Analysis of a POMDP Model for an Optimal Maintenance Problem with Multiple Imperfect Repairs

I consider a system whose deterioration follows a discrete-time and discrete-state Markov chain with an absorbing state. When the system is put into practice, I may select operation (wait), imperfect repair, or replacement at each discrete-time point. The true state of the system is not known when it is operated. Instead, the system is monitored after operation and some incomplete information concerned with the deterioration is obtained for decision making. Since there are multiple imperfect repairs, I can select one option from them when the imperfect repair is preferable to operation and replacement. To express this situation, I propose a POMDP model and theoretically investigate the structure of an optimal maintenance policy minimizing a total expected discounted cost for an unbounded horizon. Then two stochastic orders are used for the analysis of our problem.

Optimal quasi-periodic maintenance policies for two-unit series system

To investigate the effects of various random factors on the preventive maintenance （PM） decision-making of one type of two-unit series system, an optimal quasi-periodic PM policy is introduced. Assume that PM is perfect for unit 1 and only mechanical service for unit 2 in the model. PM activity is randomly performed according to a dynamic PM plan distributed in each implementation period. A replacement is determined based on the competing results of unplanned and planned replacements. The unplanned replacement is trigged by a catastrophic failure of unit 2, and the planned replacement is executed when the PM number reaches the threshold N. Through modeling and analysis, a solution algorithm for an optimal implementation period and the PM number is given, and optimal process and parametric sensitivity are provided by a numerical example. Results show that the implementation period should be decreased as soon as possible under the condition of meeting the needs of practice, which can increase mean operating time and decrease the long-run cost rate.

Optimum Maintenance and Availability of Series Systems Subject to Imperfect Repair

Optimum maintenance and availability of a series system whose components are subject to imperfect repairs are studied in this paper. Imperfect corrective maintenance is treated in a way that after it the life of each component in the system will be decreased to a fraction of its immediately previous one and the repair time will be increased to a multiple of the one immediately preceding it, where successive failure free times are independent and so are successive repair times. Under such an assumption, the limiting system availability, mean time between system failures or repairs are derived based on some related results. A numerical example is presented to compare with Barlow and Proschan's availability model. Two classes of maintenance cost models are proposed and the optimum maintenance policies are also discussed for series system with n components in this paper.

Reliability-based Maintenance Optimization under Imperfect Predictive Maintenance

The reliability-based maintenance optimization model has been focused by the engineers and scholars but it has never been solved effectively to formulate the effect of a maintenance action on the optimization model. In existing works, the system reliability was assumed to be increased to 1 after a predictive maintenance. However, it is very difficult in the most practical systems. Therefore, a new reliability-based maintenance optimization model under imperfect predictive maintenance (PM) is proposed in this paper. In the model, the system reliability is only restored to R i (0<R i <1, i∈N, N is natural number set) after the ith PM. The system uptimes and the corresponding probability in two cases whether there is an unexpected fault in one cycle are derived respectively and the system expected uptime model is given. To formulate the system expected downtime, the probability of each imperfect PM number in one cycle is calculated. Then, the system expected total time model is obtained. The total expected long-term operation cost is composed of the expected maintenance cost, the expected loss due to the downtime and the expected additional cost due to the occurrence of an unexpected failure. They are modeled respectively in this work. Jointing the system expected total time and long-term operation cost in one cycle, the expected long-term operation cost per time could be computed. Then, the proposed maintenance optimization model is formulated where the objective function is to minimize the expected long-term operation cost per time. The results of numerical example show that the proposed model could scheme the optimal maintenance actions for the considered system when the required parameters are given and the optimal solution of the proposed model is sensitive to the parameters of effective age model and insensitive to other parameters. The proposed model effectively solves the problem of evaluating the effect of an imperfect PM on the system reliability and presents a more practical optimization method for the reliability-based maintenance strategy than the existing works.

Product Modular Design Incorporating Preventive Maintenance Issues

Traditional modular design methods lead to product maintenance problems, because the module form of a system is created according to either the function requirements or the manufacturing considerations. For solving these problems, a new modular design method is proposed with the considerations of not only the traditional function related attributes, but also the maintenance related ones. First, modularity parameters and modularity scenarios for product modularity are defined. Then the reliability and economic assessment models of product modularity strategies are formulated with the introduction of the effective working age of modules. A mathematical model used to evaluate the difference among the modules of the product so that the optimal module of the product can be established. After that, a multi-objective optimization problem based on metrics for preventive maintenance interval different degrees and preventive maintenance economics is formulated for modular optimization. Multi-objective GA is utilized to rapidly approximate the Pareto set of optimal modularity strategy trade-offs between preventive maintenance cost and preventive maintenance interval difference degree. Finally, a coordinate CNC boring machine is adopted to depict the process of product modularity. In addition, two factorial design experiments based on the modularity parameters are constructed and analyzed. These experiments investigate the impacts of these parameters on the optimal modularity strategies and the structure of module. The research proposes a new modular design method, which may help to improve the maintainability of product in modular design.

Joint optimization of inspection-based and age-based preventive maintenance and spare ordering policies for single-unit systems

This paper presents a joint optimization policy of preventive maintenance(PM)and spare ordering for single-unit systems,which deteriorate subject to the delay-time concept with three deterioration stages.PM activities that combine a non-periodic inspection scheme with age-replacement are implemented.When the system is detected to be in the minor defective stage by an inspection for the first time,place an order and shorten the inspection interval.If the system has deteriorated to a severe defective stage,it is either repaired imperfectly or replaced by a new spare.However,an immediate replacement is required once the system fails,the maximal number of imperfect maintenance(IPM)is satisfied or its age reaches to a pre-specified threshold.In consideration of the spare’s availability as needed,there are three types of decisions,i.e.,an immediate or a delayed replacement by a regular ordered spare,an immediate replacement by an expedited ordered spare with a relative higher cost.Then,some mutually independent and exclusive renewal events at the end of a renewal cycle are discussed,and the optimization model of such a joint policy is further developed by minimizing the long-run expected cost rate to find the optimal inspection and age-replacement intervals,and the maximum number of IPM.A Monte-Carlo based integration method is also designed to solve the proposed model.Finally,a numerical example is given to illustrate the proposed joint optimization policy and the performance of the Monte-Carlo based integration method.

Optimizing combination of aircraft maintenance tasks by adaptive genetic algorithm based on cluster search

It is significant to combine multiple tasks into an optimal work package in decision-making of aircraft maintenance to reduce cost,so a cost rate model of combinatorial maintenance is an urgent need.However,the optimal combination under various constraints not only involves numerical calculations but also is an NP-hard combinatorial problem.To solve the problem,an adaptive genetic algorithm based on cluster search,which is divided into two phases,is put forward.In the first phase,according to the density,all individuals can be homogeneously scattered over the whole solution space through crossover and mutation and better individuals are collected as candidate cluster centres.In the second phase,the search is confined to the neighbourhood of some selected possible solutions to accurately solve with cluster radius decreasing slowly,meanwhile all clusters continuously move to better regions until all the peaks in the question space is searched.This algorithm can efficiently solve the combination problem.Taking the optimization on decision-making of aircraft maintenance by the algorithm for an example,maintenance which combines multiple parts or tasks can significantly enhance economic benefit when the halt cost is rather high.

Development and Application of Maintenance Template in Pressurized Water Reactor Nuclear Power Plant

Good practices of maintenance optimization in nuclear power field need to be effectively consolidated and inherited,and maintenance optimization can provide technology support to create a long-term reliable and economic operation for nuclear power plants( NPPs) especially for a large number of nuclear powers under construction. Based on the development and application of maintenance template in developed countries,and combining with reliability-centered maintenance( RCM) analysis results and maintenance experience data over the past ten years in domestic NPPs, the development process of maintenance template was presented for Chinese pressurized water reactor( PWR) NPP,and the application of maintenance template to maintenance program development and maintenance optimization combined with cases were demonstrated. A shortcut was provided for improving the efficiency of maintenance optimization in domestic PWR NPP,and help to realize a safe,reliable,and economic operation for domestic NPPs.

Availability-based maintenance optimization under unequal inspection period and imperfect repair

Taking the multi-component system as research object, a maintenance optimization model based on the unequal inspection period and imperfect repair is established by considering the requirement of expected availability for improving the system＇s availability. An age reduction factor is used to describe the effect of imperfect repair, and the modelling approach for the unequal inspection period is proposed. Unavailable situations are classified into three kinds of independent cases, and the availability is calculated accordingly. Based on the analysis of the relationship between the unavailable cases and the unequal inspection period, an optimization model under imperfect repair is established to optimize the system＇s expected availability. A case study of a wind turbine is provided, and three key components, i.e. gearbox, generator and spindle, are considered. The optimization results of the unequal inspection period model and the equal inspection period model are compared. The results show that the unequal inspection period model based on availability can update the maintenance plan so as to optimize maintenance activities and improve the system＇s availability.

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.

Multiobjective maintenance optimization of the continuously monitored deterioration system

With the development of the monitoring technology,it is more and more common that the system is continuously monitored.Therefore,the research on the maintenance optimization of the continuously monitored deterioration system is important.The deterioration process of the discussed system is described by a Gamma process.The predictive maintenance is considered to be imperfect and formulated.The expected interval of two continuous preventive maintenances is derived.Then,the maintenance optimization model of the continuously monitored deterioration system is presented.In the model,the minimization of the expected operational cost per unit time and the maximization of the system availability are the optimization objectives.The improved ideal point method with the normalized objective functions is employed to solve the proposed model.The validity and sensitivity of the proposed multiobjective maintenance optimization model are analyzed by a numerical example.

DEVELOPMENT OF THE RISK-BASED MAINTENANCE OPTIMIZATION SYSTEM FOR FOSSIL POWER PLANTS

Cost reduction in electric power generation is a major management concern, and it is therefore necessary to reduce maintenance expenses while upholding plant reliability. A maintenance optimization system 'FREEDOM', which uses RBM technique, DCF (discounted cash flow) and NPV (net present value) calculation functions, has been newly developed. This system probabilistically evaluates the lifetime of boiler and turbine and quantitatively calculates the risk defined as the cumulative probability of failure multiplied by the consequence of failure. Economically optimized timing of inspection and alternative countermeasure such as repair and replacement are then recommended. This system has already been applied to seven plants in Japan, and its effectiveness has been confirmed.

DELAY-TIME MODEL BASED ON IMPERFECT INSPECTION OF AIRCRAFT STRUCTURE WITHIN FINITE TIME SPAN

According to the failure characteristics of aircraft structure, a delay-time model is an effective method to optimize maintenance for aircraft structure. To imitate the practical situation as much as possible, imperfect inspections, thresholds and repeated intervals are concerned in delay-time models. Since the suggestion by the existing delay-time models that the inspections are implemented in an infinite time span lacks practical value, a de- lay-time model with imperfect inspection within a finite time span is proposed. In the model, the nonhomogenous Poisson process is adopted to obtain the renewal probabilities between two different successive inspections on de- fects or failures. An algorithm is applied based on the Nelder-Mead downhill simplex method to solve the model. Finally, a numerical example proves the validity and effectiveness of the model.

Multi-component system maintenance optimization of a rail transit train based on opportunistic correlations

ln order to deal with the problems of insufficient or excessive maintenance in the current maintenance activities of China transit trains,this paper develops a novel multi-component system maintenance optimization approach based on an opportunistic correlation model.Based on the minimal reliability and failure rate change rule of each train component,the novel proposed maintenance optimization benefits from an improved opportunistic maintenance model with system structure correlation,fault correlation and reliability correlation under imperfect maintenance.Then,different maintenance modes can be determined by a proposed mainte-nance factor under the different conditions of components.Specifically,the reliability threshold of each component is also considered to optimize the maintenance cost by the system reliability and operational availability of the train.Furthermore,as the mentioned problem belongs to the NP-Hard optimization problems,a modified particle swarm optimization(PSO)with the improvement of inertia weight is proposed to cope with the optimization problem.Based on a specific case under the practical recorded failure data,the analysis shows that the proposed model and approach can effectively cut the maintenance cost.

Optimization of Aeroengine Shop Visit Cost in its Service Life Cycle

It is an important task for airlines to make a reasonable workscope for their engines, which has effects not only on engine performance and reliability, but also on airlines operating cost. Based on the recommendations given in the engine maintenance management manual, and taking the repair levels adopted in the previous shop visits into account, a series of module repair level optimization rules were set up, and a shop visit cost optimization model was also created for engine service life cycle. The particle swarm method was used to optimize the engine workscope and overhaul cost. The method proposed in this paper will be a reference for airlines to make engine workscope and to do engine maintenance management.

An Interval Algorithm of Maintenance Windows Under Uncertain Parameters

For improving the method of finding maintenance windows under uncertain parameters, an algorithm of maintenance window under uncertainties is presented using interval analysis and sensitivity analysis. Age replacement model is selected to demonstrate how to use this new algorithm. Considered the uncertainties, the optimal maintenance interval of preventive maintenance is not only a single value, but a possible range. The requirement from maintenance engineers is also considered, the maintenance window is made as a symmetrical interval format, like(100 ± 10) day. Comparing with the methods using in the literatures, the new algorithm is without requirement of distribution assumption of uncertain parameter values and computer simulation.