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Managing Component Degradation in Series Systems for Balancing Degradation Through Reallocation and Maintenance
IISE Transactions
Abstract
In a physical system, components are usually installed in fixed positions that are known as operating slots. Due to such reasons as user behavior and imbalanced workload, the component degradation can be affected by the corresponding installation position in the system. As a result, the component degradation can be significantly different even when the components come from a homogeneous population. Dynamic reallocation of the components among the installation positions is a feasible way to balance the component degradation and hence extend the time from system installation to its replacement. In this study, we quantify the benefit of incorporating the reallocation into the condition-based maintenance framework on series systems. The degradation of components in the system is modeled as a multivariate Wiener process, where the correlation between the degradation is considered. Under the periodic inspection framework, the optimal control limits for reallocation and preventive replacement are investigated. We first propose a reallocation policy of two-component systems, where the degradation process with reallocation and replacement is formulated as a semi-regenerative process. Then the long-run average operational cost is computed according to the stationary distribution of its embedded Markov chain. We then generalize the model to general series systems and use Monte Carlo simulations to approximate the maintenance cost. The optimal thresholds for reallocation and replacement are obtained from a stochastic response surface method with the stochastic kriging model. We further generalize the model to the scenario of unknown degradation rate associated with each slot. The proposed model is applied to the tire system of a car and the battery system of hybrid-electric vehicles, where we show that the reallocation policy is capable of significantly reducing the system long-run average operational cost.
... Reassigning component positions can help take full advantage of all components and prolong the overall system lifetime to a certain degree. Many studies on CRP have also considered the joint optimization problem of component reassignment and system maintenance policy [21][22][23][24][25], which can simultaneously even the degradation degrees among components and reduce the risk of system failure. Most studies on CRP focus on systems with conventional structures, such as series system [20][21][22], parallel system [20], and -out-of-system [21]. ...
... Many studies on CRP have also considered the joint optimization problem of component reassignment and system maintenance policy [21][22][23][24][25], which can simultaneously even the degradation degrees among components and reduce the risk of system failure. Most studies on CRP focus on systems with conventional structures, such as series system [20][21][22], parallel system [20], and -out-of-system [21]. A CRP on balanced systems operating in a shock environment was developed by Wang et al. [15]. ...
... From the perspective of policy design, the joint policy of component rearrangement and preventive maintenance is constructed for the multi-stage balanced system. Previous studies on CRP are mainly concerned with conventional system structures, such as series system, parallel system and -out-of-system [20][21][22], but in this paper, a novel balanced system is taken into consideration. On the other hand, in reported research on the combination of component rearrangement and maintenance, very few has considered imperfect maintenance policy. ...
... Considering the possibility of only maintaining some of the units at the moments of inspection and decision-making, it is a tedious task of determining the renewal cycle due to the complex degradation process of multi-unit systems [31]. Under this circumstance, the semi-regenerative process is introduced by modelling the stationary distribution , and allowing for a system semiregenerative cycle in accordance with the inspection cycle, i.e., a new system semi-regenerative cycle begins from multiple steady states at each inspection moment [32]. This approach significantly makes the analysis of maintenance behavior for multi-unit systems more simplified and feasible [33]. ...
... Considering that the conventional renewal process appears tedious when modelling and optimizing maintenance strategies for multi-unit systems [32], the inspection-maintenance process of load-sharing systems can be effectively modelled and described by the popular semi-regenerative process [34]. Unlike the singular initial state in the renewal process, the semiregenerative process allows for multiple initial states to ...
For traditional degrading load-sharing systems, a typical assumption lies in the only effect of unit load on its degradation rate. However, motivated by a laser system example with positive correlation between degradation rate and volatility, we present a novel load-sharing system with general degradation rate-volatility-load correlation. Furthermore, to take account for unit economic dependence caused by sharable maintenance set-up cost, and the window period generated by the maintenance on some unit, opportunistic maintenance (OM) strategy is introduced to offer the opportunity of simultaneously maintaining another working unit under control-limit criteria. Based on the semi-regenerative process, the long-run average cost rate is minimized to obtain the optimal inspection interval, preventive maintenance and OM thresholds. Compared to the traditional condition-based maintenance strategy separately for each unit, the effectiveness of OM strategy is validated through numerical examples and case studies, offering broad managerial insights for engineers to reduce maintenance expenses.
... Then, we review the literature on reassignment [34][35][36][37], another way of managing degradation. Elements are subject to various environmental conditions and loads that affect their degradation rates, so the degradation of elements can be managed by reassigning them to suitable positions. ...
... The balance of degradation between elements has been well studied in the literature on reassignment. One of its typical policies is to swap positions so that more-degraded elements work with low environmental stress while less-degraded ones work in harsh environments [34][35][36][37]. The balance can cluster maintenance activities for economies of scale and avoid premature failure of highly degraded elements. ...
Industrial systems such as signal relay stations and oil pipeline systems can be modeled as linear multi-state consecutively connected systems, which comprise sequentially ordered elements and fail if the first and the final elements are not connected. The performance level of each element is controllable, which determines how many elements an element can connect and affects its degradation rate. Accumulated degradation can cause element failure, which may lead to costly system failure. This paper aims to minimize long-term maintenance-related costs, including system failure costs. We provide optimal maintenance planning and performance control for every system degradation state through Markov decision process modeling and a dynamic programming algorithm. Load-sharing, restricted maintenance capacity, maintenance setup costs, and the structural characteristics of the system are considered in the model, all of which influence the optimal maintenance and performance control policy. Regarding degradation management, reducing the difference in degradation levels between elements, e.g., replacing more-degraded elements first, can be cost-effective. However, increasing the difference in degradation by maintenance or performance control can also lower maintenance-related costs in specific situations, which is discussed in numerical experiments. We also illustrate structural insights regarding the proposed model, including sensitivity analyses of maintenance capacity, setup costs, and the difference between preventive and corrective replacement costs.
... Hence, fault detection of the multiple sensors without prior knowledge is one of the most significant tasks for the safety of autonomous cars. Furthermore, preventive maintenance is an effective practice for reducing the sensor failure rate [46]. The next section comprehensively summarizes the PHM of ADAS sensors. ...
... Hence, fault d multiple sensors without prior knowledge is one of the most significant task of autonomous cars. Furthermore, preventive maintenance is an effective ducing the sensor failure rate [46]. The next section comprehensively su PHM of ADAS sensors. ...
Recently, the advanced driver assistance system (ADAS) of autonomous vehicles (AVs) has offered substantial benefits to drivers. Improvement of passenger safety is one of the key factors for evolving AVs. An automated system provided by the ADAS in autonomous vehicles is a salient feature for passenger safety in modern vehicles. With an increasing number of electronic control units and a combination of multiple sensors, there are now sufficient computing aptitudes in the car to support ADAS deployment. An ADAS is composed of various sensors: radio detection and ranging (RADAR), cameras, ultrasonic sensors, and LiDAR. However, the continual use of multiple sensors and actuators of the ADAS can lead to the failure of AV sensors. Thus, the prognostic health management (PHM) of ADAS is important for the smooth and continuous operation of AVs. The PHM of AVs has recently been introduced and is still progressing. There is a lack of surveys available related to sensor-based PHM of AVs in the literature. Therefore, the objective of the current study was to identify sensor-based PHM, emphasizing different fault identification and isolation (FDI) techniques with challenges and gaps existing in this field.
... Q. Sun, Z.-S. Ye and X. Zhu [11], 'Managing component degradation in series systems for balancing degradation through reallocation and maintenance'. The control of component aging in serial systems is examined through the optimization of preventive replacement and reallocation policy by deploying stochastic optimization and Markov chain. ...
The state of a machine is modeled as a controlled continuous-time Markov chain. Moreover, the machine is being serviced at random times. The aim is to maximize the time until the machine must be repaired, while taking the maintenance costs into account. The dynamic programming equation satisfied by the value function is derived, enabling optimal decision-making regarding inspection rates, and special problems are solved explicitly. This approach minimizes direct maintenance costs along with potential failure expenses, establishing a robust methodology for determining inspection frequencies in reliability-centered maintenance. The results contribute to the advancement of maintenance strategies and provide explicit solutions for particular cases, offering ideas for application in reliability engineering.
... Reallocation and replacement of battery cells can be a way of predictive maintenance. Sun et al. [148] studied components that are in series systems and presented a maintenance policy to balance degradation degree between components in one system. This thought is potential in future battery applications. ...
Prognostics and health management (PHM) has gotten considerable attention in the background of Industry 4.0. Battery PHM contributes to the reliable and safe operation of electric devices. Nevertheless, relevant reviews are still continuously updated over time. In this paper, we browsed extensive literature related to battery PHM from 2018 to 2023 and summarized advances in battery PHM field, including battery testing and public datasets, fault diagnosis and prediction methods, health status estimation and health management methods. The last topic includes state of health estimation methods, remaining useful life prediction methods and predictive maintenance methods. Each of these categories is introduced and discussed in details. Based on this survey, we accordingly discuss challenges left to battery PHM, and provide future research opportunities. This research systematically reviews recent research about battery PHM from the perspective of key PHM steps and provide some valuable prospects for researchers and practitioners.
... Guo and Liang [31] adapt a Markovian modeling approach for the joint optimization of successive inspection times and maintenance decisions for multi-component systems. Furthermore, this literature stream has been expanding with studies that integrate condition-based maintenance planning with other types of decisions related to inventory control [32][33][34], production control [35][36][37][38][39][40], spare part selection [7], components' deterioration levels balancing [41,42], and maintenance team scheduling/allocation [43,44]. ...
With rapid advances in technology, many systems are becoming more complex, including ever-increasing numbers of components that are prone to failure. In most cases, it may not be feasible from a technical or economic standpoint to dedicate a sensor for each individual component to gauge its wear and tear. To make sure that these systems that may require large capitals are economically maintained, one should provide maintenance in a way that responds to captured sensor observations. This gives rise to condition-based maintenance in partially observable multi-component systems. In this study, we propose a novel methodology to manage maintenance interventions as well as spare part quantity decisions for such systems. Our methodology is based on reducing the state space of the multi-component system and optimizing the resulting reduced-state Markov decision process via a linear programming approach. This methodology is highly scalable and capable of solving large problems that cannot be approached with the previously existing solution procedures.
... Perceptual engineering is an emerging discipline that is reshaping product design by delving deeply into the complex relationship between human emotions and inanimate objects. Using a quantitative approach, it addresses the emotional needs of discerning consumers, reshaping the contours of product design and development [12]. Emotional design encapsulates customers' psychological responses, intricately woven into the nuances of product design. ...
This study aims to integrate data-driven methodologies with user perception to establish a robust design paradigm. The study consists of five steps: (1) theoretical research—a review of the subject background and applications of Kansei engineering and gray relational analysis (GRA); (2) algorithmic framework research—the discussion delves into the intricate realm of Kansei engineering theory, accompanied by a thorough elucidation of the gray relational analysis (GRA) algorithmic framework, a crucial component in constructing a fuzzy logic model for product image modeling; (3) Kansei data collection—18 groups of perceptual words and six classic samples are selected, and the electric recliner chair samples are scored by the Kansei words; (4) Kansei data analysis—morphological analysis categorizes the electric recliner chair into four variables. followed by the ranking and key consideration areas of each area; (5) GRA fuzzy logic model verification—the GRA fuzzy logic model performs simple–complex (S-C) imagery output on 3D models of three modeling instances. By calculating the RMSE value of the seat image modeling design GRA fuzzy logic model, it is proven that the seat image modeling design GRA fuzzy logic model performs well in predicting S-C imagery. The subsequent experimental study results also show that the GRA fuzzy logic model consistently produces lower root mean square error (RMSE) values. These results indicate the efficacy of the GRA fuzzy logic approach in forecasting the visual representation of the electric recliner chair shape’s 3D model design. In summary, this research underscores the practical utility of the GRA model, harmoniously merged with perceptual engineering, in the realm of image recognition for product design. This synergy could fuel the extensive exploration of product design, examining perceptual engineering nuances in product modeling design.
... An et al. studied the collaborative strategy of dynamic maintenance and production for serial-parallel systems, which increased economic benefits, saved production costs, and improved the efficiency of electricity utilization [26]. Ghaleb et al. aimed to solve the joint optimization problem of production scheduling and CBM planning in a flexible job shop with real-time dynamics, e.g., new job arrivals and machine breakdowns [27]. Condition information was used to estimate the machine deterioration and determine the maintenance and rescheduling activities. ...
... Moreover, when the number of shocks is difficult to measure, it may not be appropriate as an abort criterion. With the rapid advancement of condition inspection technology, operators can effectively control operation risks by using the health condition information obtained from continuous or periodic inspections [19,20]. Levitin et al. [21] extended existing mission abort models by jointly optimizing inspection scheduling and mission abort policies for systems with defective states. ...
... Assumption 1 requires constant nominal values and maximum deviations during the entire planning horizon. The assumption is commonly adopted in maintenance optimization Ye 2018, uit het Broek et al. 2020) and mild when the degradation process has stationary increments under a fixed production rate, which is reasonable for degradation resulting from wear, e.g., filters in a waterworks and car tires (Sun et al. 2020). When the degradation process is nonlinear, taking the logarithm of the degradation data often yields a linear path, e.g., rolling bearings studied in Elwany et al. (2011). ...
We study the robust production and maintenance control for a production system subject to degradation. A periodic maintenance scheme is considered, and the system production rate can be dynamically adjusted before maintenance, serving as a proactive way of degradation management. Optimal control of the degradation rate aims to strike a balance between the risk of failure and the production profit. We first consider the scenario in which the degradation rate increases linearly with the production rate. Different from the existing literature that posits a parametric stochastic degradation process, we suppose that the degradation increment during a period lies in an uncertainty set, and our objective is to minimize the maintenance cost in the worst case. The resulting model is a robust mixed‐integer linear program. We derive its robust counterpart and establish structural properties of the optimal production plan. These properties are then used for real‐time condition‐based control of the production rate through reoptimization. The model is further generalized to the nonlinear production‐degradation relation. Based on a real production‐degradation dataset from an extruder system, we conduct comprehensive numerical experiments to illustrate the application of the model. Numerical results show that our model significantly outperforms existing methods in terms of the mean and variance of cost rate when degradation model misspecification is presented.
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... With the development of inspection technology, condition-based maintenance (CBM) has received increasing research attention. There is no doubt that CBM is effective in managing system degradation and improving system availability (Sun et al., 2020). Since CBM makes maintenance decisions based on the health condition of the system , it outperforms the periodic replacement policy and the age-based maintenance policy (Qiu et al., 2017;Xiao et al., 2021). ...
... Yin et al. (2017) proposed the distributed modeling and simulation method of an equipment support system based on multiple agents. Sun et al., (2020aSun et al., ( , 2020b) studied how to manage component degradation by balancing degradation through reallocation and maintenance. Kovalenko et al. (2019) integrated new machines into the manufacturing system based on the flexible control strategy of the manufacturing resource agents, which helps to process manufacturing requirements caused by equipment performance degradation. ...
The simultaneous regulation of production efficiency and equipment maintenance in intelligent production lines poses a challenging problem. Existing approaches addressing this issue often separate the regulation of equipment maintenance and load balancing, lacking dynamic indicators to characterize the operational status and equipment workload. Inspired by the cardiac electrical activity recorded from human electrocardiogram (ECG), the electric drive signal of the equipment is proposed as an analogous measure to monitor equipment performance and workload variations. Thereby, the implementation mechanism and working characteristics of equipment ECG (EECG) are put forward for reconfigurable mixed-model assembly. Moreover, the monitoring of equipment performance based on deep learning is explored, leveraging the EECG features combined with multi-source heterogeneous data. The variations of equipment workload are tracked through the construction of a population difference hash analysis of the ECG data flow, along with the characterization of equipment power through electric signals. Additionally, an EECG-driven synchronous mapping approach is proposed to address steady disturbance, considering both workload imbalance and the degeneracy effect of the equipment. The reconfigurability of the intelligent production line enables the proposed mechanism of similarity matching of EECG features through the reconfiguration of the software manufacturing system and hardware physical equipment. Finally, the EECG-based solution is validated on a laboratory-level prototype platform, demonstrating that the robust running of the assembly process can be ensured even in the presence of internal and external disturbances.
... Fuel cost also considers travel distances (TD) and vehicle efficiency (VE) (Moon et al. 2018 Here, CE means charging efficiency of EV. Overall operating cost (OPC) can be calculated as seen below: Battery and tire replacement is dependent on maintenance, so this replacement cost is included in MC (Sun et al. 2020). Equation 7.7 is used to calculate the MC: ...
Electric vehicles (EVs) can be seen as a significant technology that can help to create a more resilient and sustainable supply chain by reducing greenhouse gas (GHG) emissions and air pollution. With the recent focus on green sustainability, EVs have grown in popularity in many counties such as the United States, Germany, and China because of their zero emission. Driven by the incentives of electrified power trains, many companies are shifting from internal combustion engine vehicles (ICEVs) to EVs. Using the economic performance analysis, this research seeks to investigate the feasibility of adopting EVs into company logistics along with the identification of the key elements that influence its feasibility. A comparative study based on the economic aspects has been conducted between the ICEV, hybrid electric vehicle (HEV), and EV. This chapter implies that both EV and HEV outperform the traditional ICEV in terms of economic performance and they also have enormous potential as sustainable and resilient mobility solutions in a supply chain.KeywordsElectric vehicleSustainabilityTransportationSupply chain
... Battery and tire replacement is dependent on maintenance, so this replacement cost is included in MC (Sun et al. 2020). Equation 7.7 is used to calculate the MC: ...
Sustainability and resilience are both fundamental to ensure the long-term survival of supply chains. Considering that synergies and trade-offs exist, ensuring that their implementation results in positive and non-detrimental applications is fundamental. Having an adequate performance measurement framework, able to include all relevant aspects of sustainability and resilience, in a comprehensive yet concise way, exploiting synergies and links between the topics, is of paramount importance. A literature review allowed retrieving that there is a lack of such a framework as well as the lack of operativity and adaptability to the changing needs of firms. Building on this, a new performance measurement framework was built to simultaneously include sustainability and resilience indicators, integrating the two concepts via the capabilities and the performances. Besides, it was designed to be operative and to be scalable, adapting to different firms and needs. Thus, it can be adapted to the needs of small and medium enterprises or firms at the beginning of their measurement journey. The framework was validated with three supply chain case studies that confirmed its usefulness, comprehensiveness, and ease of use. These results contribute to the discussion about sustainability and resilience performance measurement and provide guidance for practitioners and regulators.KeywordsSupply chainSustainabilityResiliencePerformance measurement systemIndicatorsCapabilitiesEmpirical evidenceScalabilitySmall and medium enterprisesNew adopters
... The maintenance actions considered in this work include corrective maintenance (CM) (Basciftci et al., 2020;Sun et al., 2020) and PM. CM refers to restoring the component to its required performance once it fails. ...
... where ( ) is the joint log-likelihood function of 0∶ and 0,1∶ , [ |̂− 1 ] represents the conditional expectation of ( ), and [⋅] represents the expectation operator. The EM algorithm divides the calculations of Equation (12) into two steps: the expectation step (E-step) for calculating the expectation of ( ) and the maximization step (M-step) for searching the maximum value of [ |̂− 1 ]. As the EM algorithm for the proposed model in a linear system is similar to that in a nonlinear system but simpler, we will only give the important results here. ...
... Moreover, when the number of shocks is difficult to measure, it may not be appropriate as an abort criterion. With the rapid advancement of condition inspection technology, operators can effectively control operation risks by using the health condition information obtained from continuous or periodic inspections [19,20]. Levitin et al. [21] extended existing mission abort models by jointly optimizing inspection scheduling and mission abort policies for systems with defective states. ...
The mission abort is an effective action to avoid catastrophic accidents and enhance the survivability of safety-critical systems such as unmanned aerial vehicle swarms and submarine swarms. Existing researches mainly focus on the abort policy of single equipment and lack consideration for the swarm. Furthermore, the mission abort of equipment in the swarm has operation dependence, and the state space of a swarm is far larger than that of single equipment, which leads to a curse of dimensionality. To solve the above problems, a dynamic mission abort policy is developed for the swarm to specify mission abort policies for both the equipment level and swarm level. First, considering both the degradation level, operating state of equipment, and time in the mission, a dynamic mission abort policy is proposed for the swarm with changing states. Next, the mission abort problem is formulated as a Markov decision process to maximize the expected cumulative reward of the swarm. Then, to overcome the curse of dimensionality, a deep reinforcement learning approach is tailored to optimize the proposed policy, where an action mask method is adopted to filter out infeasible actions. Finally, a case study is presented to illustrate the superiority of the proposed approach.
The reliability evaluation of multi‐component systems has attracted increasing concern in academic and industrial circles. However, the research maintenance optimization for multi‐component systems is still underexplored due to the curse of dimensionality. This paper makes a novel contribution to the existing literature by proposing a condition‐based maintenance (CBM) policy for multi‐component systems with joint consideration of stochastic dependence and quality loss. The system is composed of critical and auxiliary components. The deterioration process of the critical component can be accelerated when the auxiliary one degrades to a certain state. Based on the states of the components, the operation cost of the system owing to quality loss is analyzed, and the operation cost is used as the threshold for the preventive maintenance (PM) decision. Semi‐regenerative technology is used to model the evolution process of the system, and the long‐run average cost is calculated. The optimal inspection period and PM threshold are derived by minimizing the long‐run average cost, and the stationary distribution of the system state under the optimal long‐run average cost is derived with a proposed algorithm. Sensitivity analysis is conducted to reveal the most sensitive parameter. Finally, an illustrative example is presented, and a comparison experiment with other maintenance policies is conducted to demonstrate the effectiveness of the proposed policy.
Many physical systems contain a series of positions with different degradation characteristics and a series of functionally interchangeable components, in which the component reassignment (CR) is usually used to balance the degradation characteristics by reassigning the workloads of components. Although many research has been conducted on CR‐related problems, there is no existing research on periodic CR policy under unequal assignment, in which the number of components and positions are unequal. This paper proposes a new type of CR‐based preventive maintenance policy, namely, the periodic multiple CRs (PMCRs) policy. The PMCRs policy implements periodic CRs before the system replacement, minimal repairs for sudden failed components, and unequal assignment between positions and components. An optimization model is established to find the optimal number of CRs, the optimal interval for adjacent CRs, and the optimal assignment for CRs with the objective of minimizing the expected annual system maintenance cost. Furthermore, the upper bound and the lower bound on the optimal number of CRs are derived. Finally, based on the genetic algorithm‐based matheuristic method, numerical examples show that the proposed PMCRs policy can be used as an effective tool to improve the system's performance.
Maintenance planning of two‐component systems has been extensively studied in recent decades. In the literature, most studies assume that the failure cause of a two‐component system is self‐announcing. In some real applications, the failure cause is masked, and a diagnosis with professional equipment is needed to reveal the failed component. This study investigates a preventive replacement policy of a two‐component series system considering masked causes of failure. When an unexpected failure occurs, we can carry out a diagnosis to reveal the failed component and replace it subsequently, or we can directly replace the whole system without diagnosis. Meanwhile, when we carry out a preventive replacement on a component, the other component can be replaced opportunistically. We formulate the problem as a semi‐Markov decision process, and prove the existence of the stationary optimal policy. The optimal preventive replacement age thresholds for each component and the corresponding optimal maintenance actions upon each failure are jointly obtained to minimize the long‐term average maintenance cost per time unit. A comprehensive numerical study is provided to illustrate the effectiveness of our proposed model.
Condition‐based maintenance has been studied for managing the degradation of components in a system. However, components in different positions may undergo different workload, leading to imbalanced components degradation. Component reallocation is an effective method to balance the degradation of components in different positions with different degradation rates. Thus, this paper investigates the joint optimization of condition‐based maintenance and condition‐based reallocation for a non‐repairable system with multiple identical and functionally‐exchangeable components that undergo different continuous degradation processes due to different workload. We model this problem through Markov decision process, which is solved by a dynamic programming algorithm, and the objective is to provide the optimal maintenance and reallocation actions exactly for each system state, that is, the joint optimal policy, to minimize the discounted long‐run total cost. Especially, our joint policy is on component‐level and proved to be optimal. Finally, the numerical analysis shows the structural insights and effectiveness of the proposed joint policy, for which the sensitivity analysis on the degradation parameters, setup cost, reallocation cost, and downtime cost is performed. We also propose a new reallocation strategy and show the results and computation time for systems with different scales, which indicates that our model can handle systems with reasonable size.
Production scheduling and machine maintenance are two inseparable operational issues in multistage production systems. Previous studies attempted to deal with this issue by simplifying this problem due to the degradation uncertainties of the machines, ignoring the substantial interactions between these two tasks and leading to less efficiency of the entire production system. In this study, we fill the gap and formulate the joint optimization problem with more emphasis on the interaction between job scheduling and maintenance for a series-parallel multistage production system. Specifically, a mixed-effect degradation model is proposed to leverage the underlying interaction between job scheduling and machine maintenance. To efficiently solve this joint problem, several properties from this formulation have been derived. A two-phase method considering condition-based information, with a proactive algorithm for local intensification and a condition-based workload reallocation strategy & maintenance strategy, is then developed to address the uncertainties from the machine degradation status. A numerical study is finally borrowed to demonstrate the higher production efficiency achieved by applying the proposed method, compared with other benchmarks.
Note to Practitioners
—This study is motivated by a practical scenario where both job allocation and maintenance need to be determined simultaneously in the multistage production system by the operators to achieve time and cost efficiency. We focus on developing a new scheme that job scheduling and machine maintenance are able to be conducted simultaneously. Two issues are noteworthy to better implement this scheme. First, for characterizing the interaction between scheduling and maintenance, the data collected in real-time can provide a sufficient basis for the degradation path, and the production parameters can be acquired from real practice. Second, this scheme can be offered to help decision-making by a two-phase solution framework given the condition-based information during the production process. Specifically, an appropriate job allocation planning can be obtained offline in the first phase of the proposed two-phase solution framework under a limited computing resource. Meanwhile, a condition-based adjustment strategy in the second phase can update the solution based on the in-situ condition information collected from the data platform to achieve higher production efficiency.
Consider a system consisting of multistate components that perform the same function, and each component occupies a location in the system. The deterioration processes of components differ due to different workloads, usage rates, or environmental stresses that are associated with the locations. This article proposes a condition-based maintenance policy, in which the component reallocation (CR) with distinct assignments of components to locations and the preventive replacement of system are dynamically implemented based on the system state. A Markov decision process (MDP) is formulated to optimize the proposed condition-based multi-CR maintenance policy by determining the actions for each system state that minimize the expected long-run system maintenance cost. In the current studies on the MDP for maintenance optimization, the actions mainly include component replacement, imperfect repair, and system replacement. In this article, including CRs of distinct assignments as actions and considering multiple times of CRs increase the action space of the MDP significantly. An enumeration-based value iteration algorithm and a genetic-algorithm-based value iteration algorithm are proposed. Numerical experiments on
k
-out-of-
n
:G systems and Monte Carlo simulation tests show the effectiveness of CRs on reducing the system maintenance cost and extending system lifetime and provide structural insights on the optimal maintenance policy.
Capacity degradation of lithium-ion batteries largely determines the cost, performance and environmental impact of various products such as renewable energy production systems, portable electronics, and electric vehicles. Degradation
assessment is thus of great importance for prognostic and health management of batteries, which ensures a stable production and operation. There are typically two leading sources contributing to the degradation of a lithium-ion battery, namely, cycling aging during charge/discharge cycles and calendar aging during idle
states. However, most existing studies on degradation assessment either only consider a single source or ignore the coupling of these two sources, which makes the evaluation inefficient. A common observation in practice is that a battery tends to degrade faster when it experiences charge/discharge cycles continuously for
a longer time. To capture this feature, this paper introduces the concept of the cumulative uninterrupted cycling duration (CUCD), which is defined as the consecutive operation duration since a battery ends the idle state. The CUCD can also help to model the coupling between the calendar and cycling aging. This
paper then proposes to model the drift rate of cycling aging as a function of the CUCD and the functional form is determined with the monotonic spline. We estimate the model parameters by maximizing the likelihood function. Hypothesis testings toward the significance of the coupling between two aging sources and the monotonicity of the drift rate function under cycling aging are also provided. The effectiveness and the superiority of the model are validated using numerical and real case studies.
This paper proposes an alternative approach to the analysis and modeling of the reliability of degradation systems with rare failures. We assume that the degradation measure of the multiphase system is described by the Wiener process and instantaneous failure occurs when the process reaches a given level. Let us consider a model of a multiphase system, where the degree of degradation is described by a Wiener process and an instantaneous failure occurs when the process reaches a given level. The failure threshold value can be either a constant or a random variable that takes values on the positive semiaxis or on the fixed interval. Evaluation of the failure probability and other characteristics of the system is crucial for optimal control, however, for complex multi-phase systems with multiple failure thresholds, it is often impossible to find an analytical solution.For the process of regenerative degradation, instead of the standard Monte-Carlo procedure, it is proposed to use an accelerated version of the construction of regeneration cycles. The splitting of the Wiener process trajectory occurs at the moment of transition to the next phase of the degradation. This approach is useful when failures are rare.KeywordsDegradation processWiener processFailure probabilityReliability analysisLifetimeSpeed-up simulationRegenerative simulationSplitting method
This study aims to combine deep learning technology and user perception to propose an efficient design method that can meet the perceptual needs of users and enhance the competitiveness of products in the market. Firstly, the application development of sensory engineering and the research on sensory engineering product design by related technologies are discussed, and the background is provided. Secondly, the Kansei Engineering theory and the algorithmic process of the convolutional neural network (CNN) model are discussed, and theoretical and technical support is provided. A perceptual evaluation system is established for product design based on the CNN model. Finally, taking a picture of the electronic scale as an example, the testing effect of the CNN model in the system is analyzed. The relationship between product design modeling and sensory engineering is explored. The results show that the CNN model improves the “logical depth” of perceptual information of product design and gradually increases the abstraction degree of image information representation. There is a correlation between the user perception impression of electronic weighing scales of different shapes and the design effect of product design shapes. In conclusion, the CNN model and perceptual engineering have in-depth application significance in the image recognition of product design and the perceptual combination of product design modeling. Combined with the CNN model of perceptual engineering, product design is studied. From the perspective of product modeling design, perceptual engineering has been deeply explored and analyzed. In addition, the product perception based on the CNN model can accurately analyze the correlation between product design elements and perceptual engineering and reflect the rationality of the conclusion.
Most classical accelerated degradation test (ADT) planning models implicitly overlook the errors when measuring the degradation levels of the test units. However, the sensor measurement errors are inevitable and the magnitude of the errors may have a trend to increase over time due to sensor degradation. As a consequence improperly overlooking the sensor degradation in ADT planning could result in a test plan with unsatisfactory performance. This article addresses this issue by proposing a sequential ADT planning model that factors in sensor degradation. The system degradation level is periodically measured, based on which we dynamically adjust the stress level during ADT. We adopt a Bayesian framework that periodically updates the posterior distribution of model parameters considering the sensor degradation. An approximate Bayesian computation algorithm is developed to circumvent the difficulty of directly evaluating the complicated likelihood function in our problem. Numerical studies on a gas turbine reveal that our sequential model outperforms several traditional ADT designs that overlook the sensor degradation.
In many engineering systems, aside from the main component fulfilling the essential functions, a number of auxiliary components are configured to protect the main component and improve the reliability of the system. In actual operation, the failure or state change of the auxiliary components may affect the reliability both the main component and the remaining operational auxiliary components. However, the structure and dependence between the auxiliary components has been ignored in the existing studies. To fill this gap, we consider a system with a main component and a protective auxiliary subsystem. The latter is a load-sharing
-out-of-
system, that is, there is dependence between the auxiliary components. For such a system, an opportunistic inspection and preventive maintenance strategy is proposed. Then, we derive the system reliability using the Laplace transforms and the matrix method. The long-run average cost of the system is then derived, based on which the optimal maintenance problem is formulated and solved by an enumeration method. A numerical example, together with sensitivity studies of some model parameters, shows how the evolution of the parameters influences the optimal maintenance strategy. Finally, the model is extended by introducing periodic inspection and preventive maintenance strategy for main component, and the two strategies are compared.
In small radius curves of railway lines, the inner side and outer side rails are connected in series. The side friction taken by the outer side rail is much greater than that of the inner one. Hence, the degradation processes of them are unbalanced and component reallocation actions are implemented to prolong the lifetime of the system in the practical engineering. Motivated the aforementioned operating and maintenance processes, this paper introduces a condition-based inspection, component reallocation and replacement models for two-component interchangeable series system. The degradation processes of two components are described by Gamma processes, and their states are identified by periodic inspections. When the maximum degradation level of two components exceeds the given control limits, corrective replacement, preventive replacement and inspection interval half strategies are taken. Component reallocation is performed when the degradation level of the component with higher degradation rate exceeds the threshold. Taking the long-term average cost per unit time as the objective function, the inspection interval and reallocation thresholds are jointly optimized. Numerical examples are provided to show the effectiveness of the joint of component reallocation and inspection interval half.
This paper proposes a new aperiodic preventive maintenance policy, which involves multiple reassignments of components in a system. Considering a multi-component system, the components deteriorate according to heterogeneous stochastic processes because the components undertake different workloads and environmental stresses. Component reassignment (CR) is an action that reassigns the components to positions during system operation in order to improve overall system performance. The assignments of multiple CRs are mutually dependent decisions, and the execution times to conduct these CRs are also decision variables. All these decisions synthetically impact the system maintenance cost. The reliability functions and failure rates of components under the multiple CRs as well as the side effect of CR action on reducing the component reliability are formulated, using statistical virtual ages that establish links between decisions of consecutive CRs. To optimize the multi-CR based maintenance policy, a binary mixed integer nonlinear programming model is established with the objective of minimizing expected annual system maintenance cost that arises from the CRs, system replacement, and minimal repairs for emergency component failures. The optimal number of CRs is analytically shown to be finite and can be obtained by solving a series of optimization models. This paper proposes two matheuristic approaches, an integrative construction approach and a sequential construction approach, to solve the models. Numerical experiments show the application of the proposed model and solution approaches in maintenance policy scheduling.
This paper proposes two condition-based opportunistic maintenance policies with two-phase inspections for continuously degraded systems with real-time monitoring and periodic inspections, respectively. The degradation of the components and the system is modeled by a Gamma process. Existing literature finds the optimal maintenance strategies by monitoring the performance of all components in a multi-component system. However, it maybe unrealistic and costly to perform inspections on all components for certain systems. Hence, this study considers a two-phase inspection method, that is, the system-level inspection is conducted first, and then the decision for component-level inspection is made based on the system performance. Maintenance is performed to the component when its degradation reaches the preventive maintenance (PM) threshold or the corrective maintenance (CM) threshold at a component-level inspection. Whenever a maintenance action is implemented, the other components whose degradation exceeds an opportunistic maintenance (OM) threshold will be repaired. Then the long-run expected cost for two-component systems and multi-component systems are derived based on the semi-regenerative properties and simulation method. The combination of the system-level inspection interval, OM, PM and CM thresholds is determined to minimize the long-run expected cost. Finally, this study applies the proposed maintenance policies to the battery pack systems in electrical vehicles.
In degradation tests, the test units are usually divided into several groups, with each group tested simultaneously in a test rig. Each rig constitutes a rig-layer block from the perspective of design of experiments. Within each rig, the test units measured at the same time further form a gauge-layer block. Due to the uncontrollable factors among test rigs and the common errors incurred for each measurement, the degradation measurements of the test units may differ among various blocks. On the other hand, the degradation should be more homogeneous within a block. Motivated by an application of emerging contaminants (ECs), this study proposes a multivariate statistical model to account for the two-layer block effects in destructive degradation tests. A multivariate Wiener process is first used to model the correlation among different dimensions of degradation. The rig-layer block effect is modeled by a one-dimensional frailty motivated by the degradation physics, while the gauge-layer block effect at each measurement epoch is captured by a common additive measurement error. We develop an Expectation-Maximization (EM) algorithm to obtain the point estimates of the model parameters and construct confidence intervals for the parameters. A procedure is proposed to test significance of the block effects in the degradation data. Through a case study on an EC degradation dataset, we show the existence of the two-layer block effects from the test. By making use of the proposed model, decision makers can readily make risk assessment of each contaminant and determine the minimal water treatment time for removal of the contaminants.
Problem definition: Many production systems deteriorate over time as a result of load and stress caused by production. The deterioration rate of these systems typically depends on the production rate, implying that the equipment’s deterioration rate can be controlled by adjusting the production rate. We introduce the use of condition monitoring to dynamically adjust the production rate in order to minimize maintenance costs and maximize production revenues. We study a single-unit system for which the next maintenance action is scheduled upfront. Academic/Practical Relevance: Condition-based maintenance decisions are frequently seen in the literature. However, in many real-life systems, maintenance planning has limited flexibility and cannot be done last minute. As an alternative, we are the first to propose using condition information to optimize the production rate, which is a more flexible short-term decision. Methodology: We derive structural optimality results from the analysis of deterministic deterioration processes. A Markov decision process formulation of the problem is used to obtain numerical results for stochastic deterioration processes. Results: The structure of the optimal policy strongly depends on the (convex or concave) relation between the production rate and the corresponding deterioration rate. Condition-based production rate decisions result in significant cost savings (by up to 50%), achieved by better balancing the failure risk and production output. For several systems, a win-win scenario is observed, with both reduced failure risk and increased expected total production. Furthermore, condition-based production rates increase robustness and lead to more stable profits and production output. Managerial Implications: Using condition information to dynamically adjust production rates provides opportunities to improve the operational performance of systems with production-dependent deterioration.
A modeling and optimization framework for the maintenance of systems under epistemic uncertainty is presented in this paper. The component degradation processes, the condition-based preventive maintenance and the corrective maintenance are described through piecewise-deterministic Markov processes in consideration of degradation dependency among degradation processes. Epistemic uncertainty associated with component degradation processes, is treated by considering interval-valued parameters. This leads to the formulation of a multi-objective optimization problem whose objectives are the lower and upper bounds of the expected maintenance cost, and whose decision variables are the periods of inspections and the thresholds for preventive maintenance. A solution method to derive the optimal maintenance policy is proposed by combining finite-volume scheme for calculation, differential evolution and non-dominated sorting differential evolution for optimization. An industrial case study is presented to illustrate the proposed methodology.
This paper proposes an integrated framework for wind farm maintenance that combines i) predictive analytics methodology that uses real-time sensor data to predict future degradation and remaining lifetime of wind turbines, with ii) a novel optimization model that transforms these predictions into profit-optimal maintenance and operational decisions for wind farms. To date, most applications of predictive analytics focus on single turbine systems. In contrast, this paper provides a seamless integration of the predictive analytics with decision making for a fleet of wind turbines. Operational decisions identify the dispatch profiles. Maintenance decisions consider the tradeoff between sensor-driven optimal maintenance schedule, and the significant cost reductions arising from grouping the wind turbine maintenances together - a concept called opportunistic maintenance. We focus on two types of wind turbines. For the operational wind turbines, we find an optimal fleet-level condition based maintenance (CBM) schedule driven by the sensor data. For the failed wind turbines, we identify the optimal time to conduct corrective maintenance to start producing electricity. The economic and stochastic dependence between operations and maintenance decisions are also considered. Experiments conducted on i) a 100-turbine wind farm case, and ii) a 200- turbine multiple wind farms case demonstrate the advantages of our proposal over traditional policies.
Complex systems often consist of multiple units that are required to work together in parallel to satisfy a specific engineering objective. As an example, in manufacturing processes, several identical machines may need to operate together to simultaneously fabricate the same products in order to meet the high production demand. This parallel configuration is often designed with some level of redundancy to compensate for unexpected events. In this way, when only a small portion of units fail to operate due to either unexpected machine downtime or scheduled maintenance, the remaining units can still achieve the engineering objective by increasing their workloads up to the designed capacities. However, the workload of a unit apparently impacts the unit's degradation rate as well as its failure time. Specifically, this paper considers the case that a higher workload assignment accelerates the unit's degradation and vice versa. Based on this assumption, we develop a method to actively control the degradation as well as the predicted failure time of each unit by dynamically adjusting its workloads. Our goal is to prevent the overlap of unit failures within a certain time period through taking advantage of the natural redundancy of the parallel structure, which may potentially lead to a better utilization of maintenance resources as well as a consistently ensured system throughput. A numerical study is used to evaluate the performance of the proposed method under different scenarios.
Traditional maintenance decisions in the framework of condition-based maintenance applied to multi-component systems are performed either at the system level or at the component level. These decisions however cannot always assure the best maintenance performance. To remedy this drawback, the present paper introduces a multi-level decision-making approach that combines maintenance decisions at the system level and the component level. The effectiveness of such an approach is investigated through an -component deteriorating system with a -out-of- :F structure, and economic dependence. In fact, based on the degradation and failure model of the considered -out-of- :F system, two new opportunistic predictive maintenance strategies with different types of maintenance decision-making are proposed. In the first one, the decisions rely only on the remaining useful lifetime of the components; while in the second one, they are based on both the remaining useful lifetimes of the system and that of its components. The maintenance cost models of these strategies are developed on the basis of semi-regenerative theory, optimized, and then compared with each other. The comparison results show that the multi-level decision-making approach allows us to more effectively avoid inopportune interventions, to better take into account the interactions among components, and hence to provide more flexible and profitable predictive maintenance strategies for multi-component systems.
Motivated by high oil prices, several large fleet companies initiated future plans to hybridize their fleets to establish immunity of their optimized business models against severe oil price fluctuations, and adhere to increasing awareness of environmentally friendly solutions. The hybridization projects increased maintenance costs especially for costly and degradable components such as Li-ion batteries. This paper introduces a degradation-based resource allocation policy to optimally utilize batteries on fleet level. The policy, denoted as degradation-based swapping optimization, incorporates optimal implementation of swapping and substitution actions throughout a plan of finite-time horizon to minimize projected maintenance costs. The swapping action refers to the interchange in the placement of two batteries within a fleet. The substitution action refers to the replacement of degraded batteries with new ones. The policy takes advantage of the different degradation rates of the state of health of the batteries because of different loading conditions, achieving optimal placement at different time intervals throughout the plan horizon. A mathematical model for the policy is provided. The optimization of the generated model is studied through several algorithms. Numerical results for sample problems are obtained to illustrate the capability of the proposed policy in establishing substantial savings in the projected maintenance costs compared to other policies.
This paper deals with a continuously deteriorating system which is inspected at random times sequentially chosen by help of a maintenance scheduling function. The deterioration is modeled by a Gamma process. The system is considered as failed if its condition jumps above a pre-set failure level. Two types of replacement can take place at each inspection date depending on whether the current system state is above a pre-set critical threshold but not failed or in the failed state. This paper is focused on the development of a new probabilistic method based on the semi-regenerative property of the evolution process in order to calculate the long-time expected cost per unit of time. We use a recent result generalizing the well-known theorem usually used which says that the cost criterion is equal to the ratio of the expected cost on a renewal cycle over the expected cycle duration. Numerical experiments show that there exists a set of parameters (the critical threshold and the parameters of the maintenance scheduling function) which lead to a minimal cost.
We introduce a new framework for the global optimization of computationally expensive multimodal functions when derivatives are unavailable. The proposed Stochastic Response Surface (SRS) Method iteratively utilizes a response surface model to approximate the expensive function and identifies a promising point for function evaluation from a set of randomly generated points, called candidate points. Assuming some mild technical conditions, SRS converges to the global minimum in a probabilistic sense. We also propose Metric SRS (MSRS), which is a special case of SRS where the function evaluation point in each iteration is chosen to be the best candidate point according to two criteria: the estimated function value obtained from the response surface model, and the minimum distance from previously evaluated points. We develop a global optimization version and a multistart local optimization version of MSRS. In the numerical experiments, we used a radial basis function (RBF) model for MSRS and the resulting algorithms, Global MSRBF and Multistart Local MSRBF, were compared to 6 alternative global optimization methods, including a multistart derivative-based local optimization method. Multiple trials of all algorithms were compared on 17 multimodal test problems and on a 12-dimensional groundwater bioremediation application involving partial differential equations. The results indicate that Multistart Local MSRBF is the best on most of the higher dimensional problems, including the groundwater problem. It is also at least as good as the other algorithms on most of the lower dimensional problems. Global MSRBF is competitive with the other alternatives on most of the lower dimensional test problems and also on the groundwater problem. These results suggest that MSRBF is a promising approach for the global optimization of expensive functions.
: This paper contains a new analysis for the Generalized Pattern Search (GPS) methods of Torczon and Lewis and Torczon. The two novel aspects are that the proofs are much shorter and simpler, and they use weaker dierentiability assumptions. Specically, under very mild conditions, the method nds an interesting limit point even if the objective function is not continuous and is even extended valued. If the objective is Lipschitz near the limit point, then appropriate directional derivatives of the objective are nonnegative. If the objective is strictly dierentiable at the limit point, then the gradient exists and the limit point satises the KKT conditions. Key words: Pattern search algorithm, linearly constrained optimization, surrogate -based optimization, nonsmooth optimization, derivative-free convergence analysis. Acknowledgments: Work of the rst author was supported by NSERC (Natural Sciences and Engineering Research Council) fellowship PDF-207432-1998 during a pos...
The mission abort is an effective action to reduce
the risk of casualties and enhance the survivability of missionbased
systems such as aircrafts, submarines, and unmanned
aerial vehicles (UAVs). A main task in real operations is to
strive for balance between the mission reliability and the system
survivability via elaborate mission abort plans. In this study,
we design the optimal mission abort policies based on the
information of early-warning signals, which indicates the possible
forthcoming fatal malfunction. Depending on the acquisition time
of such information, the operator may immediately abort the
mission, or ignore the information and continue the task. Within
the framework of a constant mission duration, we carry out
an economic analysis for the above problem. The optimal abort
decision that minimizes the expected total economic loss is investigated.
We further extend the proposed model to the scenario of a
random mission duration and derive the corresponding optimal
abort decisions. A case study on a UAV executing power-grid
inspection missions is used to illustrate the applicability of the
abort policies.
We begin with congratulation to the authors on an insightful and interesting research on designs of reliability experiments. The authors were particularly efficient in charactering the difference between reliability experiments and classical experiments, i.e., the existence of non-normal response and censored observations. Although these characteristics complicate the analysis of reliability experiments, the authors have excellently shown that ideas from design of classical experiments could be borrowed to offer well-performed methods. As indicated in section 4 of Dr. Freeman’s article, incorporation of degradation data is useful in reliability analysis. In our discussion, we aim to amplify this point with a particular focus on degradation tests, an important class of reliability test to estimate lifetime distribution.
Motivated by the need to support effective asset management of infrastructure systems, this paper presents a novel reliability model for a load-sharing system where the operator can adjust component work load to balance system degradation. The operator-intervention effect, combined with other system complexities, makes modeling reliability interesting and challenging. We first develop cost modeling for a load-sharing system that has experienced operational service at the time of analysis. The system replacement process is modeled as a delayed renewal process for which the expected operational cost of the system is derived. A numerical algorithm is proposed to compute the cost, and the error bound is shown to be of order
. Next, we extend modeling to consider multiple heterogeneous systems located at different sites within the infrastructure network. Heterogeneities here refer to possible cross-site differences in the operating environments and the operators’ actions. When the heterogeneities are observable, we model as covariates; otherwise, we model as random effects. Statistical inference methods are developed for the proposed models. An example using real data from a water utility illustrates the logical model behavior given parameter choices as well as showing how analysis might inform asset management.
In a repairable system with multiple functionally interchangeable components, the components may work in different environmental or operational stresses associated with their positions, and thus, experience different failure rates and nonhomogeneous degradation processes. For such a system, the system lifetime can be improved by reassigning the components among the positions in the system after a period of operation. In this sense, the component reallocation (CR) is an option of preventive maintenances. This paper studies a new maintenance policy, which performs periodic preventive system replacements and periodic preventive CRs between system replacements as well as minimal repairs for emergency failures. An optimization model is established to determine the time and assignment for CRs and the time for system replacements with the objective of minimizing expected annual system maintenance cost. The model also justifies if the CR is economically beneficial and deserved to be implemented. The proposed CR-based maintenance policy is further specified for exponential component lifetime distributions and Rayleigh lifetime distributions, and analytical results are derived. Finally, numerical examples for general Weibull lifetime distributions are presented to demonstrate the efficiency and insights of CRs in maintenance.
During the useful life period of a costly system, it has been a common practice to perform imperfect preventive maintenances (PMs) with the purpose of failure prevention and useful life extension. Nevertheless, a system cannot be restored to an as-good-as-new state even though the imperfect PM actions are performed with a high frequency. This is known as the saturation effect and it is commonly overlooked in the existing literature. Motivated by a PM problem in a manufacturing company, this study proposes two PM models to capture the dynamics of the saturation effect. The first model divides the system deterioration into recoverable damage and irreversible intrinsic fatigue. The PMs are assumed to be effective only in healing the first type of damage. When the intrinsic fatigue for some complex systems cannot be well defined, we propose another model that generalizes the existing virtual age models by allowing the proportion of virtual age reduction to depend on the PM frequency. The long-run average costs of the two models are derived, and optimization of the cost models is investigated. The proposed PM models are then applied to two types of mechanical systems in the manufacturing company. The case study shows that ignorance of the saturation effect will make inferior maintenance policy that incurs substantial losses. The proposed models are also shown to be robust in the sense that the parameter estimation errors cannot significantly increase the system operational cost rate.
Condition-based maintenance (CBM) is proved to be effective in reducing the long-run operational cost for a system subject to degradation failure. Most existing research on CBM focuses on single-unit systems where the whole system is treated as a black box. However, a system usually consists of a number of components and each component has its failure behavior. When degradation of the components is observable, CBM can be applied to the component level to improve the maintenance efficiency. This paper aims to study the optimal inspection/replacement CBM strategy for a multi-unit system. Degradation of each component is assumed to follow a Wiener process and periodic inspection is considered. We cast the problem into a Markov decision framework and derive the optimal maintenance decisions that minimize the maintenance cost. To better illustrate the optimal maintenance strategy, we start from a 1-out-of-2: G system and show that the optimal maintenance policy is a two-dimensional control limit policy. The argument used in the 1-out-of-2: G system can be readily extended to general cases in a similar way. The value iteration algorithm is used to find the optimal control limits, and the optimal inspection interval is subsequently determined through a one-dimensional search. A numerical study and a comprehensive sensitivity analysis are provided to illustrate the optimal maintenance strategy.
Failure of a repairable system may be attributed to operators’ misuse or system deterioration. The misuse may further deteriorate the system under normal operating conditions. Motivated by a real-world data set that records the recurrence times of misuse-induced failures and the normal-operation failures, this study proposes a stochastic process model for recurrence data analysis, where one type of failures is affected by the other. A non-homogeneous Poisson process and a trend-renewal process are separately used as the baseline event process models for the misuse-induced failures and the normal-operation failures, respectively. These two models are then combined by treating the event count of misuse-induced failures as covariate of the event process of normal-operation failures. A Bayesian framework is developed for parameter estimation and dependence tests of the two failure modes. A simulation study and the recurrence data from a manufacturing system are used to demonstrate the proposed method.
Condition monitoring (CM) signals play a critical role in assessing the remaining useful life of in-service components. In this paper, an alternative view on modeling CM signals is proposed. This view draws its roots from multitask learning and is based on treating each CM signal as an individual task. Each task is then expressed as a convolution of a latent function drawn from a Gaussian process (GP), and the transfer of knowledge is achieved through sharing these latent functions between historical and in-service CM signals. Aside from being nonparametric, the flexible and individualistic approach in our model can account for heterogeneity in the data and automatically infer the commonalities between the new testing observations and CM signals in the historical dataset. The robustness and advantageous features of the proposed method are demonstrated through numerical studies and a case study with real-world data in the application to find the remaining useful life prediction of automotive lead-acid batteries. Technical details and additional numerical results are available in the supplementary materials.
It is well known that many factors can influence the rate at which a machine degrades. In this paper, we study a multi-state repairable system subject to continuous degradation and dynamically evolving regimes. The degradation rate of the system depends not only on the system states, but also on the regimes driven by the varying external environments. Movements between the system states are governed by continuous-time Markov processes but with different transition rate matrices due to different regimes, meanwhile the evolution of regime is also governed by a Markov process. Such a system can be developed by the Markov regime switching model. To derive the system performance such as the first passage time distribution, a Markov renewal process is introduced by giving its semi-Markov kernel. We also consider the system in the context of periodical inspections and maintenance and give the limiting average availability. Finally, some numerical examples are given to demonstrate and validate the proposed framework.
In reliability mathematics, optimisation of maintenance policy is derived based on reliability indexes such as the reliability or its derivatives (e.g., the cumulative failure intensity or the renewal function) and the associated cost information. The reliability indexes, also referred to as models in this paper, are normally estimated based on either failure data collected from the field or lab data. The uncertainty associated with them is sensitive to factors such as the sparsity of data. For a company that maintains a number of different systems, developing maintenance policies for each individual system separately and then allocating maintenance budget may not lead to optimal management of the model uncertainty and may lead to cost-ineffective decisions. To overcome this limitation, this paper uses the concept of risk aggregation. It integrates the uncertainty of model parameters in optimisation of maintenance policies and then collectively optimises maintenance policies for a set of different systems, using methods from portfolio theory. Numerical examples are given to illustrate the application of the proposed methods.
This paper is concerned with optimal maintenance decision making in the presence of model misspecification. Specifically, we are interested in the situation where the decision maker fears that a nominal Bayesian model may be miss-specified or unrealistic, and would like to find policies that work well even when the underlying model is flawed. To this end, we formulate a robust dynamic optimization model for condition-based maintenance in which the decision maker explicitly accounts for distrust in the nominal Bayesian model by solving a worst-case problem against a second agent, “nature,” who has the ability to alter the underlying model distributions in an adversarial manner. The primary focus of our analysis is on establishing structural properties and insights that hold in the face of model miss-specification. In particular, we prove (i) an explicit characterization of nature’s optimal response through an analysis of the robust dynamic programming equation, (ii) convexity results for both the robust value function and the optimal robust stopping region, (iii) a general robustness result for the preventive maintenance paradigm, and (iv) the optimality of a robust control limit policy for the important subclass of Bayesian change point detection problems. We illustrate our theoretical result on a real-world application from the mining industry.
Sheldon Ross's classic bestseller, Introduction to Probability Models, has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It introduces elementary probability theory and stochastic processes, and shows how probability theory can be applied fields such as engineering, computer science, management science, the physical and social sciences, and operations research. The hallmark features of this renowned text remain in this eleventh edition: superior writing style; excellent exercises and examples covering the wide breadth of coverage of probability topic; and real-world applications in engineering, science, business and economics. The 65% new chapter material includes coverage of finite capacity queues, insurance risk models, and Markov chains, as well as updated data..
Systems that require maintenance typically consist of multiple components. In case of economic dependencies, maintaining several of these components simultaneously can be more cost efficient than performing maintenance on each component separately, while in case of redundancy, postponing maintenance on some failed components is possible without reducing the availability of the system. Condition-based maintenance (CBM) is known as a cost-minimizing strategy in which the maintenance actions are based on the actual condition of the different components. No research has been performed yet on clustering CBM tasks for systems with both economic dependencies and redundancy. We develop a dynamic programming model to find the optimal maintenance strategy for such systems, and show numerically that it can indeed considerably outperform previously considered policies (failure-based, age-based, block replacement, and more restricted (opportunistic) CBM policies). Moreover, our numerical investigation provides insights into the optimal policy structure.
In this paper, we consider the replacement of a unit that is subject to a dominant failure mode. The unit is usually replaced by an age-based replacement policy, either when a preset age limit has been reached, or when failure occurs before this limit. However, the unit can also be replaced when it encounters a random production wait and its age has reached a certain threshold. Using such an opportunity for replacement can help to minimize system downtime. We formulate this joint age-based replacement limit and threshold optimization problem with the objective of minimizing the expected cost per unit time in the long run. A real-data example is presented to illustrate the applicability and effectiveness of our model.
We introduce a new framework for the global optimization of computationally expensive multimodal functions when derivatives are unavailable. The proposed Stochastic Response Surface (SRS) Method iteratively utilizes a response surface model to approximate the expensive function and identifies a promising point for function evaluation from a set of randomly generated points, called candidate points. Assuming some mild technical conditions, SRS converges to the global minimum in a probabilistic sense. We also propose Metric SRS (MSRS), which is a special case of SRS where the function evaluation point in each iteration is chosen to be the best candidate point according to two criteria: the estimated function value obtained from the response surface model, and the minimum distance from previously evaluated points. We develop a global optimization version and a multistart local optimization version of MSRS. In the numerical experiments, we used a radial basis function (RBF) model for MSRS and the resulting algorithms, Global MSRBF and Multistart Local MSRBF, were compared to 6 alternative global optimization methods, including a multistart derivative-based local optimization method. Multiple trials of all algorithms were compared on 17 multimodal test problems and on a 12-dimensional groundwater bioremediation application involving partial differential equations. The results indicate that Multistart Local MSRBF is the best on most of the higher dimensional problems, including the groundwater problem. It is also at least as good as the other algorithms on most of the lower dimensional problems. Global MSRBF is competitive with the other alternatives on most of the lower dimensional test problems and also on the groundwater problem. These results suggest that MSRBF is a promising approach for the global optimization of expensive functions.
Motivated by an industrial problem affecting a water utility, we develop a model for a load sharing system where an operator dispatches work load to components in a manner that manages their degradation. We assume degradation is the dominant failure type, and that the system will not be subject to sudden failure due to a shock. By deriving the time to degradation failure of the system, estimates of system probability of failure are generated, and optimal designs can be obtained to minimize the long run average cost of a future system. The model can be used to support asset maintenance and design decisions. Our model is developed under a common set of core assumptions. That is, the operator allocates work to balance the level of the degradation condition of all components to achieve system performance. A system is assumed to be replaced when the cumulative work load reaches some random threshold. We adopt cumulative work load as the measure of total usage because it represents the primary cause of component degradation. We model the cumulative work load of the system as a monotone increasing and stationary stochastic process. The cumulative work load to degradation failure of a component is assumed to be inverse Gaussian distributed. An example, informed by an industry problem, is presented to illustrate the application of the model under different operating scenarios.
Power intermittency and maintenance cost are the major challenges in harvesting wind energy. This paper proposes a multicriteria optimization model to design and operate a wind-based distributed generation (DG) system. The goal is to determine the equipment sizing, siting, and maintenance schedules so that the system cost is minimized while the turbine reliability is maximized. System cost comprises initial capital, operations, maintenance, downtime losses, and environmental penalty. The study makes an early attempt to incorporate the maintenance policy of generating units into the planning model. The moment method and the central limit theorem are used to characterize the power intermittency and the load uncertainty. A genetic algorithm is developed to search the nondominant solution set for the equipment siting, sizing, and maintenance intervals. The proposed model is demonstrated on the IEEE 37-node distribution network considering independent and correlated wind speed scenarios.
Stochastic control problems that arise in reliability and maintenance optimization typically assume that information used for decision-making is obtained according to a predetermined sampling schedule. In many real applications, however, there is a high sampling cost associated with collecting such data. It is therefore of equal importance to determine when information should be collected and to decide how this information should be utilized for maintenance decision-making. This type of joint optimization has been a long-standing problem in the operations research and maintenance optimization literature, and very few results regarding the structure of the optimal sampling and maintenance policy have been published. In this paper, we formulate and analyze the joint optimization of sampling and maintenance decision-making in the partially observable Markov decision process framework. We prove the optimality of a policy that is characterized by three critical thresholds, which have practical interpretation and give new insight into the value of condition-based maintenance programs in life-cycle asset management. Illustrative numerical comparisons are provided that show substantial cost savings over existing suboptimal policies.
Abstract The use of prognostic methods in maintenance in order to predict remaining useful life is receiving more attention over the past years. The use of these techniques in maintenance decision making and optimization in multi-component systems is however a still underexplored area. The objective of this paper is to optimally plan maintenance for a multi-component system based on prognostic/predictive information while considering different component dependencies (i.e. economic, structural and stochastic dependence). Consequently, this paper presents a dynamic predictive maintenance policy for multi-component systems that minimizes the long-term mean maintenance cost per unit time. The proposed maintenance policy is a dynamic method as the maintenance schedule is updated when new information on the degradation and remaining useful life of components becomes available. The performance, regarding the objective of minimal long-term mean cost per unit time, of the developed dynamic predictive maintenance policy is compared to five other conventional maintenance policies, these are: block-based maintenance, age-based maintenance, age-based maintenance with grouping, inspection condition-based maintenance and continuous condition-based maintenance. The ability of the predictive maintenance policy to react to changing component deterioration and dependencies within a multi-component system is quantified and the results show significant cost savings.
For some engineering design and manufacturing applications, particularly for evolving and new technologies, populations of manufactured components can be heterogeneous and consist of several sub-populations. The co-existence of n subpopulations is particularly common in devices when the manufacturing process is still maturing or highly variable. A new model is developed and demonstrated to simultaneously determine burn-in and age-based preventive replacement policies for populations composed of distinct subpopulations subject to stochastic degradation. Unlike traditional burn-in procedures that stress devices to failure, we present a decision rule that uses burn-in threshold on cumulative deterioration, in addition to burn-in time, to eliminate weak subpopulations. Only devices with post-burn-in deterioration levels below the burn-in threshold are released for field operations. Inspection errors are considered when screening burned-in devices. Preventive replacement is employed to prevent failures from occuring during field operation. We examine the effectiveness of such integrated polycies for non-homogeneous populations. Numerical examples are provided to illustrate the proposed procedure. Sensitivity analysis is performed to analyze the impacts of model parameters on optimal policies. Numerical results indicate there are potential cost savings from simutaneouly determining burn-in and maintenance policies as opposed to a traditional approach that makes decisions on burn-in and maintenance actions separately.
This paper develops an optimum Condition-Based Maintenance policy for continuously monitored degrading systems with multiple failure modes. The degradation of system state is described by a stochastic process, and a maintenance alarm is used to signal when the degradation reaches a threshold level. Unlike existing CBM models, we consider multiple sudden failures that can occur during system's degradation. The failure rate corresponding to each failure mode is influenced either by the age of the system, the state degradation of the system, or both. A joint model is constructed for the statistically dependent time-to-maintenance due to system degradation and time-to-failure of different failure modes. This model is then utilized to obtain the optimum maintenance threshold level that maximizes the system's limiting availability over its life cycle, or, minimizes the long-run cost per unit time. A numerical example, using real-life data from a reliability test of communication systems, is provided to demonstrate the application of the proposed approach.
Condition based maintenance (CBM) uses the operating condition of a component to predict a failure event. Compared to age based replacement (ABR), CBM usually results in higher availability and lower maintenance costs, since it tries to prevent unplanned downtime and avoid unnecessary preventive maintenance activities for a component. However, the superiority of CBM remains unclear in multi‐component systems, in which opportunistic maintenance strategies can be applied. Opportunistic maintenance aims to group maintenance activities of two or more components in order to reduce maintenance costs. In a serial system, this may also result in less downtime of the production line. The aim of this paper is to examine the impact of opportunistic maintenance on the effectiveness of CBM. We simulate a small system consisting of three components in series and vary the number of components under a CBM policy, the length of the opportunistic maintenance zone, the cost benefits of grouping maintenance activities, and the chance of a failure occurrence within a preventive maintenance (PM) interval. The results show that within the current experimental settings, CBM remains cost effective in the multi‐component serial system, but is less effective than ABR in grouping maintenance activities. When the chance of failure is small and the length of the opportunistic maintenance zone is large, ABR may even be a better option if line productivity is important.
Tire-road forces are crucial in vehicle dynamics and control because they are the only forces that a vehicle experiences from the ground. These forces significantly affect the lateral, longitudinal, yaw, and roll behavior of the vehicle. The maximum force that a tire can supply is determined by the maximum value of the tire-road friction coefficient for a given normal vertical load on the tire. For each tire, the normalized traction force rho , alternatively called the coefficient of traction, is defined as
We address the problem of determining inspection and maintenance strategy for a system whose state is described by a multivariate stochastic process. We relax and extend the usual approaches. The system state is a multivariate stochastic process, decisions are based on a performance measure defined by the values of a functional on the process, and the replacement decision is based on the crossings of a critical levels. The critical levels are defined for the performance measure itself and also as the probability of never returning to a satisfactory level of performance. The inspection times are determined by a deterministic function of the system state. A non-periodic policy is developed by evaluating the expected lifetime costs and the optimal policy by an optimal choice of inspection function. The model thus gives a guaranteed level of reliability throughout the life of the project. In the particular case studied here, the underlying process is a multivariate Wiener process, the performance measure is the ℓ2 norm, and the last exit time from a critical set rather than the first hitting time determines the policy.
This paper discusses a condition based maintenance model with exponential failures and fixed inspection intervals for a two-unit system in series. The condition of each unit, such as vibration or heat, is monitored at equidistant time intervals. The condition indicator variables for each unit are used to decide whether to repair an individual unit or to overhaul the whole system. After a maintenance action is performed the monitored condition indicator variable takes on its initial value. Each unit can fail only once within an inspection interval and when one or both units fail the system fails. The probability of failure is exponential and the failure rate is dependent on the condition. The cost to be minimized is the long-run average cost of maintenance actions and failures. We study the optimal solution to this problem obtained via dynamic programming.
This paper considers a condition-based maintenance policy for a two-unit deteriorating system. Each unit is subject to gradual deterioration and is monitored by sequential non-periodic inspections. It can be maintained by good as new preventive or corrective replacements. Every inspection or replacement entails a set-up cost and a component-specific unit cost but if actions on the two components are combined, the set-up cost is charged only once. A parametric maintenance decision framework is proposed to coordinate inspection/replacement of the two components and minimize the long-run maintenance cost of the system. A stochastic model is developed on the basis of the semi-regenerative properties of the maintained system state and the associated cost model is used to assess and optimize the performance of the maintenance model. Numerical experiments emphasize the interest of a control of the operation groupings.
We extend the basic theory of kriging, as applied to the design and analysis of deterministic computer experiments, to the stochastic simulation setting. Our goal is to provide flexible, interpolation-based metamodels of simulation out- put performance measures as functions of the controllable design or decision variables. To accomplish this we charac- terize both the intrinsic uncertainty inherent in a stochastic simulation and the extrinsic uncertainty about the unknown response surface. We use tractable examples to demonstrate why it is critical to characterize both types of uncertainty, de- rive general results for experiment design and analysis, and present a numerical example that illustrates the stochastic kriging method.
Failure of many engineering systems usually results from a gradual and irreversible accumulation of damage, a degradation process. Most degradation processes can be monitored using sensor technology. The resulting degradation signals are usually correlated with the degradation process. A system is considered to have failed once its degradation signal reaches a prespecified failure threshold. This paper considers a replacement problem for components whose degradation process can be monitored using dedicated sensors. First, we present a stochastic degradation modeling framework that characterizes, in real time, the path of a component's degradation signal. These signals are used to predict the evolution of the component's degradation state. Next, we formulate a single-unit replacement problem as a Markov decision process and utilize the realtime signal observations to determine a replacement policy. We focus on exponentially increasing degradation signals and show that the optimal replacement policy for this class of problems is a monotonically nondecreasing control limit policy. Finally, the model is used to determine an optimal replacement policy by utilizing vibration-based degradation signals from a rotating machinery application.
This paper presents a generalized periodic imperfect preventive maintenance (PM) model for a system with age-dependent failure type. The imperfect PM model proposed in this study incorporates improvement factors vis-a-vis the hazard-rate function, and effective age. As failures occur, the system experiences one of the two types of failure: type-I failure (minor), and type-II failure (catastrophic). Type-I failures are rectified with minimal repair. In a PM period, the system is preventively maintained following the occurrence of a type-II failure, or at age T, whichever takes place first. At the N th PM, the system is replaced. An approach that generalizes the existing studies on the periodic PM policy is proposed. Taking age-dependent failure type into consideration, the objective consists of determining the optimal PM & replacement schedule that minimize the expected cost per unit of time, over an infinite horizon.
This article studies the maximum likelihood inference on a class of Wiener processes with random effects for degradation data. Degradation data are special case of functional data with monotone trend. The setting for degradation data is one on which n independent subjects, each with a Wiener process with random drift and diffusion parameters, are observed at possible different times. Unit-to-unit variability is incorporated into the model by these random effects. EM algorithm is used to obtain the maximum likelihood estimators of the unknown parameters. Asymptotic properties such as consistency and convergence rate are established. Bootstrap method is used for assessing the uncertainties of the estimators. Simulations are used to validate the method. The model is fitted to bridge beam data and corresponding goodness-of-fit tests are carried out. Failure time distributions in terms of degradation level passages are calculated and illustrated.
Many models have been proposed that relate failure times and stochastic time-varying covariates. In some of these models, failure occurs when a particular observable marker crosses a threshold level. We are interested in the more difficult, and often more realistic, situation where failure is not related deterministically to an observable marker. In this case, joint models for marker evolution and failure tend to lead to complicated calculations for characteristics such as the marginal distribution of failure time or the joint distribution of failure time and marker value at failure. This paper presents a model based on a bivariate Wiener process in which one component represents the marker and the second, which is latent (unobservable), determines the failure time. In particular, failure occurs when the latent component crosses a threshold level. The model yields reasonably simple expressions for the characteristics mentioned above and is easy to fit to commonly occurring data that involve the marker value at the censoring time for surviving cases and the marker value and failure time for failing cases. Parametric and predictive inference are discussed, as well as model checking. An extension of the model permits the construction of a composite marker from several candidate markers that may be available. The methodology is demonstrated by a simulated example and a case application.
The paper considers linear degradation and failure time models with multiple failure modes. Dependence of traumatic failure intensities on the degradation level are included into the models. Estimators of traumatic event cumulative intensities, and of various reliability characteristics are proposed. Prediction of residual reliability characteristics given a degradation value at a given moment is discussed. Non-parametric, semiparametric and parametric estimation methods are given. Theorems on simultaneous asymptotic distribution of random functions characterising degradation and intensities of traumatic events are proposed. Asymptotic properties of unconditional and residual reliability characteristics estimators are given. Real tire wear and failure time data are analysed.
This paper considers a condition-based maintenance model for continuously degrading systems under continuous monitoring. After maintenance, the states of the system are randomly distributed with residual damage. We investigate a realistic maintenance policy, referred to as condition-based availability limit policy, which achieves the maximum avail- ability level of such a system. The optimum maintenance threshold is determined using a search algorithm. A numerical example for a degrading system modeled by a Gamma process is presented to demonstrate the use of this policy in prac- tical applications. � 2005 Elsevier B.V. All rights reserved.
In some applications, the failure rate of the system depends not only on the time, but also upon the status of the system, such as vibration level, efficiency, number of random shocks on the system, etc., which causes degradation. In this paper, we develop a generalized condition-based maintenance model subject to multiple competing failure processes including two degradation processes, and random shocks. An average long-run maintenance cost rate function is derived based on the expressions for the degradation paths & cumulative shock damage, which are measurable. A geometric sequence is employed to develop the inter-inspection sequence. Upon inspection, one needs to decide whether to perform a maintenance, such as preventive or corrective, or to do nothing. The preventive maintenance thresholds for degradation processes & inspection sequences are the decision variables of the proposed model. We also present an algorithm based on the Nelder-Mead downhill simplex method to calculate the optimum policy that minimizes the average long-run maintenance cost rate. Numerical examples are given to illustrate the results using the optimization algorithm.