Condition based maintenance optimization for multi-component systems using proportional hazards model

The objective of condition based maintenance (CBM) is typically to determine an optimal maintenance policy to minimize the overall maintenance cost based on condition monitoring information. The existing work reported in the literature only focuses on determining the optimal CBM policy for a single unit. In this paper, we investigate CBM of multi-component systems, where economic dependency exists among different components subject to condition monitoring. The fixed preventive replacement cost, such as sending a maintenance team to the site, is incurred once a preventive replacement is performed on one component. As a result, it would be more economical to preventively replace multiple components at the same time. In this work, we propose a multi-component system CBM policy based on proportional hazards model (PHM). The cost evaluation of such a CBM policy becomes much more complex when we extend the PHM based CBM policy from a single unit to a multi-component system. A numerical algorithm is developed in this paper for the exact cost evaluation of the PHM based multi-component CBM policy. Examples using real-world condition monitoring data are provided to demonstrate the proposed methods.     

How heterogeneity influences condition-based maintenance for gamma degradation process

In many applications, units from the same population exhibit heterogeneity that they degrade with different rates due to random factors. This article studies how this heterogeneity in degradation influences condition-based maintenance (CBM) policy. Many CBM polices are developed based on gamma process because it is popularly used to characterise monotone degradation processes. In this study, we also model the unit’s degradation by gamma process. To account for the heterogeneity among units’ degradation, we incorporate a random effect parameter in the gamma process. Then the optimal policy for CBM is obtained through Markov decision process. We show that when heterogeneity exists, the transition probability of degradation state depends on both unit’s age and observed degradation level. And consequently, the optimal maintenance policy is a monotone control limit policy. We conduct extensive numerical experiments to validate and demonstrate our findings in depth.     

Optimal joint maintenance and operation policies to maximise overall systems effectiveness

In this paper, the problem of determining the optimal maintenance and operation policies for a multi-state, multi-stage machine maintenance problem is considered. This problem has been formulated in the literature as a Partially Observed Markov Decision Process (POMDP). A new formulation that explicitly ties maintenance, operation, and quality within the POMDP framework is provided. The new formulation maximises Overall Systems Effectiveness for an n-state system with multiple speed and maintenance actions. The model provides, for each time epoch, a set of optimal maintenance and production-rate actions. The decision-maker (controller) can select the optimal policy depending on the system state occupancy vector (belief state). A realistic numerical model is presented to demonstrate the model utility.     

A full history proportional hazards model for preventive maintenance scheduling

This paper is concerned with the development of a realistic preventive maintenance (PM) scheduling model. A heuristic approach for implementing the semi-parametric proportional-hazards model (PHM) to schedule the next preventive maintenance interval on the basis of the equipment's full condition history is introduced. This heuristic can be used with repairable systems and does not require the unrealistic assumption of renewal during repair, or even during PM. Two PHMs are fitted, for the life of equipment following corrective work and the life of equipment following PM, using appropriate explanatory variables. These models are then used within a simulation framework to schedule the next preventive maintenance interval. Optimal PM schedules are estimated using two different criteria, namely maximizing availability over a single PM interval and over a fixed horizon. History data from a set of four pumps operating in a continuous process industry is also used to demonstrate the proposed approach. The results indicate a higher availability for the recommended schedule than the availability resulting from applying the optimal PM intervals as suggested by using the conventional stationary models. © 1997 John Wiley & Sons, Ltd.     

Application of the weibull proportional hazards model to aircraft and marine engine failure data

The environment in which an equipment operates and associated diagnostic variables, such as metal particle level in engine oil, are factors that can influence an equipment's failure time. These factors can be incorporated into concomitant variable models such as the proportional hazards model (PHM), which has been widely used in medical research but not in engineering reliability. A Weibull PHM is applied to both aircraft engine failure data and marine gas turbine failure data. Examination of the residuals shows a good fit of the Weibull proportional hazards model to the data.     

Real-time health prognosis and dynamic preventive maintenance policy for equipment under aging Markovian deterioration

An often seen practice of preventive maintenance (PM) is to construct a machine's reliability model based on its historical failure records. The reliability model is then used to determine the PM schedule by minimizing the machine's long-run operation cost or average machine downtime. Machines in many hi-tech manufacturing sectors are using sophisticated sensor technologies to provide sufficient immediate online data for real-time observation of equipment condition. Not only is the historical data but also the real time condition now available for scheduling a more effective PM policy. This research is to determine an effective PM policy based on real-time observations of equipment condition. We first use the multivariate process capability index to integrate the equipment's multiple parameters into an overall equipment health index. This health index serves as the basis for real-time health prognosis under an aging Markovian deterioration model. A dynamic PM schedule is then determined based on the health prognosis.     

基于故障数据的设备运行可靠性分析与评估

基于故障数据,对设备运行可靠性进行了分析与评估。对某汽车制造企业的一台卧式加工中心的故障数据进行了统计与分析,形成观测样本,并拟合出了设备故障间隔时间的概率密度分布函数和累计分布函数曲线,从而推断得出其分布规律可能服从威布尔分布。然后通过对威布尔分布函数相关性进行检验,验证了该设备的故障间隔时间分布服从威布尔分布。最后根据统计结果计算得出了该设备的各项可靠性评估指标。     

Condition‐based Maintenance Optimization Using Neural Network‐based Health Condition Prediction

Artificial neural network (ANN)‐based methods have been extensively investigated for equipment health condition prediction. However, effective condition‐based maintenance (CBM) optimization methods utilizing ANN prediction information are currently not available due to two key challenges: (i) ANN prediction models typically only give a single remaining life prediction value, and it is hard to quantify the uncertainty associated with the predicted value; (ii) simulation methods are generally used for evaluating the cost of the CBM policies, while more accurate and efficient numerical methods are not available, which is critical for performing CBM optimization. In this paper, we propose a CBM optimization approach based on ANN remaining life prediction information, in which the above‐mentioned key challenges are addressed. The CBM policy is defined by a failure probability threshold value. The remaining life prediction uncertainty is estimated based on ANN lifetime prediction errors on the test set during the ANN training and testing processes. A numerical method is developed to evaluate the cost of the proposed CBM policy more accurately and efficiently. Optimization can be performed to find the optimal failure probability threshold value corresponding to the lowest maintenance cost. The effectiveness of the proposed CBM approach is demonstrated using two simulated degradation data sets and a real‐world condition monitoring data set collected from pump bearings. The proposed approach is also compared with benchmark maintenance policies and is found to outperform the benchmark policies. The proposed CBM approach can also be adapted to utilize information obtained using other prognostics methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Predictive maintenance policy for a gradually deteriorating system subject to stress

This paper deals with a predictive maintenance policy for a continuously deteriorating system subject to stress. We consider a system with two failure mechanisms which are, respectively, due to an excessive deterioration level and a shock. To optimize the maintenance policy of the system, an approach combining statistical process control (SPC) and condition-based maintenance (CBM) is proposed. CBM policy is used to inspect and replace the system according to the observed deterioration level. SPC is used to monitor the stress covariate. In order to assess the performance of the proposed maintenance policy and to minimize the long-run expected maintenance cost per unit of time, a mathematical model for the maintained system cost is derived. Analysis based on numerical results are conducted to highlight the properties of the proposed maintenance policy in respect to the different maintenance parameters.     

A partially observable simulation model for quality assurance policies

This paper presents a simulation model of a partially observable Markov decision process (POMDP) for quality assurance policies. The model may be used as a decision aid for evaluation and comparison of different quality policies. The decision maker must decide what quality policy to adopt: a 'do-nothing' policy, an appraisal policy that prevents the nonconforming products from reaching the customer, or a prevention policy that affects process performance and leads to long term improvements. The process performance is not observed directly but its effect on the quality of products is observed. The three policies are compared based on the incurred quality costs and the average outgoing quality. A case study in a fish processing plant is presented. It is shown that if costs are the only criteria for decision making then a prevention policy that leads to process improvement may not be the best policy to adopt. Money spent in this policy may never be regained. It is also shown that the merits of each quality policy depends on the actual quality level in each organization.     

Condition-based maintenance optimization by means of genetic algorithms and Monte Carlo simulation

Efficient maintenance policies are of fundamental importance in system engineering because of their fallbacks into the safety and economics of plants operation. When the condition of a system, such as its degradation level, can be continuously monitored, a Condition-Based Maintenance (CBM) policy can be implemented, according to which the decision of maintaining the system is taken dynamically on the basis of the observed condition of the system.In this paper, we consider a continuously monitored multi-component system and use a Genetic Algorithm (GA) for determining the optimal degradation level beyond which preventive maintenance has to be performed. The problem is framed as a multi-objective search aiming at simultaneously optimizing two typical objectives of interest, profit and availability. For a closer adherence to reality, the predictive model describing the evolution of the degrading system is based on the use of Monte Carlo (MC) simulation. More precisely, the flexibility offered by the simulation scheme is exploited to model the dynamics of a stress-dependent degradation process in load-sharing components and to account for limitations in the number of maintenance technicians available. The coupled (GA[plus ]MC) approach is rendered particularly efficient by the use of the ‘drop-by-drop’ technique, previously introduced by some of the authors, which allows to effectively drive the combinatorial search towards the most promising solutions.     

Condition based maintenance in the context of opportunistic maintenance

Condition based maintenance (CBM) uses the operating condition of a component to predict a failure event. Compared to age based replacement (ABR), CBM usually results in higher availability and lower maintenance costs, since it tries to prevent unplanned downtime and avoid unnecessary preventive maintenance activities for a component. However, the superiority of CBM remains unclear in multi‐component systems, in which opportunistic maintenance strategies can be applied. Opportunistic maintenance aims to group maintenance activities of two or more components in order to reduce maintenance costs. In a serial system, this may also result in less downtime of the production line. The aim of this paper is to examine the impact of opportunistic maintenance on the effectiveness of CBM. We simulate a small system consisting of three components in series and vary the number of components under a CBM policy, the length of the opportunistic maintenance zone, the cost benefits of grouping maintenance activities, and the chance of a failure occurrence within a preventive maintenance (PM) interval. The results show that within the current experimental settings, CBM remains cost effective in the multi‐component serial system, but is less effective than ABR in grouping maintenance activities. When the chance of failure is small and the length of the opportunistic maintenance zone is large, ABR may even be a better option if line productivity is important.     

A Modeling Approach to Maintenance Decisions Using Statistical Quality Control and Optimization

Maintenance concerns impact systems in every industry and effective maintenance policies are important tools. We present a methodology for maintenance decision making for deteriorating systems under conditions of uncertainty that integrates statistical quality control (SQC) and partially observable Markov decision processes (POMDPs). We use simulation to develop realistic maintenance policies for real‐world environments. Specifically, we use SQC techniques to sample and represent real‐world systems. These techniques help define the observation distributions and structure for a POMDP. We propose a simulation methodology for integrating SQC and POMDPs in order to develop and valuate optimal maintenance policies as a function of process characteristics, system operating and maintenance costs. A two‐state machine replacement problem is used as an example of how the method can be applied. A simulation program developed using Visual Basic for Excel yields results on the optimal probability threshold and on the accuracy of the decisions as a function of the initial belief about the condition of the machine. This work lays a foundation for future research that will help bring maintenance decision models into practice. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimal variability sensitive condition-based maintenance with a Cox PH model

Condition based maintenance (CBM) is an important maintenance strategy in practice. In this paper, we propose a CBM method to effectively incorporate system health observations into maintenance decision making to minimise the total maintenance cost and cost variability. In this method, the system degradation process is described by a Cox PH model and the proposed framework includes simulation of failure process and maintenance policy optimisation using adaptive nested partition with sequential selection (ANP-SS) method, which can adaptively select or create the most promising region of candidates to improve the efficiency. Different from existing CBM strategies, the proposed method relaxes some restrictions on the system degradation model and taking the cost variation as one of the optimisation objectives. A real industry case study is used to demonstrate the effectiveness of our framework.     

Optimal maintenance policy for permanently monitored infrastructure subjected to extreme events

Structures and infrastructure management is concerned with the actions required to maximize the system availability, which is seriously challenged by structural deterioration as a result of the normal use or due to external demands imposed by adverse environmental conditions. Given the large uncertainty in the system's performance through life, an optimal maintenance policy requires both permanent monitoring and a cost-efficient plan of interventions. This paper presents a model to define an optimal maintenance policy for structures that deteriorate as a result of extreme events (e.g., earthquakes) based on an impulse control model. Furthermore, the deterioration model takes into account the effect of damage accumulation. Hence, the time at which maintenance is carried out and the extent of interventions are optimized simultaneously to maximize the cost–benefit relationship. The model is illustrated with two examples. The results show that if there exists a good permanent monitoring system, the model provides a cost-effective and practical and long-term tool for managing infrastructure.     

Optimal age-based inspection scheme for condition-based maintenance using A* search algorithm

In condition-based maintenance (CBM) with periodic inspection, the system is preventively replaced if failure risk, which is calculated based on the information obtained from inspection, exceeds a pre-determined threshold. The determination of optimal replacement threshold is often based on the minimisation of average maintenance costs per unit time due to preventive and failure replacements over a long time horizon. It is often assumed that inspections are performed at equal time intervals with no cost. However, in practice, inspections require labour, specific test devices, and sometimes suspension of operations and, thus, it is reasonable to inspect less frequently during the time the system is in its early age and/or in a healthier state and to perform inspections more frequently as time passes and/or as the system degrades. In other words, an age-based inspection scheme.

This paper proposes a novel two-phase approach for the determination of an optimal replacement threshold and an optimal age-based inspection scheme for CBM such that the total long-run average costs of replacements and inspections are minimised. First, it takes into account failure and preventive replacement costs to determine the optimal replacement threshold assuming that inspections are performed at equal time intervals with no cost. This assumption is, subsequently, relaxed and its consequences on total average cost are evaluated using a proposed iterative procedure based on A* search algorithm to obtain the optimal age-based inspection scheme. The proposed approach is illustrated through a numerical example.     

Multi-objective decision-making model based on CBM for an aircraft fleet with reliability constraint

Modern production management patterns, in which multi-unit (e.g. an aircraft fleet) are managed in a holistic manner, have brought new challenges for multi-unit maintenance decision-making. To schedule a good maintenance plan, not only does the individual aircraft maintenance have to be considered, but also the maintenance of the other aircraft in fleet have to be taken into account. Condition-based maintenance (CBM) is a maintenance scheme which recommends maintenance decisions according to equipment status collected by condition monitor over a period of time. Evaluating risk is necessary for scheduling appropriate maintenance, avoiding aircraft losses and maintaining the repairable components at a high-reliable state. In this paper, a novel two-models-fusion framework is proposed to predict the reliability of aircraft structures subjected to fatigue loads. Furthermore, we established a fleet maintenance decision-making model based on CBM for the maintenance of fatigue structures. The model concentrates on both minimising fleet maintenance cost and maximising fleet availability, overcoming the shortcomings of traditional fleet CBM research, which has simply focused on one or the other of these parameters. Finally, a case study regarding a fleet of 10 aircraft is conducted, and the results indicated that the proposed model efficiently generates outcomes that meet the schedule requirements.     

Optimal pricing policy for a deteriorating product by dynamic tracking control

We study the optimal selling price of a deteriorating product under a deterministic situation in a finite time horizon where the time horizon is either known or unknown. Inventory holding cost is expressed as a quadratic function of the current inventory level. Given a known time horizon, we develop a model by considering the deterioration dynamics of the product, and show its equivalence to a generalised optimal control problem of a linear quadratic form, i.e. an optimal dynamic tracking problem with constraints on the control variable. An optimal pricing policy is derived based on the maximum value principle. The control policy takes a state feedback form; it exhibits a closed-loop relationship between the optimal selling price (control variable) and the optimal inventory level (state variable). Given an unknown time horizon, an optimal pricing policy is derived through a similar approach when the initial inventory level meets certain conditions. Numerical situations are conducted to illustrate the effectiveness of the derived price control policies. Some interesting managerial insights are discussed.     

Optimization of condition-based maintenance considering partial opportunities

Recent studies have demonstrated the economic benefit of exploiting partial opportunities for maintenance, which arise from the reduction of costs of doing partial maintenance utilizing the opportunity given. A typical example is an externally induced production stop with a duration that may not be sufficient to a complete maintenance activity. This paper combines partial opportunities and condition-based maintenance (CBM) strategies and proposes an innovative maintenance optimization method considering time-varying economic conditions. This scenario naturally fits a broad range of assets with a finite design life (including long-life machinery and infrastructure), operating under variable economic conditions and usage-intensities. The maintenance optimization problem is formulated in this study as a finite-horizon Markov decision process, where the randomly occurring opportunities are accounted for by augmenting the time-varying, decision-dependent transition probabilities. A dynamic programming approach is subsequently used to obtain the optimal CBM policy, consisting of time-varying thresholds on equipment condition and the cost of conducting maintenance during the arrived opportunity. A case study of such a maintenance policy for an induced draft fan of a sugar production system located in Queensland, Australia, is undertaken to evaluate the benefits of the proposed methodology against more traditional approaches that neglect opportunities or consider only replete opportunity durations.     

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).