Imperfect Maintenance Research Articles

Optimal preventive replacement policy for operating products with renewing free-replacement warranty

This paper investigates the optimal preventive replacement policy for products with random work under a renewing free-replacement warranty (RFRW). To model an imperfect maintenance action when the product fails, we consider that the failed product undergoes minimal repairs at minor failures and corrective replacements at catastrophic failures. Before catastrophic failures, the product is planned to replace preventively at age T or at the completion of a working time, whichever occurs first. For both warranted and non-warranted products, preventive replacement models from customer’s perspective are developed, and the optimal schedules of age-replacement that minimize the mean cost rate functions are derived. The effects of a product warranty on the optimal preventive replacement model are investigated analytically and computed numerically. It can be seen that the proposed model is a generalization of the previous works in maintenance theory.

Optimal Maintenance Decision Based on Remaining Useful Lifetime Prediction for the Equipment Subject to Imperfect Maintenance

Focusing on the fact that the existing research on optimal maintenance decision for remaining useful lifetime (RUL) prediction and imperfect maintenance has low accuracy of RUL prediction and rationality of decision results, an optimal maintenance decision method based on RUL prediction for the equipment subject to imperfect maintenance is proposed in this paper. Firstly, the nonlinear Wiener process is used to characterize the degradation law of the equipment. Secondly, the imperfect maintenance model that meets the upper limit of the maintenance number is established based on the nonhomogeneous Poisson process. Then, based on the concept of the first hitting time, the probability density function (PDF) of the RUL is derived. Finally, based on the RUL prediction results, the optimal maintenance decision model for the equipment subject imperfect maintenance is constructed. Through the example verification and cost parameter sensitivity analysis, the proposed method can effectively improve the accuracy of the RUL prediction and the scientific of maintenance decision results, which has engineering application value.

Fleet-Level Selective Dispatch and Imperfect Maintenance Strategy Optimization Based on Evolutionary Co-Petition Game Theory

Fleet-level selective dispatch under imperfect maintenance oriented to mission reliability is a practical, multi-level maintenance strategy decision problem that becomes highly difficult since the number of potential maintenance strategies dramatically increases. In this paper, the fleet-level selective imperfect maintenance model is established, and an evolutionary co-petition game theory based approach is proposed for optimizing the fleet maintenance strategy. During the route of the proposed method, each piece of equipment is considered as a game player, and an evolutionary co-petition game strategy is adopted for the dispatch and standby groups in each game round: a cooperative game strategy with strategy space generation way for the dispatch group to decrease the maintenance cost; and a competition game strategy between the dispatch and standby groups to select the optimal dispatch equipment. And a termination condition is given upon which the optimized maintenance strategy is achieved. A case study is further conducted on a fleet of 15 pieces of equipment under 5-level imperfect maintenance actions, and is compared with numerical simulation method. And the results validate that the proposed method possesses high efficiency and effectiveness in optimizing the fleet-level selective imperfect maintenance planning problem.

A novel hybrid failure rate update model for imperfect maintenance

Imperfect maintenance models, based on general renewal processes, have been extensively researched. However, the virtual age used for measuring the effect of imperfect maintenance is an unintuitive variable in models in the literature, leading to discrepancies between evaluation results and real situations. To solve this problem, a failure rate update model that considers virtual age and failure intensity update factors is proposed. In this model, the virtual age factor is determined by intuitive variables, and the failure intensity update factor is determined on the basis of virtual age, reflected by the virtual age factor. A brief illustration of the validity and feasibility of the proposed model is presented, based on real maintenance data. The results obtained through numerical experiments, sensitivity analysis, and a case study demonstrates that the proposed model can accurately reflect system reliability level in a convenient manner.

A novel hybrid failure rate update model for imperfect maintenance

Imperfect maintenance models, based on general renewal processes, have been extensively researched. However, the virtual age used for measuring the effect of imperfect maintenance is an unintuitive variable in models in the literature, leading to discrepancies between evaluation results and real situations. To solve this problem, a failure rate update model that considers virtual age and failure intensity update factors is proposed. In this model, the virtual age factor is determined by intuitive variables, and the failure intensity update factor is determined on the basis of virtual age, reflected by the virtual age factor. A brief illustration of the validity and feasibility of the proposed model is presented, based on real maintenance data. The results obtained through numerical experiments, sensitivity analysis, and a case study demonstrates that the proposed model can accurately reflect system reliability level in a convenient manner.

Study on the decision considering imperfect maintenance of multiple components based on the exponential distribution

The real-time monitoring and the high reliability system of multiple components are studied in the mechanical system as background information. The characteristics of copula among multiple component of different systems are considered. The information of affected components is monitoring as covariate. With the prediction model of remaining useful life (RUL)based on stochastic filtering theory, and the strategy of opportunity maintenance, the maintenance decision model of dynamic is studied on the prediction information of remaining useful life. Lastly, the relevant theories are verified by simulation.

Remaining Useful Lifetime Prediction of the Equipment Subjected to Imperfect Maintenance Based on the Compound Nonhomogeneous Poisson Process

Remaining Useful Lifetime Prediction of the Equipment Subjected to Imperfect Maintenance Based on the Compound Nonhomogeneous Poisson Process

A stochastic simulation-optimization model for base-warranty and extended-warranty decision-making of under- and out-of-warranty products

In recent years, product warranties (including base-warranty and extended-warranty) have become an integral part of marketing strategy for most manufacturers as well as and a key determinant of purchasing decision for most customers. It is crucial for manufacturers or dealers who offer warranty to their customers to optimize decisions regarding price of products, durations of base-warranty and extended-warranty, price of extended-warranty, etc. On the other side, manufacturers must decide on a cost-effective imperfect maintenance strategy and spare part inventory policy for their under-warranty and out-of-warranty products. In order to solve these decision-making problems, this study proposes a novel stochastic simulation-based optimization (SBO) model with the objective of maximizing the manufacturer's profit. A metaheuristic Monte-Carlo simulation algorithm integrated with a dynamic programming approach is also presented to solve the model. A case study of vacuum cleaners is provided to illustrate the developed model and its solution procedure, and the simulation results are verified with real data. Finally, a sensitivity analysis is performed in order to evaluate the impact of key parameters on the optimal solution. Our analysis shows how different planning horizons can affect warranty-related decisions for both the manufacturers and customers, providing valuable insights to corporate decision-makers.

A condition-based maintenance model with past-dependent imperfect preventive repairs for continuously deteriorating systems

Most condition-based imperfect maintenance models developed over the last few decades are memoryless in the sense that maintenance efficiency is completely [Formula: see text]-independent of previous interventions. However, many maintenance activities exhibit their past dependency in engineering practice, and this significant property should not be ignored in maintenance modeling. In this spirit, our aim is to develop a condition-based maintenance model for continuously deteriorating systems subject to a special kind of past-dependent imperfect repairs. Such a repair can put the system back to a deterioration level better than the one at just before the current repair, but worse than the one reached at the last repair. Besides, inspection and replacement are memoryless actions available for the system. They result in different effects on the system deterioration and incur different costs. To achieve high economic performances in the long term, these actions are coordinated into a control-limit deterioration-based maintenance policy. Its long-run maintenance cost rate is analytically evaluated using the semi-regenerative process theory. Numerous sensitivity studies to maintenance costs and to system characteristics give a thorough understanding about the policy behavior. Furthermore, comparisons with more classical policies justify the importance of incorporating the past dependency in maintenance modeling.

Optimal dynamic imperfect preventive maintenance of wind turbines based on general renewal processes

With the rapid growth in wind turbine technology worldwide, the high operational and maintenance costs of wind turbines have posed a major challenge to wind power operating companies. Considering the high replacement cost, imperfect maintenance measures are employed widely once downtime failures occur. However, as the metric to describe the effect of imperfect maintenance is a non-intuitive variable, the evaluation results obtained from existing research do not conform with actual wind turbine situations. To address this issue, the virtual age factor and failure intensity update factor are expressed by intuitive variables to illustrate the imperfect maintenance effect. Additionally, we propose a failure rate function update model considering the above factors. To minimise maintenance costs while ensuring the availability of the wind turbine, we investigate a periodic dynamic imperfect preventive maintenance decision model based on the proposed failure rate function update model. We also provide a brief illustration of the accuracy and feasibility of the proposed model through optimal solution and sensitivity analyses. The results obtained from the case analysis and strategies comparison, based on actual wind turbine maintenance data, demonstrate the economic advantages of our approach.

Selective maintenance optimization for multi-state systems considering stochastically dependent components and stochastic imperfect maintenance actions

This paper presents a selective maintenance optimization problem for complex systems composed of stochastically dependent components. The components of a complex system degrade during mission time, and their degradation states vary from perfect functioning to complete failure states. The degradation rate of each component not only depends on its intrinsic degradation but also on the state of other dependent components of the system. The proposed approach captures the two-way interactions between components through system performance rates and uses Monte Carlo simulation to compute the reliability of the system in the next operational mission. Different maintenance actions such as do-nothing, perfect, and stochastic imperfect maintenance are considered during the maintenance break to improve the reliability of the system. The selective maintenance bi-objective optimization problem is modelled considering both the expected value and variance of the system reliability as objective functions. Time and budget are considered as constraints for finding the optimal maintenance strategy. Two illustrative examples are provided for a better understanding of the proposed approach and for demonstrating its effectiveness.

Dynamic selective maintenance optimization for multi-state systems over a finite horizon: A deep reinforcement learning approach

Selective maintenance, which aims to choose a subset of feasible maintenance actions to be performed for a repairable system with limited maintenance resources, has been extensively studied over the past decade. Most of the reported works on selective maintenance have been dedicated to maximizing the success of a single future mission. Cases of multiple consecutive missions, which are oftentimes encountered in engineering practices, have been rarely investigated to date. In this paper, a new selective maintenance optimization for multi-state systems that can execute multiple consecutive missions over a finite horizon is developed. The selective maintenance strategy can be dynamically optimized to maximize the expected number of future mission successes whenever the states and effective ages of the components become known at the end of the last mission. The dynamic optimization problem, which accounts for imperfect maintenance, is formulated as a discrete-time finite-horizon Markov decision process with a mixed integer-discrete-continuous state space. Based on the framework of actor-critic algorithms, a customized deep reinforcement learning method is put forth to overcome the “curse of dimensionality” and mitigate the uncountable state space. In our proposed method, a postprocess is developed for the actor to search the optimal maintenance actions in a large-scale discrete action space, whereas the techniques of the experience replay and the target network are utilized to facilitate the agent training. The performance of the proposed method is examined by an illustrative example and an engineering example of a coal transportation system.

Enhanced POM strategy and its application to wind turbines

Deficiencies exist during applying the traditional preventive opportunistic maintenance (POM) strategy to wind turbines. For example, its rough cost analysis only provides a total instead of the staged cost of once maintenance, which cannot give precise cost composition. Setting identical thresholds for all subassemblies reduces the potential of cost saving etc. An enhanced POM strategy for wind turbines is presented in this study with the consideration of maintenance modes including no maintenance, imperfect maintenance and replacement. The reliability variations of subassemblies under different maintenance modes are described by Weibull distribution with an age reduction factor. On the basis of reliability variations, a formula is proposed to uniformly compute maintenance cost under each maintenance mode via subdividing the cost in the light of diverse maintenance stages. An integrated objective function minimising the maintenance cost is established and solved, where reliability thresholds of each subassembly are separately set as optimisation variables. The enhanced POM strategy is applied to a wind farm in North China, verifying its effectiveness.

A Hybrid Condition-Based Maintenance Model for Deteriorating Systems Subject to Nonmemoryless Imperfect Repairs and Perfect Replacements

Condition-based maintenance (CBM) is popularly recognized as a key lever that enables organizations to gain a competitive advance in the context of the fourth industrial revolution. Combining both the perfect and imperfect maintenance actions into CBM policies seems to be an efficient way to achieve high economic performances. Following this view, we propose and optimize in this article a hybrid deterioration-based maintenance model for continuously deteriorating systems subject to nonmemoryless imperfect repairs and perfect replacements. Compared to existing related works, the originality of our model is threefold. First, an innovative model representing both the positive and memory effects of imperfect repairs is developed. Second, a new decision rule for switching between perfect and imperfect maintenance actions is proposed. Finally, the mathematical cost model of the proposed hybrid maintenance policy is fully formulated on the basis of the sophisticated semiregenerative theory. Numerous sensitivity studies and comparisons with benchmark policies under various configurations of maintenance costs and system characteristics allow to better understand the behaviors of our hybrid maintenance policy and to confirm its effectiveness.

Semiparametric estimate of the efficiency of imperfect maintenance actions for a gamma deteriorating system

A system is considered, which is deteriorating over time according to a non homogeneous gamma process with unknown parameters. The system is subject to periodic and instantaneous imperfect maintenance actions (repairs). Each imperfect repair removes a proportion ρ of the accumulated degradation since the previous repair. The parameter ρ hence appears as a measure for the maintenance efficiency. This model is called arithmetic reduction of degradation of order 1. The system is inspected right before each maintenance action, thus providing some multivariate measurement of the successively observed deterioration levels. Based on these data, a semiparametric estimator of ρ is proposed, considering the parameters of the underlying gamma process as nuisance parameters. This estimator is mainly based on the range of admissible ρ’s, which depends on the data. Under technical assumptions, consistency results are obtained, with surprisingly high convergence rates (up to exponential). The case where several i.i.d. systems are observed is next envisioned. Consistency results are obtained for the efficiency estimator, as the number of systems tends to infinity, with a convergence rate that can be higher or lower than the classical square root rate. Finally, the performances of the estimators are illustrated on a few numerical examples.

Robust selective maintenance strategy under imperfect observations: A multi-objective perspective

Selective maintenance, as a pervasive maintenance policy in both military and industrial environments, aims to achieve the maximum success of subsequent missions under limited maintenance resources by choosing an optimal subset of feasible maintenance actions. The existing works on selective maintenance optimization all assume that the condition of components in a system can be perfectly observed after the system completes the last mission. However, such a premise may not always be true in reality due to the limited accuracy/precision of sensors or inspection instruments. To fill this gap, a new robust selective maintenance model is proposed in this work to consider uncertainties that originate from imperfect observations. The uncertainties associated with imperfect observations are incorporated into the states and effective ages of components via Bayes rule. The Kijima type II model, as a specific imperfect maintenance model, is used to characterize the imperfect maintenance efficiency of each selected maintenance action. The expectation and variance of the probability of a repairable system successfully completing the subsequent mission are derived to quantify the uncertainty that is propagated from imperfect observations. To guarantee the robustness of a selective maintenance strategy under uncertainties, a multi-objective selective maintenance model is constructed with the aims of maximizing the expectation of the probability that a system successfully completes the subsequent mission and to simultaneously minimizing the variance in this probability. The Pareto-optimality approach is utilized to offer a set of non-dominated solutions. Two illustrative examples are presented to demonstrate the advantages of the proposed method.

Condition-based maintenance policies under imperfect maintenance at scheduled and unscheduled opportunities

Motivated by the cost savings that can be obtained by sharing resources in a network context, we consider a stylized, yet representative, model for the coordination of maintenance and service logistics for a geographic network of assets. Capital assets, such as wind turbines in a wind park, require maintenance throughout their long lifetimes. Two types of preventive maintenance are considered: planned maintenance at periodic, scheduled opportunities, and opportunistic maintenance at unscheduled opportunities. The latter type of maintenance arises due to the network context: When an asset in the network fails, this constitutes an opportunity for preventive maintenance for the other assets in the network. So as to increase the realism of the model at hand and its applicability to various sectors, we consider the option of not-deferring and of deferring planned maintenance after the occurrence of opportunistic maintenance. We also assume that preventive maintenance may not always restore the condition of the system to ‘as good as new.’ By formulating this problem as a semi-Markov decision process, we characterize the optimal policy as a control limit policy (depending on the remaining time until the next planned maintenance) that indicates on the one hand when it is optimal to perform preventive maintenance and on the other hand when maintenance resources should be shared if an opportunity in the network arises. In order to facilitate managerial insights on the effect of each parameter on the cost, we provide a closed-form expression for the long-run rate of cost for any given control limit policy (depending on the remaining time until the next planned maintenance) and compare the costs (under the optimal policy) to those of suboptimal policies that neglect the opportunity for resource sharing. We illustrate our findings using data from the wind energy industry.

Optimum Consecutive Preventive Maintenance Scheduling Model Considering Reliability

As an effective means for improving system condition and reducing failures, a reasonable preventive maintenance scheduling guarantees the stability and safety of the system. This paper studies a consecutive maintenance scheduling problem for single-component systems with imperfect maintenance, and an optimum model with minimum reliability constraint for minimal cost rate is developed based on the renewal theory. The age-based and reliability-based maintenance strategies are modeled and compared according to a numerical example based on the degradation data of the actual system, which also verifies the optimality of the reliability-based strategy. At last, the influence of some key parameters is discussed by sensitive analysis.

Optimization of preventive maintenance for series manufacturing system by differential evolution algorithm

The costs of preventive maintenance have been extensively studied by scholars across all preventive optimization model disciplines. However, one phenomenon fails to be fully studied: breakdown and breakdown maintenance costs. We set out to fill this gap in this study. This study considered the cost of equipment preventive maintenance, and the breakdown maintenance cost caused by an accidental breakdown. In order to more accurately establish the reliability model of equipment breakdown, the three-parameter Weibull distribution was applied to set up the reliability model of equipment and the differential evolution algorithm was adopted to optimize the parameters. On this basis, preventive maintenance was regarded as imperfect maintenance in the study of preventive maintenance strategies for single equipment. In consideration of the combined influence of preventive maintenance and breakdown maintenance, a maintenance strategy in which preventive maintenance times N served as the decision variable was obtained to build a mathematical model on benefit expectation of single equipment in unit time. Based on the research of single equipment, a further study was performed on the multi-equipment series system. Moreover, two strategies were given, both of which use preventive maintenance times N as the decision variable. The first strategy is to take the average cost rate of the system under long-term operation as the optimization objective, while the second strategy is to apply single component maintenance strategy in series system. In the numerical example study, a series manufacturing system composed of two devices was chosen as the research object. Interestingly, we discussed the effect of initial conditions of two-parameter DE on output results. After acquiring the optimal initialization parameters, the failure rate function was achieved by the DE to estimate the parameters of three-parameter Weibull distribution. Meanwhile, the maintenance times N was optimized according to the two strategies respectively. The best result were selected from the results of both strategies based on availability. Thus, the validity and practicability of the proposed research methods are verified.

Prognostic Model Development with Missing Labels

Condition-based maintenance (CBM) has emerged as a proactive strategy for determining the best time for maintenance activities. In this paper, a case of a milling process with imperfect maintenance at a German automotive manufacturer is considered. Its major challenge is that only data with missing labels are available, which does not provide a sufficient basis for classical prognostic maintenance models. To overcome this shortcoming, a data science study is carried out that combines several analytical methods, especially from the field of machine learning (ML). These include time-domain and time–frequency domain techniques for feature extraction, agglomerative hierarchical clustering and time series clustering for unsupervised pattern detection, as well as a recurrent neural network for prognostic model training. With the approach developed, it is possible to replace decisions that were made based on subjective criteria with data-driven decisions to increase the tool life of the milling machines. The solution can be employed beyond the presented case to similar maintenance scenarios as the basis for decision support and prognostic model development. Moreover, it helps to further close the gap between ML research and the practical implementation of CBM.