Preventive Maintenance Threshold Research Articles

An integrated framework of preventive maintenance and task scheduling for repairable multi-unit systems

Preventive maintenance and task scheduling are both crucial activities in industrial practice. Although they are interdependent and mutually influential, most existing studies typically analyze them separately. In this paper, an integrated framework of preventive maintenance planning and task scheduling is explored. On one hand, while most scholars focus on the system as a whole in scheduling studies, we further take into account the degradation and maintenance of multiple units during the task scheduling process. On the other hand, instead of only using "direct replacement" as the main maintenance method, we further consider the repairability of the unit by incorporating imperfect maintenance effects into the maintenance modeling. Additionally, the lifecycle partitioning method is proposed to analyze the maintenance groups for multiple units at the completion of scheduling tasks and their corresponding probabilities. Based on this foundation, an integrated decision model is established with the preventive maintenance threshold and scheduling task sequence as decision variables to minimize the total weighted expected completion time. Finally, a novel genetic algorithm based on hybrid encoding is proposed, and the effectiveness of integrated decision-making was validated using a practical example.

Condition-based opportunistic maintenance strategy for multi-component wind turbines by using stochastic differential equations

The components of wind turbines are complex in structure and the working environment is harsh, which makes wind turbines face problems such as high failure rates and high maintenance costs. In this paper, the stochastic differential equation model has been established for the harsh operating environment of wind turbines, and used Brownian motion to simulate random disturbances; aiming at the problem of high failure rate of wind turbines, based on Weibull distribution, a new model has been established by combining operating time and equipment state to calculate the failure rate; in the analysis of monitoring data, the Higher-Order Moment method and Bayesian method were used to solve the parameters. The opportunity maintenance threshold curve and preventive maintenance threshold curve were obtained by analyzing Time-Based Maintenance and Condition-Based Maintenance. Therefore, the Condition-Based Opportunistic Maintenance strategy was obtained. The effectiveness of the proposed method was finally verified by arithmetic examples.

A novel condition‐based maintenance policy considering imperfect switching for warm standby systems

AbstractThis paper proposes a novel condition‐based maintenance model for a two‐component warm standby system considering an imperfect switching policy. Unlike the conventional models, joint optimization of preventive and failure switching strategies is investigated. The standby component can be switched preventively when the component reaches the preventive maintenance (PM) threshold before the online one fails. The failure switching is triggered when the online component reaches the corrective maintenance (CM) threshold. In addition, the switching mechanism between the two components is related to the order fulfillment rate. The optimal PM threshold and order fulfillment rate can be derived by minimizing the long‐term average cost rate. A numerical example is provided to demonstrate the robustness of the decision model under different scenarios through sensitivity analysis. Ultimately, the effectiveness of the proposed model in this article was verified by comparing the models.

Multi-objective optimal maintenance strategy considering imperfect preventive maintenance: A case study on railway VOBC

Preventive maintenance procedures for systems are designed to improve long-term operating performance and reduce maintenance costs. This paper attempts to seek a trade-off between system reliability and maintenance costs and explores the optimal multi-objective maintenance strategy applicable to different field situations. We first provide an overview of the problem and analyze the impacts of varying different maintenance activities on reliability. Then, a mathematical model of reliability losses and maintenance costs is defined and derived, which will be used to construct a multi-objective maintenance strategy. In this research, the PSO-SA stochastic optimization algorithm is proposed to discover the Pareto frontier to find the optimal preventive maintenance threshold and inspection interval that minimizes reliability loss and maintenance costs. Finally, a case study is performed with railway VOBC as an illustration. The analysis results illustrate that the proposed multi-objective maintenance strategy can satisfy the preferences of various decision-makers. It is suitable for different maintenance needs and can support the development of on-site maintenance strategies.

A novel modeling framework for a degrading system subject to hierarchical inspection and maintenance policy

Most engineering systems exhibit degrading performance in their designated service times as influenced by their working conditions. Thus, inspection and maintenance actions are crucial for maintaining their performance. Among these, critical engineering systems, such as compressors and safety valves, are typically subject to a multi-level inspection scheme consisting of partial and full inspections. In this study, inspired by this inspection scheme, we propose a hierarchical maintenance model to incorporate collected system performance information from these inspection interventions. Partial inspections verify whether the system is functional or not, and then partial preventive maintenance is performed; a more accurate system state is known at the instant of full inspections, which serve as windows for the conduction of condition-based maintenance. The proposed maintenance policy is then applied to a system undergoing monotone stochastic degradation. Subsequently, the average cost per unit time in the operational phase and the sensitivity analysis with respect to variables, such as the preventive maintenance threshold, inspection intervals, and the maintenance effect factors, are investigated. Theoretical results and numerical examples are obtained to examine the applicability of the generalized model.

Optimal production lot-sizing and condition-based maintenance policy considering imperfect manufacturing process and inspection errors

In this paper, we propose an integrated Economic manufacturing quantity (EMQ) model combining both the concepts of condition-based maintenance (CBM) and imperfect manufacturing process. The manufacturing process is modelled by two indicators. One possesses binary state, indicating whether the manufacturing process is in-control or not. The other one is modelled by a homogeneous Gamma process, representing the degradation of the manufacturing equipment. The system is inspected at the end of each production run, upon which, the deterioration level can be perfectly observed, while two types of errors may occur in revealing the state of the manufacturing process. Defective products can be fabricated when the manufacturing state degrades. An integrated production and CBM policy is proposed. The objective is to develop the optimal production lot-sizing and preventive maintenance threshold in order to minimize the expected cost rate in the long-time horizon. We model the problem in the framework of a semi-Markov decision process. The successive-approximations method is applied to solve the problem numerically. The applicability of the proposed model and some sensitivity analysis are presented in a numerical illustration. It can provide theoretical reference to the decision-maker in production and maintenance planning.

A Comparative Study of Preventive Maintenance Thresholds for Deteriorating Systems

Degradation of engineering systems is a phenomenon that affects the reliability and the lifetime of systems. Maintenance of deteriorating systems has been widely studied over the past 50 years. Numerous maintenance models have been proposed in the literature to manage degradation. In this paper, we focus on a condition-based maintenance strategy for those systems suffering a continuous deterioration process. We propose the use of a non-constant maintenance threshold to determine when a preventive action is required. The main goal is to analyse the effect of non-constant threshold in the long-term maintenance cost rate. We demonstrate numerically the convergence of the long run cost rate and some statistical properties of the proposed model. We compare the use of a constant threshold with a non-constant threshold through two different simulated case studies. The simulations provide some statistical results that reveals interesting advantages and drawbacks of using a non-constant threshold.

Joint Optimization Strategy of Condition-Based Maintenance and Spare Parts Ordering for Nonlinear Degraded Equipment under Imperfect Maintenance

When existing methods consider the impact of the imperfect maintenance activities on random degraded equipment, they usually assume that the degraded equipment is linear, and set the number of imperfect maintenance activities in advance. However, in engineering practice, most of the degraded equipment is nonlinear, and the number of imperfect maintenance activities has an impact on the development of maintenance strategies. Therefore, this paper proposes a new joint maintenance strategy considering the uncertainty of the number of imperfect maintenance activities for nonlinear degraded equipment. First, nonlinear degradation data are linearized based on Box-Cox transformation (BCT), and the degradation model under the influence of imperfect activities is constructed by the random coefficient regression model. Accordingly, the remaining useful life (RUL) probability distribution can be derived. Secondly, the number of maintenances is calculated by imperfect maintenance level and success probability. Then, the detection cycle, preventive maintenance threshold and maintenance times are taken as decision variables. The optimization objective is to minimize the expected average cost. However, this is restricted by availability and probability of success for imperfect maintenance activities. A multi-objective joint optimization model of condition-based maintenance and spare parts ordering is constructed. Finally, the analysis results based on numerical examples verify the feasibility of the proposed joint optimization strategy.

Reliability Modelling Considering Self-Exciting Mechanisms of Shock Damage

This study investigates reliability modelling and optimal preventive maintenance polices for engineering systems subject to shocks, considering two types of self-exciting mechanisms. Under trigger mechanism 1, if the accumulative number of δ—ineffective shocks reaches the trigger threshold k1 among the run of ineffective shocks, then the self-exciting mechanism will be activated, resulting in the accumulative number of effective shocks increasing by m1. Under trigger mechanism 2, if the consecutive number of δ—ineffective shocks reaches a fixed threshold K2 among the run of ineffective shocks, then the self-exciting mechanism will be triggered and the accumulative number of effective shocks will increase by m2. The system breaks down when the accumulative number of effective shocks exceeds the fixed threshold. Based on the established shock models, the reliability indices are obtained through the finite Markov chain imbedding approach. According to the operation of the system under different monitoring conditions, two types of preventive maintenance strategies are considered; then, optimization models are established, and the optimal preventive maintenance thresholds are determined. Finally, the proposed models are illustrated by numerical examples.

Condition-based opportunistic maintenance policies with two-phase inspections for continuous-state systems

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.

Joint Optimization of Production Lot Sizing and Preventive Maintenance Threshold Based on Nonlinear Degradation

In a manufacturing system, lot sizing and maintenance are interdependent and interact with each other. Few studies jointly investigated production lot sizing and maintenance management considering system degradation. However, during the production process, the system and critical component performance will undergo inevitable degradation over time. For example, equipment wears out due to both its own internal causes and the external environment. To monitor the degradation process, interval inspection is usually performed to obtain information about the system degradation and nonlinear degradation is more general. Thus, based on the nonlinear degradation of the production system, this study developed a joint optimization model of production lot sizing and preventive maintenance (PM) thresholds with the goal of maximizing profit per unit of time. The maintenance decision follows the control limit principle, i.e., the choice between preventive maintenance (PM), corrective maintenance (CM), or neither (do nothing) is based on the magnitude of degradation. A simulation algorithm is proposed to obtain the optimal lot-sizing allocation and PM thresholds. The effectiveness of this joint optimization model algorithm is illustrated by numerical examples and the results show that the maximum profit per unit time can be obtained by reasonably formulating PM thresholds and production lot sizing.

A dynamic condition-based maintenance optimization model for mission-oriented system based on inverse Gaussian degradation process

An effective maintenance policy optimization model can reduce maintenance cost and system operation risk. For mission-oriented systems, the degradation process changes dynamically and is monotonous and irreversible. Meanwhile, the risk of early failure is high. Therefore, this paper proposes a dynamic condition-based maintenance (CBM) optimization model for mission-oriented system based on inverse Gaussian (IG) degradation process. Firstly, the IG process with random drift coefficient is used to describe the degradation process and the relevant probability distributions are obtained. Secondly, the dynamic preventive maintenance threshold (DPMT) function is used to control the early failure risk of the mission-oriented system, and the influence of imperfect preventive maintenance (PM) on the degradation amount and degradation rate is analysed comprehensively. Thirdly, according to the mission availability requirement, the probability formulas of different types of renewal policies are obtained, and the CBM optimization model is constructed. Finally, a numerical example is presented to verify the proposed model. The comparison with the fixed PM threshold model and the sensitivity analysis show the effectiveness and application value of the optimization model.

A condition-based maintenance policy considering failure dependence and imperfect inspection for a two-component system

In this paper, a condition-based maintenance of a two-component system under imperfect inspection is studied: component 1 is repairable and only two states (working and failed) are observable. Component 2 degrades with time. The degradation of component 2 is modelled by a Wiener process with different drift and volatility parameters depending on the working state of component 1. Component 2 fails if its degradation level exceeds a pre-defined threshold. A dual periodical inspection policy is proposed to monitor the system condition: component 1 is imperfectly inspected and the whole system is perfectly inspected with a longer period. Upon inspection, component 1 is replaced if a failure is detected. The whole system is renewed if the degradation of component 2 exceeds its preventive maintenance threshold. The problem is very complex due to the failure dependence between the two components and the partial revealed information within the system inspection period. Component 1 is impacted by the imperfect inspection. Component 2 may experience multiple changes of its degradation regime while only imperfect, partial change information is available. In this study, we intend to address these problems. The expression of the maintenance cost rate in the long-run is given to evaluate the maintenance policy. An algorithm is proposed to achieve the maintenance optimization. Numerical examples show the applicability of the model. It can provide reference to the decision-maker for optimizing the maintenance budget.

Modeling the effects of dependence between competing failure processes on the condition-based preventive maintenance policy

This paper explores how the dependence between competing failure processes affects the condition-based preventive maintenance policy. The exposed failures caused by degradation and random shock are explicitly modeled respectively through two stochastic processes, i.e. Gamma process and compound Poisson process. Condition-based inspections are scheduled by introducing a convex function describing the relationship between degradation level and inspection interval. The preventive maintenance policy is planned to improve the operation efficiency which is adversely affected by the existing failures. The effect of failure dependence on the condition-based maintenance is analyzed through the preventive maintenance threshold of which initial value is fixed and is weaken by the following arrived shocks then. Imperfect maintenance effect is also considered to describe the irreversible aging process. Monte Carlo simulation technique and genetic algorithm are both employed to obtain the optimal parameters which determine the frequencies of inspection and maintenance. An illustrate example of a gearbox in the wind power industry is studied to demonstrate how the proposed maintenance policy balances the conflicting objectives in engineering practice.

Condition-based maintenance planning for multi-state systems under time-varying environmental conditions

Systems commonly operate under time-varying environmental condition (EC). Since the EC can affect the degradation process of a system, maintenance planning can be quite challenging. This study focuses on a case where the evolution processes of the system degradation and the EC are governed by Markov processes, for which the transition rate matrix of degradation states varies with the EC. To maintain the system, an inspection/maintenance policy is adopted, where a maintenance action is carried out immediately when a failure occurs during an inspection interval or upon an inspection epoch when the system’s degradation state reaches a certain threshold. Imperfect maintenance (IM) and replacement are considered in this study, where a certain number of consecutive IM actions can be carried out before each replacement. We first derive the long-run average cost based on the semi-regenerative properties of the system, and then jointly determine the inspection interval, preventive maintenance threshold and number of IM actions before a replacement by minimizing the long-run average cost. A numerical study is conducted to demonstrate the proposed maintenance policy.

Condition-based maintenance strategy optimization of meta-action unit considering imperfect preventive maintenance based on Wiener process

With the popularization and application of technologies such as monitoring and sensing, the application of condition-based maintenance has become increasingly widespread. However, most traditional condition-based maintenance strategies focus on a component or system, which is too large for fault diagnosis and location. Moreover, imperfect maintenance is seldom considered and most of them only optimize the single variable in condition-based maintenance decision. In this paper, the meta-action unit is taken as the research object, and the Wiener process is used to describe the performance degradation of the meta-action unit. Considering that the maintenance quality deteriorates with the increase of the number of maintenance, and has randomness, the beta distribution is used to establish an imperfect preventive maintenance quality model. A new maintenance optimization strategy is proposed, with the long-term maintenance cost rate as the goal, to obtain the best preventive maintenance threshold, inspection cycle and the optimal number of maintenance. Finally, a Monte Carlo simulation was used to solve numerically and analyze the influence of each parameter on the optimal decision. It can provide a reference for the decision-making when developing maintenance policies.

A Combined Maintenance Strategy Considering Spares, Buffer, and Quality

This paper studies an innovative maintenance model for an upstream machine in a common production system. Multiple system-wise features are integrated in the model, including maintenance, spare parts, buffer inventory, and product quality. The objective is to minimize the system expected cost rate by determining the optimal inspection interval, preventive maintenance threshold, corrective maintenance threshold, reorder level of spare parts, maximum stock level of spare parts, and maximum inventory level of the buffer. In this maintenance model, both the hazard rate and the product qualification rate can trigger maintenance activities. The well-known proportional hazard model (PHM) is adopted to describe the state of the upstream machine. The effect of machine state on product quality is explicitly characterized. Due to the complexity of the mathematical model, simulation and a genetic algorithm are employed to determine the optimal solution. A case study of bearings is presented to demonstrate the performance of the proposed maintenance policy. The results show that this policy is practical and can reduce system cost significantly.

Maintenance Optimization for Two-Component Series Systems With Degradation Dependence

This paper proposes a model of maintenance optimization for a system consisting of two dependent components in long-term operation, where both components are subject to dependent degradation. Gamma process is used to model the degradation, and Frank Copula is applied to describe the degradation dependence between the two components. We then consider degradation dependence to optimize maintenance strategy for the system to maximize its availability. The improved Artificial Bee Colony (ABC) algorithm is used to jointly determine inspection interval, opportunistic and preventive maintenance thresholds of the system. Finally, an example is provided to validate the proposed model.

Reliability and maintenance analysis of a degradation-threshold-shock model for a system in a dynamic environment

In this paper, a degradation-threshold-shock model for a system in a dynamic environment is studied. Unlike most existing works assuming the independence between different failure mechanisms, this study considers a two-fold stochastic dependence between the degradation process and the shock arrival process. First, the evolutions of the two processes depend on the changing environment; secondly, shocks may trigger the system failure or increase the degradation level alternatively. The degradation is generally described by a monotone Stochastic process. Upon periodical inspection, the system is preventively replaced whenever its degradation level exceeds a pre-determined threshold or failure occurs. Under this policy, the reliability measures, the maintenance costs in the short-run and long-run, and the optimization of the maintenance cost with respect to the decision parameters: the preventive maintenance threshold and the inspection period are investigated. Theoretical results are presented and numerical examples are given to illustrate the applicability of the proposed model.

Condition-based maintenance optimization for continuously monitored degrading systems under imperfect maintenance actions

Condition-based maintenance (CBM) is receiving increasing attention in various engineering systems because of its effectiveness. This paper formulates a new CBM optimization problem for continuously monitored degrading systems considering imperfect maintenance actions. In terms of maintenance actions, in practice, they scarcely restore the system to an as-good-as new state due to residual damage. According to up-to-data researches, imperfect maintenance actions are likely to speed up the degradation process. Regarding the developed CBM optimization strategy, it can balance the maintenance cost and the availability by the searching the optimal preventive maintenance threshold. The maximum number of maintenance is also considered, which is regarded as an availability constraint in the CBM optimization problem. A numerical example is introduced, and experimental results can demonstrate the novelty, feasibility and flexibility of the proposed CBM optimization strategy.