The spray-painting system in automotive manufacturing characterizes a large amount of energy consumption at a time, thus exposing the process to potential overload risks. It becomes imperative to dynamically predict the energy consumption of spray-painting systems to facilitate preventive and security measures. However, the monitoring data derived from the spray-painting system exhibits high dimensionality and non-linearity, posing challenges to prediction accuracy. Therefore, this paper proposes a methodology framework of real-time energy consumption prediction for the automotive spray-painting system, termed ePreS. First, a hybrid feature extraction approach is designed to cope with multi-domain data concerning device, process, production, and multiple energy sources, thus reducing model complexity and elevating training efficiency. Second, a deep learning model CNN-BiLSTM-Attention (CBA) is proposed for the real-time energy consumption prediction, while the coati optimization algorithm (COA) is employed for network structure optimization. Finally, a real-world case study is implemented in an electric vehicle painting workshop, with a smart energy management system module developed, to verify the effectiveness and superiority of the proposed method. This study is expected to serve as a tool for practitioners to meet similar requirements and spark new ideas for future research.

Computer numerical control (CNC) machine tools consume a large amount of raw materials in its manufacturing process. With the emphasis on the economy of machine tools, reducing the material consumption becomes significant. The lightweight optimization is regarded an effective way for material saving, since it can reduce the cost while improving machining performance. However, existing lightweight studies of machine tool mainly depend on experience, which cannot ensure the accuracy and efficiency, and the design scheme is hard for manufacturing. On this basis, a novel data-driven lightweight optimization method with meta-structure integrating the topological and size optimization is proposed in this article. Meta-structures are modeled to form the topological configuration of machine tool for avoiding time-consuming design analysis. The surrogate models with a novel adaptive sequential sampling method are built to fit accurate relationships between structure and performances. A multi-objective size optimization frame is developed for further reducing the mass, deformation and enhancing natural frequency of machine tool. The gear honing machine tool is taken as the case study, where results indicate that the lightweight optimization can reduce mass by 13.72% under the premise of structure safety.

Design parameters optimization is regarded as an effective way to reduce energy consumption of a machine tool, which are contributed by several subsystems with coupling relationships affecting the total energy consumption. Therefore, it is of importance to study the coupling relationships between subsystems at the design stage for energy saving. However, there are multiple key energy consuming subsystems associated with various design parameters, leading to a complex optimization model of this problem. It is rather time-consuming to optimize such a complex model and hard to obtain global optimal results. To address this challenging problem, this article proposes an energy saving design approach of a gear hobbing machine based on Analytical Target Cascading (ATC) method. Firstly, the energy consumption models of each subsystem are established and the coupling relationships are analyzed. Then, the decomposition of the energy coupling model is conducted and the comprehensive optimization model is constructed by ATC. One novel adaptive sequential sampling method is proposed with the surrogate model to achieve the collaborative optimization of both structural parameters and control parameters. Finally, three optimization algorithms are developed to comparatively study the energy-optimal schemes. Testing results indicate that the energy consumption can be reduced by 9.72%, with lighter moving component and reduced deformation.Note to Practitioners—This article provides one method for the energy saving of the gear hobbing machine at the design stage. Previous studies only focus on the influence of one design factor on energy consumption, and the optimization is under a mixed optimization model, which is hard to obtain global optimal results. This article develops an energy saving design method considering the comprehensive influence of design factors for energy saving of multiple subsystems. Based on ATC, an energy coupling model can be divided into several energy consuming subsystems and the independent optimization of each subsystem can be achieved. To ensure the lightweight and control abilities, a surrogate model and a novel sequential sampling method are applied. Results show the effectiveness of the proposed method and the energy reduction can be achieved with a good structural and control performance.

The internal gear power honing process is widely used in gear machining for electric vehicles because of the advantages of high-precision and high-efficiency machining. The gear honing process involves six axes and high spindle speeds, this process contributes a substantial amount of energy consumption but has less attention on energy saving. To improve the energy efficiency of gear honing process, this paper proposes an energy consumption modeling and process parameter optimization method under multi-axis coupling. The multi-axis coupling motion and energy consumption characteristics of gear honing process are analyzed. The energy consumption model of gear honing process under multi-axis coupling is then established, and the influence law of process parameters on honing energy consumption is investigated. Furthermore, a multi-objective process parameter optimization model for minimizing energy consumption and machining time is constructed. An improved multi-objective atomic orbital search (IMOAOS) algorithm is developed to solve the multi-objective optimization problem. The gear honing experiment results demonstrate that the optimized scheme reduces energy consumption by 39.75% and machining time by 8.48% compared to the empirical scheme. The proposed multi-objective optimization scheme also significantly balances the energy consumption and machining time of gear honing process compared with single-objective optimization.

The integration of flexible process planning and cutting parameter optimization is of great significance to reduce energy consumption and shorten production time. Flexible manufacturing system brings great uncertainty to the flexible process planning and cutting parameter optimization. Most studies are conducted in a static manufacturing environment and lack of adaptive capacity to the uncertainty of the machining resources. To this end, an integrated decision-making method of flexible process plan and cutting parameter is proposed to improve energy efficiency. Specifically, the improved AND/OR network graph is employed to describe various types of process flexibility. Secondly, the coupling characteristics between energy consumption and machining resources, cutting parameters, and operation sequences are analyzed. Then, a Markov Decision Process is utilized to simulate the dynamic generation process of flexible process plans and cutting parameters, and the integrated decision-making method considering dynamic machining resources is designed with actor-critic framework. Finally, extensive comparative experiments are carried out to verify the validity of the proposed method. Experimental results indicate that: 1) the proposed method can determine flexible process plans and cutting parameters to adapt to the dynamics of machining resources. 2) The integrated optimization method reduces$E_{total} $and$T_{p}$by 3.59% and 3.45% compared to the two-stage optimization methodNote to Practitioners—Decision making of flexible process plans and cutting parameters relies on machining resources in the machining process. Dynamic changes in machining resources make the energy-aware decision of the flexible process plans and cutting parameters a challenging problem. To the best of our knowledge, this paper develops an integrated method of flexible process planning and cutting parameter optimization considering dynamic machining resources that can adapt to the change of machining resources. It may assist decision-makers to provide more practical flexible process plans and cutting parameters based on dynamic machining resources in the machining process.

The production of automobile engines primarily concerns three workshops: casting, machining and assembly. Any stagnation in any of these stages will have a detrimental impact on the operation of downstream production, resulting in increased costs and production delays. Hence, it is imperative to establish a rational scheduling system for the whole production. Therefore, this study proposes a collaborative scheduling optimization method for multi-level hybrid flow shop of automobile engine. Initially, the collaborative production relationships between the workshops are examined. Subsequently, an optimization model of collaborative scheduling for the multi-stage hybrid flow shop is formulated, focusing on reducing collaborative production costs and minimizing the maximum completion time. Furthermore, considering the discrete nature of the scheduling problem, the study explores encoding/decoding strategies based on random key techniques to bridge the gap between continuous algorithms and discrete problems. Consequently, a distributed reference vector guided evolutionary algorithm (DRVEA) is introduced to solve the model. Finally, the effectiveness and superiority of the proposed method are validated through a case study using practical data from an automobile engine enterprise.

Energy consumption of machine tools has always been a hot issue in the manufacturing sector due to the concern about climate change. To decrease the energy consumption of machine tools, this paper investigates the multi-axis coupling mechanism of a hobbing machine tool during machining from the design stage, and develops an energy consumption model under multi-axis coupling of the whole machine. Firstly, the multi-axis coupling mechanism in the actual machining process is studied. The hob speed and the feed speed of Z axis moving component will affect the hobbing force, and the component of hobbing force in each direction will affect the load and energy consumption of each axis. Meanwhile, the tracking error of each axis is reduced by a sliding mode controller. Next, a comprehensive energy consumption optimization model of a hobbing machine tool under multi-axis coupling is constructed. Furthermore, three optimization algorithms are implemented to the energy consumption model. Compared with the initial scheme, the simulation experiment results of the case-study indicate that the hobbing machine tool energy consumption is reduced by 1.19%, the steady-state error of each axis is reduced by 35.27%, 21.70%, and 36.34%, respectively, and the maximum deformation of the tool holder is reduced by 10.91%.Note to Practitioners—This work is dedicated to dealing with the issue of a hobbing machine tool energy consumption. Based on our previous work, the multi-axis coupling mechanism of the gear hobbing machine tool is investigated, and a comprehensive energy consumption model of the gear hobbing machine tool is proposed. The design variables of the energy consumption optimization model include the structural parameters of the Z axis moving component and the sliding mode controller parameters of the three axes (B, C, and Z axis). Three optimization algorithms are used to drive the optimization model. The simulation results verify the feasibility of the method. The control performance of the system is improved, and the mass of moving component is reduced.

In multi-stage automotive production lines (MSAPLs), unforeseen disturbance events such as emergency order can disturb the initial production plan, leading to higher production cost and order delivery delay. To address this issue, an emergency order-oriented collaborative resequencing optimization method for MSAPL based on improved multi-objective particle swarm optimization algorithm (MOPSO) is proposed in this paper. First, a resequencing strategy is proposed for automotive orders based on their production status. Then, a collaborative resequencing mathematical model for MSAPL that selects the production cost and order delivery delay as the objectives is established, and an improved MOPSO is developed to optimize the mathematical model. Finally, a case study is implemented by citing a MSAPL as the example, which verifies the effectiveness and superiority of the proposed method.

In a machining process, proper selection of process plans and cutting parameters can effectively reduce energy consumption and shorten production time. Traditionally, studies on process planning and cutting parameter optimization for energy saving are mostly concentrated on electrical energy consumption. Since the preparation process of cutting tools and cutting fluid consumes a considerable amount of energy, conservation of this part of energy consumption, namely, the embodied energy consumption, will achieve a more energy-efficient machining process. In this article, an integrated model for process planning and cutting parameter optimization is proposed to shorten production time and reduce the energy footprint (namely, electrical energy consumption and embodied energy consumption of cutting tools and cutting fluid) of a machining process. Considering that the optimization of process plan and cutting parameters in an integrated manner is a hybrid programming process, simulated annealing and quantum-behaved particle swarm optimization (SA-QPSO) hybrid algorithm is employed to solve the proposed model. Results of the case study show that: 1) embodied energy consumption of cutting tools and cutting fluid accounts for a nonnegligible proportion of energy footprint of the machining process and 2) there is a tradeoff between energy footprint and production time, and the balance of them is achieved through the proposed optimization approach.Note to Practitioners—This article, for the first time, to the best of our knowledge, proposes an integrated approach to reduce both electrical and embodied energy consumption of a machining process through optimizing process plan and cutting parameters. Such broader consideration makes this integrated optimization approach more applicable to real industry settings and contributes to the comprehensive improvement of energy efficiency in the machining process. To better use this approach, the following three steps should be highlighted: 1) the energy footprint characteristics of the machining process should be comprehensively analyzed and modeled; 2) the integrated optimization model for minimizing energy footprint and production time needs to cooperate with machining constraints, such as process centralization, machining sequence, and process requirements; and 3) solving the proposed model is a hybrid programming process since there are discrete decision variables and continuous variables. A proper algorithm should be used to solve the proposed model.

The moving components and servo control systems of computer numerical control (CNC) machine tools spent a substantial energy but received less attention regarding energy saving. This article presents a novel energy saving methodology of feed system using a data-model hybrid driven design optimization approach for the integrated design of moving component structural geometry and control system. Surrogate models are built based on the design of experimental data to avoid time-consuming finite element analysis. The energy consumption mechanism model is constructed via energy flow analysis method. The data-model hybrid modeling method realizes the collaborative optimization of the machine tool feed system structure and controller, while simultaneously accelerating the optimization process. A multi-objective trade-off model with energy consumption and deformation is established. Three different multi-objective optimization approaches are taken to drive the developed multi-objective optimization model. The control performance of the feed system is demonstrated through simulation analysis. Results indicate that the optimized scheme can reduce energy consumption by over 10% and maximum deformation of the tool holder by over 14%. Note to Practitioners—This article is motivated by the problem that a significant energy consumption occurs when the CNC machine tool feed system continuously drives the moving components to move, accelerate or decelerate. The previous studies to cope with this problem broadly are to separately analyze energy-saving characteristics of the structure or control system of the CNC machine tool feed system. This article suggests a novel data-model hybrid approach for energy saving of machine tool feed system, which simultaneously integrates design of moving component structural geometry and servo control system. In this article, we mathematically derive an energy consumption mechanism model of the CNC machine tool feed system. By using surrogate assisted method, a multi-objective trade-off model with energy consumption and deformation is established. Simulation experiments indicate that this approach is feasible and can significantly reduce the energy consumption of CNC machine tool feed system.

With the surging energy cost and environmental impacts, strategies to achieve energy-efficient production have attracted increasing concerns of the manufacturing enterprises. For the fact that most manufacturing systems operate in a dynamic and nondeterministic environment, rescheduling strategies may be beneficial as it serves for adaption of initial schedule to dynamic events. Besides that, the development of modern information technology in manufacturing practice enables the flexibility of production toward alternative process plans. However, very little research has focused on the rescheduling problem integrated with process planning for energy saving. Hence, this work undertakes this challenge by proposing rescheduling decision mechanisms in response to two typical dynamic events with alternative process plans for energy-efficient flexible job shops. More specifically, by modeling the energy consumption of the flexible manufacturing system, the problem is first formulated as a mixed-integer programming optimization model. Rescheduling mechanisms for both new job arrivals and machine tool breakdowns are then designed, based on which a rescheduling algorithm is proposed in the form of a heuristic framework. The significance of the proposed algorithm is exemplified by a comparative case study under various scenarios. Note to Practitioners—The complex process plan selection and dynamic events in flexible job shops make the energy-aware schedule decision a challenging problem. Rescheduling addresses this issue, however, most existing rescheduling algorithms assume that only one process plan is given with a predetermined process route and machine tool allocation. This reduces the effectiveness of energy-saving for such a dynamic and flexible manufacturing system. This article, for the first time, to the best of our knowledge, proposes rescheduling decision mechanisms to generate schedules that can adapt to dynamic events and are energy-efficient with process plan flexibility. It may assist decision-makers to provide more practical and applicable energy-efficient schedules for flexible job shops, particularly when dynamic variations of the production environment occurred frequently.

Series elastic actuator (SEA) is a promising compliance device due to its lower output mechanical impedance, and it is widely applied to ensure safe human–robot interaction. Although some efforts have been made to achieve accurate stiffness tracking, the time-delay issue in SEA control has still not been well investigated. However, the time delay can cause an inaccurate response and increase the risk of injury. To overcome this problem, this article proposes a fast-response admittance control method for SEAs. First, an admittance control scheme considering the external force estimation is developed for a hydraulic SEA. Then, a parallel adaptive time-series (ATS) (P-ATS) compensator is proposed and further adopted in the admittance control scheme to compensate for the time delay and tracking error. The P-ATS compensator is a modification of the ATS compensator, which is enhanced with a unique parallel mechanism. Such a mechanism can save more computational resources on locating better parameters the for P-ATS compensator, thus improving its performance. Moreover, the parameter setting is converted to an optimization task, which is solved by the whale swarm algorithm (WSA) to achieve higher accuracy. The newly located parameters are compared to the current parameters based on a proposed evaluation criterion, thus guaranteeing the quality of the updated parameters. All the above strategies are employed to improve the SEA admittance control performance. The results obtained from both simulation and real-world experiments validate that, compared to conventional methods, the proposed method achieves a better performance in SEA stiffness tracking with lower time delay and tracking error.Note to Practitioners—Accurate stiffness tracking of SEAs can achieve safe human–robot interaction. However, the time delays introduced by the imprecise movement and estimation of external force can lead to inaccurate actuator response that may limit the capacity of safety insurance. To overcome this issue, a fast-response admittance control method is proposed for SEAs by adopting a novel P-ATS compensator. Thus, the time delays and errors from both load movement and external force estimation can be adaptively compensated. Several strategies have been adopted to enhance the compensator for parameter determination to achieve better performance. The proposed method requires no additional previous information about the system except load mass and spring stiffness, which makes it easy to implement for different types of SEAs. Experimental results show that the proposed method can achieve faster and more accurate stiffness tracking under different conditions. Future work aims to address the control problem under random disturbances and apply the proposed method to human–robot collaboration tasks to further test its performance.

In the field of sculptured surfaces machining, the robot trajectory planning, under high-order complex constraints, aiming at minimizing energy or time, is always a challenge. The complexity of curvature characteristics of sculptured surfaces and the nonlinearity of relevant constraints are the main reasons. This article proposes an efficient planning method of minimum-energy robot trajectory, for high-speed machining of sculptured surfaces. First, the energy characteristic model of the robot machining system (RMS) is established, to acquire the energy-optimal feedrate, under velocity constraints, to use in the subsequent trajectory planning. Next, a trajectory planning model, with complex constraints, is developed. The proposed method transforms the original trajectory planning into a minimal modification of the initial objective-optimal B-spline feedrate curve (BFC). Furthermore, two main coupling problems, which influence the minimal change of curves, in the direct evolution-based BFC modification, are addressed. Based on the derived solutions, a novel modification algorithm of BFC, with a callback mechanism (CBM), is proposed. Finally, the performance of the proposed method and the specific algorithm is validated by two case studies. Results show that the proposed method can significantly improve the efficiency of robot trajectory planning, aiming at minimum energy, while exhibiting excellent performance.Note to Practitioners—This work was motivated by how to automatically and effectively acquire the energy-saving trajectory of a robotic system, executing sculptured surface machining. This article suggests a new approach that transforms the original trajectory optimization into a minimal modification of the initial energy-optimal BFC, obtained under velocity constraints. This approach calculates the complex energy formula only once. A CBM, for constraint-based BFC modification, is proposed, to revise the redundant reduction of the feedrate. The proposed modification algorithm significantly decreases the detrimental effect of two coupling problems, on the adjustment of the BFC. Results show that the computational efficiency of the proposed method is significantly superior to the one of the direct optimization method. The performance of the proposed modification algorithm is obviously advanced compared to the existing B-spline evolution algorithm. In blade machining, after optimizing the trajectory using the proposed method and algorithm, both energy and time decrease by more than 45% compared to the conservative feed. The proposed algorithm improves significantly the trajectory compared to the prior art algorithm. Technologists benefit from reduced planning time and improved machining performance. However, incorporation into a CAM or manufacturing system has not yet been realized and remains a significant work to be done in the future.

Energy places an important role in a new scale of urbanization, digitization, and industrialization. Going “energy-efficient” then becomes a major component of the missions for manufacturers and service providers to stay globally competitive. In recent years, the newly emerging intelligent technologies are enhancing the production process and control management in an energy-effective and -efficient manner. In order to apply and implement these innovations, many new challenges and opportunities have emerged and significantly expanded the scopes of typical production and service automation.

Energy efficiency modeling is of great importance to energy management and conservation for machinery enterprises. To improve the generalization ability, this article combines the machining parameters and the configuration parameters into energy efficiency models, for which machine-learning (ML) algorithms are used considering the lack of theoretical formulas. Based on the three-year data collected in a shop floor, a comparative study for two different cases is conducted with a particular focus on prediction accuracy, stability, and computational efficiency. In Case 1, only cross-sectional data are used to predict energy efficiency, ignoring the deterioration of spindle motors and cutting tools. Three traditional ML algorithms, i.e., artificial neural networks, support vector regression, and Gaussian process regression, are evaluated with the help of five error metrics. In Case 2, we construct the models in a more realistic situation that considers the dynamic aspects of spindle motor aging and tool wear. A convolutional neural network, a stacked autoencoder, a deep belief network and the aforementioned traditional ML algorithms are investigated. The comparison shows that all the models in Case 1 suffer from performance degradation, while deep learning achieves the long-term improvement in accuracy. Note to Practitioners-Energy efficiency models deliver many advantages, ranging from energy-aware machine design to process optimization. Although a large amount of works in the past focused on physics-based and experimental modeling for specific machining configurations, it can be more effective to improve the applicability of the modeling methods by involving the configuration variables into the models. Due to the uncertainties in both the machine and the operation environment, machine learning is adopted to fit the high-dimensional and high-nonlinear energy system. To the best of our knowledge, this is the first article that provides a comprehensive survey on ML-based modeling in terms of data sizes, temporal granularities, feature selection, and algorithm performance. Such a survey helps engineers quickly justify the appropriate ML methods to meet the actual requirements.

Energy-efficient machining has become imperative for energy conservation, emission reduction, and cost saving of manufacturing sectors. Optimal machining parameter decision is regarded as an effective way to achieve energy efficient turning. For flexible machining, it is of utmost importance to determine the optimal parameters adaptive to various machines, workpieces, and tools. However, very little research has focused on this issue. Hence, this paper undertakes this challenge by integrated meta-reinforcement learning (MRL) of machining parameters to explore the commonalities of optimization models and use the knowledge to respond quickly to new machining tasks. Specifically, the optimization problem is first formulated as a finite Markov decision process (MDP). Then, the continuous parametric optimization is approached with actor-critic (AC) framework. On the basis of the framework, meta-policy training is performed to improve the generalization capacity of the optimizer. The significance of the proposed method is exemplified and elucidated by a case study with a comparative analysis.

Going “energy efficient” has been one of the missions for manufacturers to stay globally competitive. Considering machining as a major manufacturing activity, how to effectively model and control its energy consumption becomes critical. Although researchers have analyzed the energy consumption of machining from the machine, process planning, or shop-floor perspective individually, very litter work has comprehensively studied the concurrent interactions among energy-aware decisions for machine parameter settings, process planning, and shop-floor control. Hence, the work presented in this article undertakes this challenge in the context of a resource-constrained machining system. In particular, the energy characteristics of machining are first analyzed with the consideration of various machine tools, cutting tools, cutting parameters, operation sequences, as well as machine availability. A multiobjective optimization model is then developed to minimize both energy consumption and makespan. The solution is provided through honey bee mating optimization algorithm (HBMOA) combined with shop-floor simulation. In addition, the significance of the proposed approach is exemplified and elucidated by a case study. Note to Practitioners-A well-informed decision made in cutting parameter optimization or process planning relies heavily on the accurate data delivered from the shop floor. In other words, the decision made without the consideration of the shop-floor situation might not achieve the original goal or even fail to materialize. As these factors exist in a real manufacturing cycle, how to integrate shop-floor scheduling with process planning and machining parameter optimization becomes essential for energy-efficient manufacturing. This article undertakes this challenge and develops a multiobjective optimization model, where energy consumption of machining, for the first time to the best of our knowledge, is comprehensively analyzed at both the machine level and shop-floor level. Such broader integration makes this approach more practical and applicable to real industry settings, particularly when the shop-floor resource is limited.

This paper investigated a dynamic rescheduling problem for a flexible machining system with random machine breakdown and urgent job arrivals. The energy consumption characteristics of the machining system is explicitly analyzed by considering multiple flexibilities with related to process routes and machine tool selection as well as dynamic events. Then a multi-objective optimization model of dynamic rescheduling is presented to take minimum energy consumption and minimum makespan as objectives, which is solved by a MOGSA algorithm. Case studies with random urgent job arrival and machine breakdown are implemented and the experimental results show that the proposed approach is effective for energy saving through rescheduling.

Traditionally process planning is concerned with reducing energy consumption at a machining process level and is done on the assumption that the manufacturing resources at the shop floor are sufficient and available all the time. This paper presents an energy-efficient process planning approach for resource-constrained machining systems. The interactive effects of process routes and cutting parameters on energy consumption at machining process level and at shop floor level are explicitly analyzed. A multi-objective optimization model of process planning is presented to take minimum energy consumption and minimum makespan as objectives, which is solved by a HBMOA algorithm. The energy saving performance of the proposed process planning approach is demonstrated through case studies.

This paper studies a predictive modeling for cutting energy consumption in CNC turning process by using deep learning methods. An analysis of energy consumption in cutting period is firstly presented, based on which the impact factors of energy are clarified. Then the data collection platform and data pre-processing are introduced, followed by a brief review of Convolutional Neural Network (CNN), Stacked Auto-Encoder (SAE) and Deep Belief Network (DBN). These modeling methods are tested by k-fold cross-validation. The obtained results show that SAE is the most suitable method to model the relationship between process parameters, machining configuration and cutting energy.

This paper studies the energy characteristics with respect to process parameters from a systematic point of view, in terms of electricity and materials. A detail analysis of energy characteristics of a CNC machining system is firstly presented, based on which the calculation models of energy efficiency are formulated. Then the effects of process parameters on energy and processing time are investigated by using S/N analysis. The results show different optimization trends for two kinds of specific energy consumption considered in this work and detail explanations of the trends are given afterwards.

Remanufacturing is a practice of growing importance due to increasing environmental awareness and regulations. However, little research focuses on stochastic remanufacturing process routings (RPR). This paper presents an analytical method, where four Graphical Evaluation and Review Technique (GERT)-based RPR models are proposed to mathematically represent and analyze the variability of remanufacturing task sequences. In particular, with the method, the probability of individual processes being taken in a remanufacturing system and the time associated with them can be efficiently determined. The proposed method is demonstrated through the remanufacturing of used lathe spindles and telephones, and verified by Arena simulation. Numerical experiments that investigate the relationships between RPR dynamics and other system parameters (such as inventory control for due-time performance and time buffer size for bottleneck control) are included.