which traditional FORM struggles with due to computational inefficiency and non-convergence in nonlinear scenarios. Zhu et al. [43] proposed an RUL prediction method integrating the Attention-Mamba network with a Physics-Informed Neural Network (PINN) framework, validated on the C-MAPSS dataset, which enhances prediction accuracy via PINN and supports intelligent maintenance of industrial equipment. Despite the challenges in integrating multi-physical field phenomena (e.g., degradation involving both thermal and mechanical stresses) and enhancing computational efficiency for real-time prediction, PINN has significantly improved the accuracy and practicality of degradation trend prediction by deeply integrating physical constraints and data-driven learning, which opens up innovative paths for the development of intelligent maintenance strategies for complex systems.

To sum up, Physics-Informed Neural Networks (PINN) integrate physical laws such as partial differential equations (PDEs), fatigue crack growth equations, and Wiener processes directly into neural network architectures, combining them with data-driven learning to predict degradation trends [44]. Compared to traditional methods, PINN offers significant advantages: it overcomes limitations of rigid mathematical optimization, high computational complexity, and poor adaptability to complex nonlinear degradation mechanisms in data-scarce scenarios. By embedding “physical consistency constraints”, PINN enhances model robustness and extrapolation capabilities while improving prediction accuracy. This dual capability is critical for optimizing maintenance strategies, enabling early failure warnings, and advancing intelligent maintenance frameworks for complex systems.

3. Reliability Modeling of Complex Degradation Systems

3.1. The System Modeling

It is assumed that systems and their components only possess two states in traditional system reliability theory: operational and failed. This binary-state approach simplifies the reliability assessment process by enabling direct calculation of system reliability based on the failure probabilities of its components and system configuration. However, as equipment systems increase in complexity, the limitations of binary-state models become evident, as they fail to adequately capture the intricate structural relationships and dynamic performance degradation characteristics inherent in real-world systems [45]. Consequently, research in system reliability has shifted from binary-state systems to multi-state systems, which better accommodate the demands of performance-degrading system reliability analysis. Currently, methodologies for modeling and evaluating the reliability of complex multi-state systems include Monte Carlo Simulation (MCS), Multi-State Fault Tree Analysis (MSFTA), Multi-Valued Decision Diagrams (MVDDs), Universal Generating Function Method (UGF), and Goal-Oriented (GO) methodology. These methods are being extensively researched and applied to address the challenges faced in the reliability assessment of complex systems. The comparative summary of system reliability models is shown in

Table 3. Comparative summary of system reliability models.

Method Name	Features	Advantages and Disadvantages	Typical Applications
Monte Carlo Simulation	Avoids complex modeling; efficient for large-scale/intricate systems.	Advantage: No need for complex modeling. Disadvantage: Time-consuming simulation with approximate results.	Large-capacity power systems, offshore wind systems, complex pipeline networks.
Fault Tree Analysis	Handles multi-failure modes and dynamic traits.	Advantage: Addresses multi-failure systems. Disadvantage: Poor for repairable systems with fault dependence.	Fault-tolerant computer systems, CNC hydraulic systems, complex equipment safety assessment.
Multi-Valued Decision Diagrams	Reduces computational complexity.	Advantage: Extends binary diagram applicability. Disadvantage: Higher complexity in traditional models.	Multi-stage multi-state systems, simplified evaluation algorithms.
Universal Generating Function	Directly represents system-component state relations.	Advantage: High computational efficiency. Disadvantage: Requires integration for complex structures.	Redundant systems, shared-performance series systems, offshore AC/DC collector systems.
GO Method	Simple, intuitive modeling process.	Advantage: Intuitive modeling. Disadvantage: Increased complexity due to common signals.	Inertial navigation systems, redundant backup systems, feedback engineering systems, repairable systems.

.

3.1.1. The Monte Carlo Simulation Model

Monte Carlo Simulation (MCS), a stochastic simulation approach, assesses system reliability by statistically analyzing the dynamic characteristics of system components through computer sampling [46]. This method effectively avoids the complexity of system modeling, particularly demonstrating high computational efficiency for systems with large-scale components and intricate structural relationships.

Geng et al. [47] proposed a simplified sequential Monte Carlo simulation method that significantly improves the efficiency of reliability assessment in large-capacity power systems. Li et al. [48] developed a system reliability analysis model based on Markov Monte Carlo, aimed at evaluating the reliability of wind power generation systems affected by harsh marine environments. In recent years, the Monte Carlo algorithm has been widely applied in the field of reliability assessment for complex Offshore Wind Systems, Water Supply Systems, and Power Systems [49,50,51].

3.1.2. Multi-State Fault Tree Model

Multi-state fault trees (MSFTs) [52,53,54] identify various failure factors systems affecting reliability through bottom-up analysis, encompassing component failures, environmental variations, and human errors. In contrast to traditional Boolean logic gate operations, MSFTs employ non-Boolean logical operations to tackle systems exhibiting multiple failure modes and dynamic failure traits. Dugan et al. [55,56] introduced a method for constructing fault tree models using dynamic logic gates, demonstrating its effectiveness in solving reliability modeling and assessment problems for complex systems through case studies of fault-tolerant computer systems. Qi et al. [57] proposed a system reliability analysis method based on multidimensional MSFT by combining it with the multidimensional polymorphic output rule algorithm. Li et al. [58] developed an improved dynamic fault tree model using fuzzy set theory to address uncertainties and dynamic failure characteristics in systems, applying it to the reliability analysis of hydraulic systems in numerical control machining centers. In recent years, MSFTs have been extensively applied to reliability analysis and safety assessments of complex equipment systems [59,60,61].

3.1.3. The Multi-Valued Decision Diagrams Model

Multi-valued decision diagrams (MDDs) [62,63] extend traditional binary decision diagrams by reflecting both system states and component states. Miller [64] expanded Boolean variables in binary decision diagrams to multi-state variables, proposing an analytical method for MDDs. Shresta et al. [65] combined decision diagrams with Markov processes to analyze the reliability of multi-state systems with multiple stages. Xing and Dai [66] introduced a multi-state multi-valued decision diagram model, which reduces computational complexity and simplifies evaluation algorithms compared to binary decision diagrams. Amari et al. [67], Wang and Hu [68], and Shrestha [69] have validated the effectiveness of MDDs in evaluating the reliability of multi-state systems.

3.1.4. The Universal Generating Function Model

The Universal Generating Function (UGF) method was formally proposed by Ushakov [70] in 1986. Lisnianski and Levitin, among others, extensively studied UGF and introduced it into the field of multi-state system reliability analysis and design [71,72,73]. Since then, UGF has been widely recognized as an effective reliability analysis tool for multi-state systems. Lisnianski and Ding [74] combined UGF with Markov processes to evaluate the reliability of complex systems with redundant structures. Wang et al. [75] applied UGF to assess the reliability of series systems with shared performance characteristics. Sun et al. [76] utilized UGF to analyze the reliability of multi-state offshore AC/DC collector systems.

3.1.5. The GO Method Model

The Generalized Opposition method can be employed for system modeling by analyzing unit sequence logic or by converting schematic diagrams, flowcharts, or engineering blueprints directly into GO graph models. Consequently, the GO method is particularly suited for systems with physical flow characteristics, such as airflow, water flow, or electrical current, in complex engineering structures. As demonstrated by Jiang et al. [77,78], who introduced an improved multi-state GO operator and enhanced the GO operation and a common signal correction algorithm leveraging a state probability matrix (SPM). Additionally, the GO method constructed a reliability analysis model for inertial navigation systems, grounded in the refined GO method [79]. Yi et al. [80] proposed a novel combination of GO operators and integrated them with Markov process models to directly develop reliability models for complex systems featuring redundant backups. In another study, Yi et al. [81] conducted a quantitative analysis of the reliability of closed-loop feedback systems with two inputs using the GO method. Li et al. [82] extended the application of the GO method by developing a modeling approach based on cyclic Bayesian networks, successfully applying it to complex engineering systems with feedback loops. Additionally, Yi et al. [83] defined the operational logic of enhanced GO operators and applied the improved GO method to analyze the reliability of multi-functional repairable systems operating in various modes.

These research efforts have effectively utilized the GO method in complex systems, yielding diverse computational approaches for reliability assessment. Despite this, despite the widespread application of the GO method, algorithmic research focusing on improving its computational efficiency and enhancing common signal correction techniques remains scarce.

Generally, while the Monte Carlo method eliminates the necessity for system modeling, it entails a complex and time-consuming simulation process, yielding merely approximate statistical results. The extension methods of Boolean models, such as multi-state fault trees/multi-state decision diagrams, are primarily used to establish relational models between systems and the failure events causing their failures. However, these methods are not well-suited for describing complex repairable systems with issues related to fault propagability and interdependence. The universal generating function method is characterized by its fast computation speed, ease of numerical implementation, and ability to directly represent the state relationships between a system and its components. The GO method offers a simple and clear process for system reliability modeling; however, during calculations, it requires consideration of common signals and signal non-independence issues, which increases computational complexity. In practical engineering applications, selecting an appropriate reliability analysis method based on the specific characteristics of the system under study is crucial.

3.2. System Reliability Analysis

The complex degrading systems, particularly those with multi-type degrading components, are critical to model and assess for their reliability to ensure stable performance and longevity. In the operation of complex equipment, system performance often exhibits a degrading trend; nevertheless, it retains functionality until ultimate failure ensues. As Qi [84] described, the overall performance of high-speed railway EMUs is influenced by real-time location, external operational environment, component degradation, and optimization of key components such as the bogie. Zhang [85] investigated the performance degradation of ground-based high-mobility radar mechanical structures caused by material property decline and structural damage under continuous environmental load effects. In the early stages of system reliability theory development, researchers began to pay attention to the degradation characteristics of such systems; however, due to limitations in theoretical advancement at that time, research on degradation-related theories and methods was still in its exploratory phase [86]. It was not until the late 20th century that studies on reliability analysis based on performance degradation gradually emerged [87]. Subsequently, researchers, building upon system reliability theory, developed various methodologies to assess system reliability by leveraging statistical information inferred from component degradation processes. Depending on the focus of research on system objects, studies related to the degradation of system reliability can be categorized into several aspects, as shown in Figure 3.

3.2.1. Degradation Characteristics of Key System Components

Research has focused on the degradation characteristics of key system components. For instance, Li et al. [88] proposed a mathematical model that correlates the failure probability density functions of system components with system reliability functions, based on degradation path equations. This model assumes that components degrade along linear paths influenced by weighted factors. This approach is similar to the system reliability modeling methods discussed in [1], which focuses on the reliability assessment of systems with multiple types of degrading components. Li and Pham [89] proposed a degradation system reliability model considering competing failure modes, including both degradation and random shocks. Gong et al. [90] introduced a generalized shock model with bivariate thresholds, employing phase-type distributions to simulate shock damage sizes and arrival intervals while incorporating Markov processes to analyze the reliability of multi-state systems influenced by shocks.

3.2.2. Internal Interconnection Structures

Research has focused on the internal interconnection structures between systems and their components. For example, Peng et al. [91] utilized component degradation data to develop Markov Chain Monte Carlo algorithms and approximate analytical methods to investigate the relationship between component performance and system reliability, and to calculate system reliability. Reshid et al. [92,93] analyzed the reliability of a power plant cooling water system by combining Markov chains with system reliability block diagrams. Li et al. [94] extended binary-state reliability analysis to continuous states through the construction of degradation models and employed multi-state fault trees to conduct reliability analyses of system degradation and catastrophic failures.

3.2.3. Special-Structured Degradation Systems

Research has focused on reliability assessment of special-structured degradation systems (e.g., shared systems, redundant backup systems, multi-task systems, and k-n(G) systems). Lisnianski et al. [74,95,96] developed a reliability analysis method by integrating universal generation function techniques with Markov stochastic processes, enabling accurate short-term and long-term performance predictions for repairable redundant multi-state systems. Zhao et al. [97] established a reliability model for load-sharing k-n systems by describing the degradation process of system units at different loading stages as Gamma processes. Jia et al. [98] introduced a multi-state decision diagram approach to tackle reliability assessment challenges in hot standby systems with general demand-type configurations, taking into account the degradation of component performance. Levitin et al. [99] established models for evaluating reliability and structural optimization of phased task systems by considering the effects of internal faults and external shocks on system component degradation performance. Wang et al. [100] developed a reliability evaluation model for staged-task systems based on Markov processes, incorporating propagating failures and functional dependency behaviors. Faghih-Roohi et al. [101] combined universal generation functions with Markov processes to propose a dynamic reliability assessment model for multi-state weighted k-n systems and optimized the time-varying probabilities of system components in different states using genetic algorithms.

4. Maintenance Strategies for Complex Degradation Systems

Maintenance strategies for complex systems primarily include post-failure maintenance, time-based maintenance, and condition-based maintenance. Post-failure maintenance strategies are mainly applicable to small and non-critical systems, where repairs are conducted following system failures. However, this approach is characterized by high repair costs and poor economic efficiency. Time-based maintenance involves scheduling maintenance operations at predetermined intervals. Compared to post-failure maintenance leads to lower repair costs; however, it may also pose challenges such as over-maintenance or under-maintenance [102].

In response to the limitations of traditional maintenance approaches, researchers have developed condition-based maintenance (CBM) decision-making methods centered on system reliability, using performance degradation data from systems and their components [103,104]. These methods have yielded numerous applied results. For instance, Zhang et al. [105] proposed a dual-threshold CBM strategy, which encompasses preventive maintenance thresholds and corrective maintenance thresholds, for daily maintenance management in wind farms. Heo et al. [106] developed a CBM strategy for power transmission systems and optimized it using genetic algorithms. Yssaad et al. [107] devised cost-effective condition-based maintenance programs for distribution systems. CBM decision-making focuses on integrating system reliability assessment models with component degradation models to ensure the maintenance and restoration of equipment reliability with minimal resource consumption. Additionally, by implementing predictive maintenance activities, risks associated with equipment operation and repair costs are reduced. This approach involves conducting regular inspections or continuous monitoring of complex systems experiencing performance degradation over time. When reliability degradation levels reach or exceed predetermined preventive maintenance thresholds, appropriate maintenance actions are implemented. Currently, most research achievements in CBM decision-making have been realized for single-component degradation systems [108,109,110]. For example, Do et al. [111] described the system’s degradation process using Gamma processes and proposed an adaptive CBM strategy based on imperfect repairs. Grall et al. [112] addressed single-component systems subject to both stochastic and progressive degradations by developing multi-level control limit maintenance strategies. Dieulle et al. [113] modeled component degradation using Gamma processes, determined maintenance states based on critical failure thresholds, and described long-term expected costs as semi-regenerative processes. To address the trend of increasing complexity in equipment systems, research focus is shifting toward CBM decision-making for multi-component complex systems. Nguyen et al. [114,115] described system component degradation processes using Gamma processes and proposed a multi-level decision preventive maintenance strategy. They also investigated the impact of degraded components on complex systems influenced by system structures. Guo et al. [116] modeled task-oriented degrading systems using Wiener stochastic processes and studied optimal maintenance decisions under multi-task constraints and imperfect repairs. Zhou et al. [117] proposed a maintenance optimization approach for multi-state series/parallel systems that considers economic correlations and inspection interval states. Zhao et al. [118] employed Weibull proportional hazards models and Weibull proportional intensity models to describe system component degradation and proposed a new condition-based maintenance strategy for complex systems. Huynh et al. [119] used component degradation states as maintenance decision variables and established CBM strategies for k-n degraded systems.

5. Results and Discussion

Based on the review of the aforementioned literature, it can be concluded that significant progress has been made in CBM, where both degradation path models (e.g., random slope-intercept, Paris, and power-law models) and stochastic process models (e.g., Wiener, Gamma, and inverse Gaussian processes) have been successfully applied to characterize component degradation. Recent developments in physics-informed neural networks (PINNs) further demonstrate the potential of intelligent models in capturing complex degradation mechanisms. For system-level reliability assessment, methodologies such as Monte Carlo simulation (MCS), multi-state fault tree analysis (MSFTA), universal generating function (UGF), and goal-oriented (GO) methods have proven effective in evaluating the performance of multi-state systems under varying degradation scenarios. In terms of maintenance strategies, CBM has been widely adopted for single-component systems, with advanced frameworks incorporating dual-threshold policies and optimization algorithms to balance preventive and corrective actions. Recent studies have proposed hierarchical decision-making frameworks and condition-based policies to address the complexities of multi-component systems, including structural dependencies, economic correlations, and task constraints.

Despite these advancements, several challenges persist. First, accurately modeling coupled degradation mechanisms and their interactions in multi-component systems requires further refinement. Second, the integration of real-time adaptive learning strategies into maintenance frameworks is essential to enhance responsiveness to evolving system conditions. Finally, the application of emerging technologies—such as deep learning and digital twins—holds promise for improving predictive accuracy and decision-making but necessitates rigorous validation in real-world scenarios. The coordination of interdependent components under dynamic degradation remains an open research problem, highlighting the need for more integrated and robust maintenance strategies.

6. Conclusions

This transition from traditional maintenance approaches to CBM underscores the importance of integrating degradation modeling, system reliability analysis, and maintenance strategies to meet the demands of modern engineering systems. Future research should prioritize the development of adaptive CBM strategies capable of handling dynamic and interdependent degradation processes, as well as the seamless incorporation of intelligent prediction tools into maintenance frameworks. Addressing these challenges will not only advance the theoretical foundations of CBM but also facilitate its practical implementation in increasingly complex engineering systems, ultimately contributing to improved reliability, cost efficiency, and sustainability.