Condition-based Maintenance Policy Research Articles

Joint optimization of maintenance and spares inventory policy for a series-parallel system considering dependent failure processes

This paper investigates the joint optimization of condition-based opportunistic maintenance and spare inventory policies for a series-parallel system consisting of software and components. Software failure follows a homogeneous Poisson process. Components are subject to mutually dependent competing failure processes. When the software failure occurs, an opportunistic inspection will be implemented for the components. Besides the maintenance policy, the (s, S) inventory policy is applied for components. The maintenance and order decisions will be made according to the conditions of the components and inventory level at each inspection. The state transition probabilities and expected sojourn times can be obtained by the formulated semi-Markov decision process. The optimal inspection interval, the preventive replacement threshold of the component, and the order point can be derived by minimizing the expected average cost rate. Finally, the effectiveness and superiority of the proposed joint optimization model are verified by an illustrative example.

Joint optimization of condition-based maintenance policy and buffer capacity for a two-component self-repairable serial system

This paper investigates a self-repairable serial system with two components and a buffer. Competitive failure processes are considered due to the internal degradation and external shock processes of components. The system reliability is calculated based on the integration of the internal degradation process and external shock process. When one of the components deteriorates to the PM or CM thresholds, it is restored to an imperfect state under dynamic time limitations based on the previous internal degradation and external shocks. As for the other component, it needs to be repaired or not according to the reliability of the component; it needs to be shut down or not based on the buffer status and the allocation of the component in the system. The optimal initial buffer capacity setting and PM threshold at minimum cost are found by minimizing the system's total cost in a given running cycle. Finally, numerical and case studies are provided to demonstrate the feasibility and superiority of the presented model.

Condition-based maintenance policy for systems under dynamic environment

This paper addresses the challenge of optimizing maintenance for systems with varying degradation characteristics in dynamic environment. The focus is on repairable systems, where degradation is characterized by a Wiener process that incorporates the dynamic influence of the environment. We investigate a condition-based maintenance model aiming at minimizing the expected cost over a finite and infinite horizon. Firstly, the model considers the evolution of environment as a Markov process, which influences the drift parameter in the Wiener process. The choice between a corrective and preventive replacement rests on the periodic inspections on the system and environment. Subsequently, the maintenance model is formulated in the framework of Markov decision process. Meanwhile, the backward dynamic programming algorithm and value iteration algorithm are employed to gain the optimal maintenance policies over the finite and the infinite planning horizons, respectively. Finally, the proposed model is further explained with concrete examples and a comprehensive sensitivity analysis. Numerical results clearly demonstrate notable variations in the optimal maintenance strategies in different periods and underscore the importance of taking proactive maintenance measures in harsh environmental conditions, even if the degradation level of the system is relatively low.

Joint optimization of inspection and condition-based maintenance for a deteriorating product under extended warranty

Condition-based maintenance (CBM) has been widely applied in engineering practice, but it has been rarely integrated into extended warranty policies. When the inspection cost is high, it becomes important to schedule the inspection plan when making CBM decisions. This paper jointly optimizes inspection and CBM for a deteriorating product under extended warranty. The deterioration of the product is characterized as a non-stationary gamma process. At each inspection epoch, the decision maker needs to determine whether to repair the product and when to perform the next inspection. The objective is to simultaneously optimize the inspection policy and the maintenance policy that minimize the warranty servicing cost. The joint optimization problem is formulated by stochastic dynamic programming. The optimal policy is proven to be of a control-limit form. A backward induction algorithm integrating the obtained structural properties is proposed to find the optimization results. A numerical example is conducted to illustrate the effectiveness of the proposed approach. A graphical representation of the obtained policy is provided to support practical maintenance implementation. The comparison with a popular CBM policy confirms the superiority of the proposed policy.

A dynamic condition-based maintenance policy for heterogeneous-wearing tools with considering product quality deterioration

The wear of a cutting tool can lead to tool failure and product quality deterioration, and thus timely maintenance of tools is crucial. Meanwhile, the wear of tools from a same population usually exhibits heterogeneous patterns. Therefore, this paper proposes a dynamic condition-based maintenance (CBM) policy for heterogeneous-wearing tools with considering the product quality deterioration caused by tool wear. The tool wear is modelled by an Inverse Gaussian (IG) process, and the wear rate is assumed to be a random variable to characterise the heterogeneity among tool wear processes. The posterior distribution of reciprocal of tool wear rate is dynamically estimated using the online wear data based on a Bayesian approach. Moreover, the impact of tool wear on product quality deterioration is modelled. The IG process is discretized into a discrete time Markov chain (DTMC). Under the frame of the DTMC, a cost function, containing product quality loss, preventive maintenance (PM) cost and corrective maintenance cost, is developed to determine the optimal PM threshold. The cost function updates dynamically with the dynamic estimation of tool wear rate and thus enables the optimal PM threshold to be dynamically revised. The effectiveness of the proposed CBM policy is demonstrated through a case study.

Quality driven maintenance policies for a deteriorating system subject to non-self-announcing failures

. In this study, we develop condition-based maintenance policies for a multi-state system subject to continuous-time Markovian deterioration that can result in non-self-announcing degradation including failure. Periodic inspections reveal the true state of the system; “good”, “medium”, “poor”, or “failed”. Upon receiving this piece of information, one of “do-nothing”, “minor repair”, “major repair”, “fix repair”, or “replace” maintenance actions is taken. On one hand, the system brings monetary rewards commensurate with system state–different rewards are earned per unit time spent in different states. On the other hand, quality loss that results from degraded system state is converted into monetary units–inspection and maintenance costs. Therefore, our objective is to determine the optimum inspection period and the corresponding maintenance policy that maximizes the expected long-run profit rate. We provide numerical examples to conduct sensitivity of the optimum inspection period and policy to system parameters, and to present the practical utility of our results.

Adopting New Machine Learning Approaches on Cox’s Partial Likelihood Parameter Estimation for Predictive Maintenance Decisions

The Proportional Hazards Model (PHM) under a Condition-Based Maintenance (CBM) policy is used by asset-intensive industries to predict failure rate, reliability function, and maintenance decisions based on vital covariates data. Cox’s partial likelihood optimization is a method to assess the weight of time and conditions into the hazard rate; however, parameter estimation with diverse covariates problem could have multiple and feasible solutions. Therefore, the boundary assessment and the initial value strategy are critical matters to consider. This paper analyzes innovative non/semi-parametric approaches to address this problem. Specifically, we incorporate IPCRidge for defining boundaries and use Gradient Boosting and Random Forest for estimating seed values for covariates weighting. When applied to a real case study, the integration of data scaling streamlines the handling of condition data with diverse orders of magnitude and units. This enhancement simplifies the modeling process and ensures a more comprehensive and accurate underlying data analysis. Finally, the proposed method shows an innovative path for assessing condition weights and Weibull parameters with data-driven approaches and advanced algorithms, increasing the robustness of non-convex log-likelihood optimization, and strengthening the PHM model with multiple covariates by easing its interpretation for predictive maintenance purposes.

A Condition-Based Maintenance Policy Considering Batch Sizes for Warm Standby Systems With Priority to Repair

A Condition-Based Maintenance Policy Considering Batch Sizes for Warm Standby Systems With Priority to Repair

A condition-based maintenance policy with non-periodic inspection for k-out-of-n: G systems

A condition-based maintenance policy with non-periodic inspection for k-out-of-n: G systems

Optimal condition-based maintenance policy for multi-component repairable systems with economic dependence in a finite-horizon

Optimal condition-based maintenance policy for multi-component repairable systems with economic dependence in a finite-horizon

A condition-based maintenance policy for reconfigurable multi-device systems

A condition-based maintenance policy for reconfigurable multi-device systems

Dynamic loading and condition-based maintenance policies for multi-state systems with periodic inspection

Dynamic loading and condition-based maintenance policies for multi-state systems with periodic inspection

Hierarchical condition-based maintenance planning for corrosion process considering natural environmental impact

Condition-based maintenance (CBM) powered by corrosion inspection is vital to ensure the service safety and availability of equipment structure, especially in harsh natural environments. Preventive repair and coating are two effective measures widely adopted in corrosion-centered CBM implementation, whose collaborative planning, however, is rarely reported in corrosion control models. This paper proposes a hierarchical CBM policy oriented to gradual corrosion deterioration, which quantifies the comprehensive effect of corrosive environment and uncertain coating lifetime. The long-term corrosion is governed by a generalized stochastic process incorporating multiple environmental factors. Inspections are equally spaced to reveal corrosion severity, followed by a combination of recoating, imperfect repair and replacement to restore structure health. In particular, repair is executed if the accumulated corrosion exceeds a safe control limit, and replacement is immediate if (a) the repair number attains a pre-set threshold, and (b) the residual corrosion after repair remains above the limit. The impact of random coating lifetime on CBM performance is also analytically analyzed. The long-run maintenance cost is minimized through the joint optimization of inspection interval, corrosion control limit, and imperfect repair number. The model applicability is demonstrated through numerical experiments conducted on ship deck structures under marine environment.

Joint optimization of performance-based contracting, condition-based maintenance and spare parts inventory for degrading production systems

As a novel supporting approach, performance-based contracting (PBC) ties the service supplier’s compensation to the performance outcome of the system owned by the customer. It enables the service supplier to implement an effective maintenance and spare parts inventory policy so as to improve system performance. In this paper, we propose a principal–agent modeling framework for deteriorating production systems operating under PBC, with the objective of maximizing the expected utilities of both stakeholders. The customer (principal) offers PBC with a fixed payment plus performance incentive form to the service supplier (agent), who in turn implements a condition-based maintenance (CBM) policy based on the system prognostic condition at periodic inspections, and sets an investment level of spare parts inventory. Considering the partial observability of the service supplier’s actions, the optimal combination of performance incentive in PBC provided by the customer, and the joint CBM and spare parts inventory policy implemented by the service supplier, are determined through a two-stage and heuristic approach. Finally, a numerical example and sensitivity analysis based on a real-world scenario are presented to illustrate and verify the applicability of the proposed model.

An intelligent maintenance policy for a latent degradation system

This paper looks at the challenge of making maintenance decisions for deteriorating systems when the degradation process leading to failure cannot be directly observed or measured. In this scenario, the system’s health is monitored by observing the progression of a degradation-related marker index, which can be obtained through inspections. To model this configuration, a bivariate gamma process is employed. One component represents the marker process, while the other represents the degradation process, which dictates the time of failure. Two condition-based maintenance (CBM) policies are proposed and analyzed. The first policy is based on a conventional decision structure, utilizing a fixed preventive threshold directly applied to the measured process. The second policy relies on monitoring data related to the marker process to estimate the level of latent degradation at inspections. We demonstrate that the second policy is equivalent to a policy employing an adaptive preventive threshold that sequentially evolves. We provide insights into some key properties associated with this approach. The expected cost rate is calculated and employed for policy optimization. Additionally, a numerical study is presented that showcases the practical implementation of the method and highlights the effectiveness of the second approach, even when the correlation between degradation and the marker process is low.

Optimal condition-based maintenance policy for leased equipment considering hybrid preventive maintenance and periodic inspection

Innovations in technology have made the structure of leased equipment more complex, which poses a challenge for lessors to develop maintenance policies. In view of the situation that the single periodic preventive maintenance (PM) policy during leasing activities may cause excessive or insufficient maintenance on the leased equipment, a condition-based maintenance (CBM) policy considering hybrid preventive maintenance (HPM) and periodic inspections is proposed. This policy contains imperfect preventive maintenance (IPM), preventive replacement (PR) and corrective maintenance (CM). The lessor can decide to take maintenance actions depending on whether the state of the equipment reaches the corresponding maintenance threshold. The warranty period of the leased equipment is also considered. To seal the deal, the lessor will give a discount on the rental to cover the CM costs and penalties out of the warranty period. To minimize the lessor's costs, we propose a CBM decision model to determine the optimal inspection period, PM threshold and PR period. The results show that the HPM policy can reduce leasing costs by about 5 –15 % for the lessor compared to that of the single PM policy.

Maintenance policy of degradation components based on the two-phase Wiener process

This paper proposes a condition-based maintenance policy for the two-phase Wiener degradation process components. The main contribution of this article is to provide the time distribution of degradation failures for the two-phase Wiener process degradation component, as well as the modeling and solving methods for two-phase maintenance. The two-phase maintenance policy includes two-phase inspection and preventive replacement maintenance operations. The established optimization maintenance policy model aims to minimize long-term operation costs. The specific cost calculation equation and the solution method of the maintenance model are given. The feasibility of the maintenance policy model is verified using the two-phase degradation data of the Liquid Coupling Devices. The Particle swarm optimization algorithm can stably solve the described problem, and the results show that the two-phase maintenance policy can be more economical and improve components availability. After that, we also analyzed the impact of the cost parameters on the maintenance policy through sensitivity analysis.

Condition-Based Maintenance for Performance Degradation Under Nonperiodic Unreliable Inspections

With the development of monitoring technology, increasing attention has been paid to condition-based maintenance (CBM). Also, if condition information for maintenance can be obtained with fewer inspections, the cost of the entire maintenance process could be reduced. However, in application, the monitoring equipment cannot maintain always a reliable operating state, for example, due to various uncertain factors, such as sensor errors, component tolerances, and environment disturbances, the inspections from the sensors are often unreliable. Motivated by these simple observations, we propose a non-periodic condition-based maintenance policy under unreliable inspections. The time interval of the non-periodic inspections is obtained via an inspection scheduling function. The unknown parameters of the component degradation process are updated by gradient descent, while simultaneously the maintenance decision variables are adjusted. A catastrophe strategy-based particle swarm optimization is used to set the optimal decision variables by minimizing the long-run cost rate. Application to laser degradation data illustrates the effectiveness of the proposed method.

Optimal switching and condition-based maintenance of cold standby systems subject to competitive failure and imperfect switchover

Cold standby redundant structures can improve system reliability and availability but are subjected to internal degradation and external shocks during operation. Thus, the switching process in a standby system is prone to failures. This study investigates the optimal switching and condition-based maintenance (CBM) decision of a two-unit cold standby system subject to mutually dependent competitive failure processes with an imperfect switchover. First, periodic switching and offline CBM policies under imperfect switchover are proposed; second, the reliability models of competitive failure—between soft failure caused by system degradation subject to nonfatal shock and hard failure caused by fatal shock—are established. An iterative model of the system state probability distribution is subsequently derived by analysing the characteristics of state transitions in alternate use and maintenance of the active and standby units. An analytical decision model is also established to minimise the average cost rate in a finite horizon to obtain the optimal switching period and maintenance threshold. Finally, a case study of a coal mine main ventilator system validates the proposed model.

Deep reinforcement learning for cost-optimal condition-based maintenance policy of offshore wind turbine components

The high cost of operation and maintenance can impede the development of offshore wind turbines (OWTs). With advancements in detection technology, condition-based maintenance (CBM) has emerged as a promising approach to managing maintenance. Numerous CBM polices have been studied to achieve a cost-effective maintenance. However, little research has been conducted on discovering the cost-optimal CBM policy for OWTs. With this motivation, a deep reinforcement learning (DRL) framework for exploring the cost-optimal CBM policy is proposed in this paper. Four CBM policies (i.e. uniform or dynamic inspection interval, and fixed or adaptive repair threshold) are formulated as the Markov decision process model. Two DRL algorithms (deep Q network and proximal policy optimization) are applied to derive the dynamic inspection interval and the adaptive repair threshold. To illustrate this framework, a fatigue OWT component is used as an example. The four policies are optimized under varying conditions to find the cost-optimal CBM policy. Moreover, performance comparison of DRL algorithms is performed. The case study illustrates the advantage of DRL in deriving optimal maintenance policies for fatigue-sensitive OWT components and highlights the interrelationship between maintenance policy and economic performance. This paper concludes by discussing the effect of cost elements on the CBM policies.