Optimal Bayesian maintenance policy for a gearbox subject to two dependent failure modes

Most maintenance optimization models of gear systems have considered single failure mode. There have been very few papers dealing with multiple failure modes, considering mostly independent failure modes. In this paper, we present an optimal Bayesian control scheme for early fault detection of the gear system with dependent competing risks. The system failures include degradation failure and catastrophic failure. A three‐state continuous‐time–homogeneous hidden Markov model (HMM), namely the model with unobservable healthy and unhealthy states, and an observable failure state, describes the deterioration process of the gear system. The condition monitoring information as well as the age of the system are considered in the proposed optimal Bayesian maintenance policy. The objective is to maximize the long‐run expected average system availability per unit time. The maintenance optimization model is formulated and solved in a semi‐Markov decision process (SMDP) framework. The posterior probability that the system is in the warning state is used for the residual life estimation and Bayesian control chart development. The prediction results show that the mean residual lives obtained in this paper are much closer to the actual values than previously published results. A comparison with the Bayesian control chart based on the previously published HMM and the age‐based replacement policy is given to illustrate the superiority of the proposed approach. The results demonstrate that the Bayesian control scheme with two dependent failure modes can detect the gear fault earlier and improve the availability of the system.     

Optimal inspection policies with predictive and preventive maintenance

A model is proposed to study the inspection and maintenance policy of systems whose failures can be detected only by periodic tests or inspections. Using predictive techniques, the time of the system failure can be predicted for some failure modes. If the system is found failed in an inspection, a corrective maintenance action is carried out. If the system is in a good condition but the predictive test diagnoses a failure in the period until the next inspection, then the system is replaced. The cost rate function is obtained for general distribution function of the signal time of a future failure and for one specific distribution function recently proposed. An algorithm is presented to find the optimal time between inspections and predictive tests and the optimal system replacement times for an age replacement policy. Numerical experiments illustrate the model.     

An inspection model for a multi‐component system subject to 2 types of failures

Group maintenance is common and of significant importance for complex systems in industrial applications. This paper proposes a novel inspection and replacement model for a multi‐component system whose components are all subject to 2 typical failure modes, ie, catastrophic failure and minor failure. A catastrophic failure stops the system immediately, whereas a minor failure is not fatal and could only be identified by periodic inspection. At either a catastrophic or a minor failure, replacement is immediate. The maintenance cost model could be constructed through calculating the distribution of the “forward time”, which denotes the time elapse to a catastrophic failure since the previous inspection. The objective of this paper is to minimize the expected cost per unit time of the system via the optimization of the inspection interval. A case study on offshore wind turbine blades is presented to illustrate the maintenance model.     

Quality issue in forecasting problem of production and maintenance policy for production unit

In this study, we consider an unreliable deteriorating production system that produces conforming and non-conforming products to satisfy a random demand under a given service level and during a finite horizon. The production system is subjected to a failure-prone machine. The quality of the produced products is affected by the machine deterioration since the rate of defectives increases as the deterioration increases. Preventive maintenance actions can be piloted on the production system to reduce the influence of deterioration and the defective rate. A joint control policy is based on a stochastic production and maintenance planning problem with goals to determine, firstly, the economic plan of production and secondly, the optimal maintenance strategy. The proposed jointly optimisation minimises the total cost of production, inventory, maintenance and defectives. A failure rate and quality relationship are defined to show the influence of the production rates variation on the failures rate as well as on the defective rate. A numerical example and an industrial case study are adopted to illustrate the proposed approach and a sensitivity analysis to validate the jointly optimisation.     

On preventive maintenance policy of a critical reliability level for system subject to degradation

Conventional preventive maintenance (PM) policies generally hold same time interval for PM actions and are often applied with known failure modes. The same time interval will give unavoidably decreasing reliabilities at the PM actions for degradation system with imperfect PM effect and the known failure modes may be inaccurate in practice. Therefore, field managers would prefer policy with an acceptable reliability level to keep system often at a good state.A PM policy with the critical reliability level is presented to address the preference of field managers. Through assuming that system after a PM action starts a new failure process, a parameter so-called degradation ratio is introduced to represent the imperfect effect. The policy holds a law that there is same number of failures in the time intervals of various PM cycles, and same degradation ratio for the system reliability or benefit parameters such as the optimal time intervals and the hazard rates between the neighboring PM cycles. This law is valid to any of the failure modes that could be appropriately referred as a ‘general isodegrading model’, and the degradation ratio as a ‘general isodegrading ratio’. In addition, life cycle availability and cost functions are derived for system with the policy. An analysis of the field data of a loading and unloading machine indicates that the reliability, availability and cost in life cycle might be well modeled by the present theory and approach.     

Optimal maintenance models with minimal repair, periodic overhaul and complete renewal

This paper investigates the maintenance decision situation in which three actions, minimal repair, periodic overhaul and complete renewal, may be applied to the system under consideration. A new mathematical model is proposed to describe system improvement due to the maintenance action of an overhaul that differs from the virtual age approach by considering a direct reduction on the system's failure rate. Based on this improvement model, two cost models for determining the optimal overhaul interval and the number of overhauls in a renewal cycle, that minimize the expected unit-time cost or the total discounted cost, are established. Existence conditions of optimal solutions are obtained and special cases of the two cost models are discussed.     

Optimal replacement and overhaul decisions with imperfect maintenance and warranty contracts

In this article, we develop a model to help a maintenance decision making situation of a given equipment. We propose a novel model to determine optimal life-cycle duration and intervals between overhauls by minimizing global maintenance costs. We consider a situation where the costumer, which owns the equipment, may negotiate a better warranty contract by offering an improved preventive maintenance program for the equipment. The equipment receives three kind of actions: repairs, overhauls, and replacement. An overhaul represents an imperfect maintenance action, that is, the failure rate is improved but not a point that the equipment is as good as new. Corrective maintenance actions are minimal, in the sense that the failure rate after each repair is the same as before the failure. The proposed strategy surpasses others seen in the literature since it considers at the same time the warranty negotiation situation and the optimal life-cycle duration under imperfect preventive actions. We also propose a simplified approach that facilitates the task of implementing the method in standard solvers.     

Influence of maintenance policies on multi-stage manufacturing systems in dynamic conditions

Manufacturing systems are subject to a degradation process that leads to machine failure if no action is taken. Machine failures reduce the performance of the manufacturing system with loss of profits. The research proposed here concerns the evaluation of the manufacturing system performance in dynamic conditions when different maintenance policies are implemented in a multi-machine manufacturing system controlled by multi-agent-architecture. There are two extreme maintenance policies that can be applied: no preventive maintenance, where action is taken on the failure state, and intensive preventive maintenance, which can eliminate unforeseen failures, but at a high cost. Dynamic policy maintenance is proposed to reduce the number of maintenance operations of the preventive policy. A discrete simulation environment has been developed in order to investigate the performance measures and the indexes of the costs of maintenance policies. The simulations have been conducted for several levels of mix, product demand and working time uncertainty. The simulation results show that the proposed approach leads to better performance for the manufacturing system and reduces the number of maintenance operations (cost index of the maintenance policy), except in the case of the mean time between failure, which is characterised by a very low standard deviation.     

Evaluation of maintenance policies for equipment subject to quality shifts and failures

We develop an economic model for the optimization of maintenance procedures in a production process with two quality states. In addition to deteriorating with age, the equipment may experience a jump to an out-of-control state (quality shift), which is characterized by lower production revenues and higher tendency to failure. The times to quality shift and failure are allowed to be generally distributed random variables. We consider two types of maintenance: minimal maintenance (MM) that upgrades the quality state of the equipment without affecting its age and perfect preventive maintenance (PM) that fully upgrades the equipment to the as-good-as-new condition. We derive the expression for the expected profit per time unit and we investigate, through a large number of numerical examples, the type of the optimal solution. It is concluded that in practically every case the optimal maintenance policy is an extreme one: it either calls for immediate MM as soon as a quality shift occurs (active policy) or it allows operation in the out-of-control state until the time of a scheduled PM action (passive policy).     

A study of availability-centered preventive maintenance for multi-component systems

This paper studies preventive maintenance (PM) in simultaneously considering three actions, mechanical service, repair and replacement for a multi-components system based on availability. Mechanical service denotes the activities including lubricating, cleaning, checking and adjusting, etc. which is set to alleviate strength degradation. Repair is defined on that not only slow down the degraded velocity but also restore the degraded strength partly. Replacement is settled to recover a component to its original condition. According to the definitions, the degradation of components is analyzed from its failure mechanisms and the improvements of various actions to it in reliability were measured by using two improved factors. Following the proposed model of reliability, the mean-up and mean-down times of each component are also investigated and the replacement intervals of components are determined based on availability maximization. Here, the minimum one among the intervals is chosen as the PM interval of system for programming the periodical PM policy. The selection of action for the components on every PM stage is decided by maximizing system benefit in maintenance. Repeatedly, the scheduling is progressed step by step and is terminated until the system extended life reaching to its expected life. The complete schedule provides the information, the actions adopted for the components, the availability and the total cost of system on each stage. Validly, a multi-components system is used as an example to describe the proposed algorithm.     

Optimal replacement policy and inspection interval for condition-based maintenance

In condition-based maintenance (CBM), replacement policy is often defined as a rule for replacement or leaving an item (or a system) in operation until the next inspection, depending on monitoring results. The criterion for determining the optimal threshold for replacement, also known as optimal control limit, is to minimise the average maintenance costs per unit time due to preventive and failure replacements over a long time horizon. On the one hand, higher frequency of inspections provides more information about the condition of the system and, thus, maintenance actions are performed more effectively, namely, unnecessary preventive replacements are avoided and the number of replacements due to failure is reduced. Consequently, the cost associated to failure and preventive replacements are decreased. On the other hand, in many real cases, inspections require labour, specific test devices, and sometimes suspension of the operations and, thus, as the number of inspections increase, the inspection cost also increases. In this paper, preventive and failure replacement costs as well as inspection cost are taken into account to determine the optimal control limit and the optimal inspection interval simultaneously. The proposed approach is illustrated through a numerical example.     

基于遗传算法和状态信息的多设备混联系统维护调度优化

针对多设备混联系统维护优化的建模复杂性,系统分析了设备间的相互依赖性,建立了混联系统的维护调度模型。首先利用威布尔分布模拟设备的衰退过程;定义小修、大修和更换3种维护方式,以及3种维护方式对设备故障率的影响;考虑故障成本、维护成本、资源成本和停机成本,建立了系统一次维护活动的费用模型。其次,基于每次维护活动的费用模型,建立了系统维护多阶段的总费用率模型。最后,通过算例证明了提出的多设备混联系统维护调度优化模型的有效性     

Determination of Pareto frontier in multi-objective maintenance optimization

The objective of a maintenance policy generally is the global maintenance cost minimization that involves not only the direct costs for both the maintenance actions and the spare parts, but also those ones due to the system stop for preventive maintenance and the downtime for failure. For some operating systems, the failure event can be dangerous so that they are asked to operate assuring a very high reliability level between two consecutive fixed stops. The present paper attempts to individuate the set of elements on which performing maintenance actions so that the system can assure the required reliability level until the next fixed stop for maintenance, minimizing both the global maintenance cost and the total maintenance time. In order to solve the previous constrained multi-objective optimization problem, an effective approach is proposed to obtain the best solutions (that is the Pareto optimal frontier) among which the decision maker will choose the more suitable one. As well known, describing the whole Pareto optimal frontier generally is a troublesome task. The paper proposes an algorithm able to rapidly overcome this problem and its effectiveness is shown by an application to a case study regarding a complex series-parallel system.     

A study of time‐between‐events control chart for the monitoring of regularly maintained systems

Owing to usage, environment and aging, the condition of a system deteriorates over time. Regular maintenance is often conducted to restore its condition and to prevent failures from occurring. In this kind of a situation, the process is considered to be stable, thus statistical process control charts can be used to monitor the process. The monitoring can help in making a decision on whether further maintenance is worthwhile or whether the system has deteriorated to a state where regular maintenance is no longer effective. When modeling a deteriorating system, lifetime distributions with increasing failure rate are more appropriate. However, for a regularly maintained system, the failure time distribution can be approximated by the exponential distribution with an average failure rate that depends on the maintenance interval. In this paper, we adopt a modification for a time‐between‐events control chart, i.e. the exponential chart for monitoring the failure process of a maintained Weibull distributed system. We study the effect of changes on the scale parameter of the Weibull distribution while the shape parameter remains at the same level on the sensitivity of the exponential chart. This paper illustrates an approach of integrating maintenance decision with statistical process monitoring methods. Copyright © 2008 John Wiley & Sons, Ltd.     

用加权最小二乘法评价公共汽车预防维修效果

本文采用加权最小二乘法拟合可修系统失效点过程数据到幂律模型以评价预防维修的质量。权函数与正态密度函数成正比,它赋予靠近维修时间的失效数据大的权值,而赋予远离维修时间的失效数据小的权值。分析了一个实际案例,对比了加权与不加权的最小二乘法所得到的结果。结果表明,对于维修质量评价,加权的最小二乘法优于普通的最小二乘法。     

Risk Failure Deployment: A novel integrated tool to prioritize corrective actions in failure mode and effects analysis

In this paper, a novel integrated tool for failure mode and effects analysis (FMEA), opportunely named Risk Failure Deployment (RFD), which is able to evaluate the most critical failure modes and provide analyst with a practical and step-by-step guidance by selecting the most effective corrective actions for removal/mitigation process of root causes, is presented. Thanks to the modification of the framework of the Manufacturing cost deployment (MCD) and to its well-structured use of matrices, the novel RFD is able both to handle the dependencies and interactions between different and numerous failures and to evaluate the most critical ones on the basis of the risk priority number (RPN). Thereafter, the logical relationship between root causes and failure modes is assessed. Successively, the prioritization of corrective actions that are the most suitable for root causes is executed using not only the RPN but also other criteria, such as the economic aspect and the ease of implementation, that are unavoidable to execute a rational and effective selection of improvement activities. The effectiveness and usefulness in practice of the original tool for the prioritization of corrective actions to mitigate the risks due to failure modes collected during FMEA are presented in a case study.     

Two types of learning effects on maintenance activities

This paper studies a manufacturer with a system prone to failure. The manufacturer performs two types of maintenance activities: preventive maintenance (PM), performed periodically, resets the system, and Minimal Repair (MR), performed after breakdowns, restores the system to working condition. It is assumed that two different types of learning take place: (i) repetition learning: due to the repetitive nature of PM, the manufacturer gains experience and learns to perform the PM activities faster and at a lower cost and (ii) failure learning: each failure gives the manufacturer the opportunity to find the root causes, to learn from mistakes and to improve the system. This paper, the first one to quantify failure learning in maintenance literature, assumes that such learning can then be applied during the next PM activity, which brings down the failure rate for the next PM cycle. For the increasing failure rate case, repetition learning increases the PM frequency, whereas failure learning causes the manufacturer to reduce the optimal number of PM activities. However, for the constant failure rate, repetition learning has no effect on the PM frequency, whereas failure learning may actually increase it.     

Reliability Analysis and Condition‐based Maintenance for Failure Processes with Degradation‐dependent Hard Failure Threshold

In this study, we introduce reliability models for a device with two dependent failure processes: soft failure due to degradation and hard failure due to random shocks, by considering the declining hard failure threshold according to changes in degradation. Owing to the nature of degradation for complex devices such as microelectromechanical systems, a degraded system is more vulnerable to force and stress during operation. We address two different scenarios of the changing hard failure threshold due to changes in degradation. In Case 1, the initial hard failure threshold value reduces to a lower level as soon as the overall degradation reaches a critical value. In Case 2, the hard failure threshold decreases gradually and the amount of reduction is proportional to the change in degradation. A condition‐based maintenance model derived from a failure limit policy is presented to ensure that a device is functioning under a certain level of degradation. Finally, numerical examples are illustrated to explain the developed reliability and maintenance models, along with sensitivity analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

Joint optimisation of maintenance and production policies considering random demand and variable production rate

This paper deals with a randomly failing manufacturing system M1 which has to satisfy a random demand during a finite horizon given a required service level. To help meet this demand, subcontracting is used through another production system M2. M1 operates with a variable production rate and its failure rate depends on both time and the production rate. In these conditions, as a first step, we establish a preliminary production plan corresponding to a given service level. In a second stage, we integrate the effect of the machine degradation introducing a unitary degradation cost. The optimal production plan is then obtained by minimising the sum of the production, the inventory and the degradation costs. In the final stage, we propose another optimal plan combined with a preventive maintenance policy aiming at reducing the machine degradation while minimising the total cost including the production, inventory and maintenance costs.     

Optimizing preventive maintenance for mechanical components using genetic algorithms

This paper presents periodic preventive maintenance (PM) of a system with deteriorated components. Two activities, simple preventive maintenance and preventive replacement, are simultaneously considered to arrange the PM schedule of a system. A simple PM is to recover the degraded component to some level of the original condition according to an improvement factor which is determined by a quantitative assessment process. A preventive replacement is to restore the aged component by a new one. The degraded behavior of components is modeled by a dynamic reliability equation, and the effect of PM activities to reliability and failure rate of components is formulated based on age reduction model. While scheduling the PM policy, the PM components within a system are first identified. The maintenance cost and the extended life of the system under any activities-combination, which represents what kind of activities taken for these chosen components, are analyzed for evaluating the unit-cost life of the system. The optimal activities-combination at each PM stage is decided by using genetic algorithm in maximizing the system unit-cost life. Repeatedly, the PM scheduling is progressed to the next stage until the system's unit-cost life is less than its discarded life. Appropriately a mechatronic system is used as an example to demonstrate the proposed algorithm.