Condition-based maintenance (CBM) has attracted significant attention in advanced manufacturing systems. In practice, degradation of production units is often influenced by their production rates. Unlike traditional CBM models that treat maintenance optimization as a stand-alone problem, we develop a joint optimization model of condition-based maintenance and production for multi-stage manufacturing systems. The resulting joint dynamic optimization problem is formulated as a Markov decision process (MDP) with the aim at maximizing the expected total production benefit. To address the curse of dimensionality and improve scalability in decision-making, a hierarchical multi-agent reinforcement learning framework is put forth to solve the MDP, leveraging a two-level architecture that decomposes the problem into manageable subtasks for maintenance and production. A distributed training strategy is introduced to independently train stage-level agents, significantly improving scalability. Experimental results from a semiconductor manufacturing facility demonstrate that the proposed joint dynamic optimization method significantly improves production benefit by maintaining a balance between production efficiency and system reliability.

The Internet of Things (IoT) represents a transformative convergence of traditional manufacturing systems with advanced information technologies, collectively referred to as smart manufacturing. The interconnected nature of IoT facilitates real-time data collection and analysis, optimizing production processes and improving operational efficiency. However, the increased complexity and interdependence of IoT systems pose significant challenges in reliability modeling and assessment. This article introduces a novel reliability model that comprehensively integrates factors such as degradation of physical systems and information networks, along with their interactive impacts on system performance and reliability. A modular Petri net approach is developed to efficiently assess reliability of IoT systems by leveraging a structured framework to model the intricate interdependencies within IoT. The modular nature of the proposed approach enables targeted analysis and scalability enhancements, addressing the critical need for models that can adapt to the evolving landscape of IoT in smart manufacturing systems. A vehicle manufacturing system example is introduced to demonstrate the proposed approach. The results reveal the distinct impact pathways of the physical system and information network on overall system reliability. Statistical analysis across various system configurations shows that modifying the architecture of the information network can lead to an average improvement of 20.67% in system reliability.

Selective maintenance, as a prevalent maintenance policy for engineered systems under limited maintenance resources, has been widely adopted in industrial and military settings. Most existing works on selective maintenance only considered limited consumable resources, such as time and budget. In many real-world applications, the implementation of maintenance activities, however, has to be supported by several maintenance capacities, including repairpersons and repair facilities, which are occupied during the execution of a maintenance action and released upon its completion. Moreover, due to the stochasticity of maintenance actions’ durations, the available number of maintenance capacities in each period is also uncertain. In this article, a novel dynamic selective maintenance model is introduced by taking account of the limited maintenance capacities and stochastic action durations. The dynamic optimization problem is formulated as a Markov decision process where maintenance actions are dynamically selected in accordance with components’ states, remaining consumable resources, and available maintenance capacities. An approximate dynamic programming algorithm based on the rollout policy is put forth to estimate the optimal selective maintenance policy, and an importance-based heuristic is proposed to enhance its performance. To overcome the inefficiency of the solution algorithm in coping with large-scale instances, a machine learning-enhanced framework that enables neural networks trained by small-scale instances to solve large-scale instances is developed. A manufacturing system and an aircraft fleet are exemplified to demonstrate the effectiveness of the proposed approach.

The degradation of power converter performance is one of the most critical issues of complex system with the improvement of power capacity and density. Power converter bears severe electrical and thermal stress, resulting in an increase in the probability of failure and significant economic losses. Most research addresses performance evaluation either through reliability theory without physical understanding or through data-driven methods requiring high experimental cost. Few studies focus on predicting system-level performance degradation, which is technically difficult as many components degrade randomly. Identifying the parameters of electronic components based on sensor data has become possible with the development of neural networks and computational power. Therefore, in this article, we propose a novel system-level power degradation predicting framework, which combines the advantages of neural networks in nonlinear fitting and empirical knowledge to predict the degradation of the power converter. In addition, a comprehensive and improved feature parameter screening method is proposed to identify the most critical feature parameters of the power converter systems. Furthermore, the neural network parameter identification method based on the sparrow search algorithm–Elman neural network is introduced to improve prediction accuracy. Finally, the result shows that the proposed method can accurately predict the degradation of the system by using a DC–DC converter as an example.

Expert knowledge is an important information source for system reliability assessment, especially when historical data are limited. However, when elicited, expert knowledge is often imprecise with large uncertainty. Moreover, as experts usually own different expertise and knowledge, the elicited knowledge from different experts might be conflicting. In this article, a two-stage optimization model is put forth to fuse the imprecise and conflicting information from multiple sources to assess reliability of multistate systems. The degradation of the components in the multistate system is modeled via imprecise Markov models. Then, in the first-stage optimization, upper and lower bounds of the degradation model parameters are determined by minimizing the conflict between the prediction of the model and the multisource imprecise information elicited from experts. A particle swarm optimization algorithm is tailored to solve the computational problems brought by the presence of high-dimensional decision variables and resolve the optimization problem. The second-stage optimization is, then, conducted to identify the upper and lower bounds of the system reliability function given that the degradation model parameters are constrained in the bounds obtained from the first-stage optimization. A numerical example, along with a radar display and control system, is used to demonstrate the effectiveness and applicability of the proposed method.

In engineering scenarios, expert judgments play an essential role in reliability assessment, especially for those systems with few historical data. To achieve a rational result, experts from different areas should be involved, and the uncertainties in their assessments should be properly addressed. Such information is often referred to as multisource imprecise information (MSII) and might contain high degree of conflicts, as different experts usually have different expertise and knowledge. Properly quantifying the conflicts among the MSII, then, becomes a critical issue, as the subsequent processing of MSII (e.g., combination and calibration), depends on the degree of conflict in the MSII. To this end, a new conflict measure is put forth based on the Dempster–Shafer theory (DST) to quantify and visualize the conflict in the MSII from a group of experts. In the first place, the MSII from each expert is used to construct the basic belief assignment (BBA) of the reliability estimates for the corresponding expert under the DST. A 2-D conflict measure, which combines the conflict factor and Jousselme distance in DST, is, then, proposed to measure the conflict between the experts’ BBAs. The conflict is quantified from two perspectives, viz., mutual conflict and total conflict. Finally, a Bhattacharyya distance-based method is developed to further quantify the informativeness of each expert's MSII to the system reliability estimate. A numerical example along with an engineering case is used to validate the effectiveness of the proposed approach.

This article develops a generalized deep convolutional neural network (DCNN)-Bootstrap-based prognostic approach for remaining useful life (RUL) prediction of rolling bearing. The proposed architecture includes two main parts: first, a hybrid DCNN model is utilized to simultaneously extract informative representations hidden in both time series-based and image-based features and predict RUL of bearing; second, the proposed hybrid DCNN model is embedded into the Bootstrap-based implementation framework for quantification of RUL prediction interval. Unlike other deep learning (DL)-based prognostic approaches, the proposed DCNN-Bootstrap method has two innovative features: first, both time series-based and image-based features of bearings, which can multi-dimensionally characterize the degradation of bearing, are comprehensively leveraged by the proposed hybrid DCNN model; second, the RUL prediction interval can be effectively quantified without relying on any bearing's physical and statistical prior information recurring to Bootstrap implementation paradigm. Moreover, the proposed approach is experimentally validated with a case study on rolling element bearings, and comparisons with other popular techniques widely employed in this field are also presented.

This article proposes a novel deep learning based fusion prognostic method for remaining useful life (RUL) prediction of engineering systems. The proposed framework strategically combines the advantages of bidirectional long short-term memory (BLSTM) networks and particle filter (PF) method and meanwhile mitigates their limitations. In the proposed framework, BLSTM networks are applied for further extracting, selecting, and fusing discriminative features to form predicted measurements of the identified degradation indicator. Simultaneously, PF is utilized to estimate system state and identify unknown parameters of the degradation model for RUL prediction. Hence, the proposed fusion prognostic framework has two innovative features: first, the preprocessed features from raw multisensor data can be intelligently extracted, selected, and fused by the BLSTM networks without specific domain knowledge of feature engineering; second, the predicted measurements with uncertainties obtained from the BLSTM networks will be properly represented by the PF in a transparent manner. Moreover, the developed approach is experimentally validated with machining tool wear tests on a computer numerical control (CNC) milling machine. In addition, the popular techniques employed in this field are also investigated to compare with the proposed method.

A novel supervised particle swarm optimization (S-PSO) classification algorithm is proposed for fault diagnosis. In order to improve the accuracy of fault diagnosis and obtain the global optimal solutions with a higher probability, two strategies, i.e. a hybrid particle position updating strategy a nd a fixed iteration interval intervention updating strategy, are designed to balance the effect of the local and the global search. These methods increase the diversity of particles, expand the particles ability of searching the entire solution space, and guide the particles adaptively jumping out of the local optimal area. Meanwhile, based on the shorter intra-class distance, longer inter-class distance and maximum classification accuracy of training samples, a fitness function is designed to constraint the output optimal class centers. Experimental results demonstrate that the proposed S-PSO classification algorithm can overcome the problems in the classical clustering algorithms, which only consider the similarity of data instead of their physical meanings. The comparison on GE90 engine borescope image texture feature classification is also conducted. The results show that the performance of S-PSO classification algorithm is robust. Its classification accuracy is higher than those of popular methods, including support vector machine (SVM), neural network, Bayesian classifier, and k-nearest neighbor (k-NN) algorithm.

Degradation observations of modern engineering systems, such as manufacturing systems, turbine engines, and high-speed trains, often demonstrate various patterns of time-varying degradation rates. General degradation process models are mainly introduced for constant degradation rates, which cannot be used for time-varying situations. Moreover, the issue of sparse degradation observations and the problem of evolving degradation observations both are practical challenges for the degradation analysis of modern engineering systems. In this paper, parametric inverse Gaussian process models are proposed to model degradation processes with constant, monotonic, and S-shaped degradation rates, where physical meaning of model parameters for time-varying degradation rates is highlighted. Random effects are incorporated into the degradation process models to model the unit-to-unit variability within product population. A general Bayesian framework is extended to deal with the degradation analysis of sparse degradation observations and evolving observations. An illustrative example derived from the reliability analysis of a heavy-duty machine tool's spindle system is presented, which is characterized as the degradation analysis of sparse degradation observations and evolving observations under time-varying degradation rates.

Modern engineering systems are generally composed of multicomponents and are characterized as multifunctional. Condition monitoring and health management of these systems often confronts the difficulty of degradation analysis with multiple performance characteristics. Degradation observations generally exhibit an s-dependent nature and sometimes experience incomplete measurements. These issues necessitate investigating multiple s-dependent degradations analysis with incomplete observations. In this paper, a new type of bivariate degradation model based on inverse Gaussian processes and copulas is proposed. A two-stage Bayesian method is introduced to implement parameter estimation for the bivariate degradation model by treating the degradation processes and copula function separately. Degradation inferences for missing observation points, and for future observation points are investigated. A simulation study is presented to study the effectiveness of the dependence modeling and degradation inference of the proposed method. For demonstration, a bivariate degradation analysis of positioning accuracy and output power of heavy machine tools subject to incomplete measurements is provided.

In order to arrange maintenance resources according to system condition, the lead time needs to be considered within the context of condition-based maintenance (CBM). Therefore, a scheduling threshold is introduced to replace the time to schedule, which is used as a decision variable in combination with a maintenance threshold and a failure threshold. The long-run expected cost rate for maintenance considers the maintenance cost, the cost of the waiting time of suppliers and customers. In this way, suppliers can schedule maintenance services in advance when the system condition reaches the scheduling threshold, and perform maintenance when the system condition exceeds the maintenance threshold. Furthermore, the optimal maintenance plan is updated dynamically in the framework of Prognostics and Health Management (PHM). Finally, a numerical example is provided to demonstrate the effectiveness and the dynamic nature of the proposed method.

This paper develops a Bayesian framework to assess the reliability and performance of multi-state systems (MSSs). An MSS consists of multiple multi-state components of which the degradation follows a Markov process. Due to the lack of sufficient data, and only vague knowledge from experts, the transition intensities of multi-state components between any pair of states and the state probabilities cannot be precisely estimated. The proposed Bayesian method can merge prior knowledge from experts' judgments with continuous and discontinuous inspection data to obtain posterior distributions of transition intensities. A simulation method embedded with the universal generating function (UGF) is developed to estimate the posterior state probabilities, the reliability, and the performance of the entire MSS. Two numerical experiments are presented to demonstrate the effectiveness of the proposed method.

Traditional time-based reliability assessment methods evaluate the reliability of a multi-state system (MSS) from a population or a statistical perspective that the reliability of a system is computed purely based upon historical time-to-failure data collected from a large population of identical components or systems. These methods, however, fail to characterize the stochastic behaviors of a specific individual system. In this paper, by utilizing system-level observation history, a dynamic reliability assessment method for MSSs is put forth. The proposed recursive Bayesian formula is able to dynamically update the reliability function of a specific MSS over time by incorporating system-level inspection data. The dynamic reliability function, state probabilities, and remaining useful life distribution of an MSS in residual lifetime are derived for two common cases: the degradation of components follows a homogeneous continuous time Markov process, and a non-homogeneous continuous time Markov process. The effectiveness and accuracy of the proposed method are demonstrated via two numerical examples.

Because of the complexity of engineering systems, and the fact that insufficient data are only available to obtain the precise state probability of components, an extended universal generating function (UGF) based on belief function theory is introduced in this paper to conduct the reliability analysis of multi-state systems (MSSs) with epistemic uncertainty. The behavior of common cause failures (CCFs) is further incorporated, and the occurrence probability of CCFs is evaluated using a weighted impact vector method. A numerical example is used to illustrate how the proposed method works. In addition, a global optimization method is used to obtain the truth interval of the system reliability, and the results are compared with those obtained by using some existing methods. The case study shows that the belief UGF method can effectively avoid the interval expansion problem and the overestimation problem involved in the interval UGF method, and the proposed method can be used to provide a reliable way to evaluate the reliability of MSSs with interval data and CCFs.

Traditionally, degradation testing and condition monitoring are used separately to investigate field reliability. Barriers are naturally formed between these two types of methods due to condition-discrepancies between lab testing and field monitoring, as well as time-varying missions among product population groups. In this paper, a joint framework for field reliability analysis is presented by integrating degradation testing data as well as mission operating information with condition monitoring observations. A coherent modeling strategy is introduced for the information integration by gradually adopting random effects, dynamic covariates, and marker processes into a baseline stochastic degradation model. In detail, random effects are introduced to cope with the inherent unit-to-unit variation. Dynamic covariates are adopted to deal with the external condition heterogeneity. Marker processes are used to account for the time-varying missions. To facilitate information integration and reliability analysis, the Bayesian method is used to implement parameter estimation and degradation analysis. The reliability assessment of products' populations, degradation prediction, and residual life prediction of individual products are investigated. Finally, an illustrative example for field degradation analysis of oil debris in a lubrication system of a machine tool's spindle system is presented. The effectiveness of information integration and the capability of degradation inference are demonstrated through this example.

The redundancy allocation problem has been extensively studied with the aim of determining optimal redundancy levels of components at various stages to achieve the required system reliability or availability. In most existing studies, failed elements are assumed to be as good as new after repair, from a failure perspective. Due to deterioration, the repaired element cannot always be restored to a virtually new condition unless replaced with a new element. In this paper, we present an approach of joint redundancy and imperfect maintenance strategy optimization for multi-state systems. Along with determining the optimal redundancy levels, the element replacement strategy under imperfect repair is also optimized simultaneously, so as to reach the desired availability with minimal average expenditure. A generalized imperfect repair model is proposed to characterize the stochastic behavior of multi-state elements (MSEs) after repair, and a replacement policy under which a MSE is replaced once it reaches the pre-determined number of failures is introduced. The cost-repair efficiency relation, which regards the imperfect repair efficiency as a function of assigned repair cost, is put forth to provide a flexibility of assigning repair efforts strategically among MSEs. The benefits of the proposed method compared to the existing ones are demonstrated and verified via an illustrative case study of a three-stage coal transportation system.

Reliability analysis of complex systems is a critical issue in reliability engineering. Motivated by practical needs, this paper investigates a Bayesian approach for system reliability assessment and prediction with multilevel heterogeneous data sets. Two major imperatives have been handled in the proposed approach, which provides a comprehensive Bayesian framework for the integration of multilevel heterogeneous data sets. In particular, the pass-fail data, lifetime data, and degradation data at different system levels are combined coherently for system reliability analysis. This approach goes beyond the alternatives that deal with solely multilevel pass-fail or lifetime data, and presents a more practical tool for real engineering applications. In addition, the indices for reliability assessment and prediction are constructed coherently within the proposed Bayesian framework. It gives rise to a natural manner of incorporating this approach into a decision-making procedure for system operation and management. The effectiveness of the proposed approach is illustrated with reliability analysis of a navigation satellite.

Reliability growth testing becomes difficult to implement as the product development cycle continues to shrink. As a result, the new design is prone to latent failures due to design immaturity and uncertain operating condition. Reliability growth planning emerged as a new methodology to drive the reliability across the product lifetime. We propose a multiphase reliability growth model that sequentially determines and implements corrective actions (CAs) against surfaced and latent failure modes. Such a holistic approach enables the manufacturer to attain the reliability goal while ensuring the product time to market. We devise a CA effectiveness function to assess the tradeoff between the failure removal rate and the required resources. Rosen's gradient projection algorithm is used to determine the optimal resource allocation in each phase. The applicability and performance of the reliability growth model are demonstrated on a fleet of semiconductor testing equipment.

Many imperfect maintenance models have been developed to mathematically characterize the efficiency of maintenance activity from various points of view. However, the adequacy of an imperfect maintenance model must be validated before it is used in decision making. The most adequate imperfect maintenance model among the candidates to facilitate decision making is also desired.

Evidence conflict that may cause the counter-intuitive results is one of the most concerns for information fusion by Dempster-Shafer's (D-S) evidence theory. To deal with the issue and manage evidence conflict greatly for the improvement of belief co

There has been quite some research on the development of tools and techniques for grid systems, yet some important issues, e.g., grid service reliability and task scheduling in the grid, have not been sufficiently studied. For some grid services which have large subtasks requiring time-consuming computation, the reliability of grid service could be rather low. To resolve this problem, this paper introduces Local Node Fault Recovery (LNFR) mechanism into grid systems, and presents an in-depth study on grid service reliability modeling and analysis with this kind of fault recovery. To make LNFR mechanism practical, some constraints, i.e. the life times of subtasks, and the numbers of recoveries performed in grid nodes, are introduced; and grid service reliability models under these practical constraints are developed. Based on the proposed grid service reliability model, a multi-objective task scheduling optimization model is presented, and an ant colony optimization (ACO) algorithm is developed to solve it effectively. A numerical example is given to illustrate the influence of fault recovery on grid service reliability, and show a high efficiency of ACO in solving the grid task scheduling problem.

Product performance usually degrades with time. When shocks exist, the degradation could be more rapid. This research investigates the reliability analysis when typical degradation and shocks are involved. Three failure modes are considered: catastrophic (binary state) failure, degradation (continuous processes), and failure due to shocks (impulse processes). The overall reliability equation with three failure modes is derived. The effects of shocks on performance are classified into two types: a sudden increase in the failure rate after a shock, and a direct random change in the degradation after the occurrence of a shock. Two shock scenarios are considered. In the first scenario, shocks occur with a fixed time period; while in the second scenario, shocks occur with varying time periods. An engineering example is given to demonstrate the proposed methods.

Many systems are required to perform a series of missions with finite breaks between any two consecutive missions. In such a case, one of the most widely used maintenance policies is a selective maintenance in which a subset of feasible maintenance actions is chosen to be performed with the aim at achieving the subsequent mission success under limited maintenance resources. Traditional selective maintenance optimization reported in the literature only focuses on binary state systems. Most systems in industrial applications, however, have more than two states in the deterioration process. In this work, a selective maintenance policy for multi-state systems (MSS) consisting of binary state elements is investigated. Taking the imperfect maintenance quality into consideration, the Kijima model is reviewed, and a cost-maintenance quality relationship which considers the age reduction factor as a function in terms of maintenance cost is established. Moreover, with the assistance of the universal generating function (UGF) method, the probability of the repaired MSS successfully completing the subsequent mission is formulated. In place of enumerative methods, a genetic algorithm (GA) is employed to solve the complicated optimization problem where both multi-state systems, and imperfect maintenance models are taken into account. The effectiveness of the proposed method is demonstrated via a case study of a power station coal transportation system. Finally, a comparative analysis between the strategies with and without considering imperfect maintenance is conducted, and it is concluded that incorporating imperfect maintenance quality into selective maintenance achieves better outcomes.

A multi-state system (MSS) has more than two discrete states corresponding to different performance rates. Usually, MSS is viewed as in a failure state once its performance rate falls below user demand, and maintenance is carried out immediately. Generally, the repaired system cannot be regarded as good as new, and oftentimes the system restoration is stochastic. We introduce an optimal replacement policy for MSSs, called policyN. Under this policy, a MSS is replaced whenever its failure number reachesN. We assess the dynamic element state probabilities of each aging multi-state element (MSE) using a stochastic process model which is identified as a non-homogeneous continuous time Markov model (NHCTMM), and we evaluate the state distribution of the entire MSS via the combination of the stochastic process, and the universal generating function (UGF). To quantify the quality of imperfect maintenance, a quasi-renewal process is used to describe the stochastic behavior of each individual MSE after repair. Moreover, we derive an explicit expression of the long-run expected profit per unit time, and determine the optimal failure numberN*to replace the entire system. The proposed models are demonstrated via an illustrative case, followed by some comparative studies.

In structural reliability engineering, one often encounters situations where the strength of a structure is influenced by the stress, but the stress is irrelevant to the strength. This phenomenon can be called a unilateral dependency of strength on stress. To evaluate structural reliability in such cases, the stress on a structure is proposed to be a discrete random variable, and the stress dependent strength is represented by a discrete random variable that has different conditional probability mass functions under different stress amplitudes. Then a discrete stress-strength interference model with stress dependent strength is presented based on the universal generating function technique. Finally, the effectiveness of this model is demonstrated by an illustrative example.

Algorithms have been available for exact performance evaluation of multi-state k-out-of-n systems. However, especially for complex systems with a large number of components, and a large number of possible states, obtaining "reliability bounds" would be an interesting, significant issue. Reliability bounds will give us a range of the system reliability in a much shorter computation time, which allow us to make decisions more efficiently. The systems under consideration are multi-state k-out-of-n systems with i.i.d. components. We will focus on the probability of the system in states below a certain state d, denoted by Qsd. Based on the recursive algorithm proposed by Zuo & Tian [14] for performance evaluation of multi-state k-out-of-n systems with i.i.d. components, a reliability bounding approach is developed in this paper. The upper, and lower bounds of Qsdare calculated by reducing the length of the k vector when using the recursive algorithm. Using the bounding approach, we can obtain a good estimate of the exact Qsdvalue while significantly reducing the computation time. This approach is attractive, especially to complex systems with a large number of components, and a large number of possible states. A numerical example is used to illustrate the significance of the proposed bounding approach.

Current studies of the optimal design of multi-state series-parallel systems often focus on the problem of determining the optimal redundancy for each stage. However, this is only a partial optimization. There are two options to improve the system utility of a multi-state series-parallel system: 1) to provide redundancy at each stage, and 2) to improve the component state distribution, that is, make a component in states with respect to higher utilities with higher probabilities. This paper presents an optimization model for a multi-state series-parallel system to jointly determine the optimal component state distribution, and optimal redundancy for each stage. The relationship between component state distribution, and component cost is discussed based on an assumption on the treatment on the components. An example is used to illustrate the optimization model with its solution approach, and that the proposed reliability-redundancy allocation model is superior to the current redundancy allocation models.

The contents and meanings of mapping relationships between physical domain and function domain in different design stages, such as conceptual design, detail design and enhancement design, were analyzed. According to the analysis results, the fuzzy mapping between physical domain and function domain in different design stages was established by integrating objective information and subjective information in the design process, such as expert's knowledge, designer's preferences and customer's requirements, where the fuzzy sets, fuzzy mapping and fuzzy transition were used. The property table of structure behavior parameters was established based on the fuzzy mapping relationships. The fuzzy mapping is very important to optimize product structure, perfect product function, meet the diversified and individual requirements of customers. Finally, an example was used to illustrate the fuzzy mapping relationships between physical domain and function domain in different design stages.