Control-limit preventive maintenance policies for components subject to imperfect preventive maintenance and variable operational conditions

This paper develops two component-level control-limit preventive maintenance (PM) policies for systems subject to the joint effect of partial recovery PM acts (imperfect PM acts) and variable operational conditions, and investigates the properties of the proposed policies. The extended proportional hazards model (EPHM) is used to model the system failure likelihood influenced by both factors. Several numerical experiments are conducted for policy property analysis, using real lifetime and operational condition data and typical characterization of imperfect PM acts and maintenance durations. The experimental results demonstrate the necessity of considering both factors when they do exist, characterize the joint effect of the two factors on the performance of an optimized PM policy, and explore the influence of the loading sequence of time-varying operational conditions on the performance of an optimized PM policy. The proposed policies extend the applicability of PM optimization techniques.     

Two alternative imperfect multiaction maintenance models

Systems such as civil structures ( e.g. building and bridges) and man-machine-software ( e.g. large servers and control systems) can be categorised into certain operational states with respect to the structural conditions. Different operational states result in different abilities to perform the given missions and different system failure rates. To improve the current operational states, a preventive maintenance (PM) action involving implementation of a recovery procedure for a system's hardware, software and operational environment ( e.g. temperature and pressure) is needed. The above problem is captured in a multiaction maintenance model with imperfect maintenance caused by the number of PMs. Two alternative imperfect multiaction maintenance models are proposed in this paper. One considers that the behavior with respect to the transition of states is not in order and the transition rate is independent of the number of PMs. The other supposes that the behavior of the state transition is in order and the transition rate depends upon the number of PMs. Based on such alternative models, the optimal PM periods and the optimal number of PMs before replacing/restructuring the overall system are obtained, which minimize the cost rate function over an infinite horizon.     

Optimization of imperfect preventive maintenance for multi-state systems

The paper generalizes a preventive maintenance optimization problem to multi-state systems, which have a range of performance levels. Multi-state system reliability is defined as the ability to satisfy given demand. The reliability of system elements is characterized by their hazard functions. The possible preventive maintenance actions are characterized by their ability to affect the effective age of equipment. An algorithm is developed which obtains the sequence of maintenance actions providing system functioning with the desired level of reliability during its lifetime by minimum maintenance cost.To evaluate multi-state system reliability, a universal generating function technique is applied. A genetic algorithm (GA) is used as an optimization technique. Basic GA procedures adapted to the given problem are presented. Examples of the determination of optimal preventive maintenance plans are demonstrated.     

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.     

A summary of maintenance policies for a finite interval

It would be an important problem to consider practically some maintenance policies for a finite time span, because the working times of most units are finite in actual fields. This paper converts the usual maintenance models to finite maintenance models. It is more difficult to study theoretically optimal policies for a finite time span than those for an infinite time span. Three usual models of periodic replacement with minimal repair, block replacement and simple replacement are transformed to finite replacement models. Further, optimal periodic and sequential policies for an imperfect preventive maintenance and an inspection model for a finite time span are considered. Optimal policies for each model are analytically derived and are numerically computed.     

Addressing imperfect maintenance modelling uncertainty in unavailability and cost based optimization

Optimization of testing and maintenance activities performed in the different systems of a complex industrial plant is of great interest as the plant availability and economy strongly depend on the maintenance activities planned. Traditionally, two types of models, i.e. deterministic and probabilistic, have been considered to simulate the impact of testing and maintenance activities on equipment unavailability and the cost involved. Both models present uncertainties that are often categorized as either aleatory or epistemic uncertainties. The second group applies when there is limited knowledge on the proper model to represent a problem, and/or the values associated to the model parameters, so the results of the calculation performed with them incorporate uncertainty. This paper addresses the problem of testing and maintenance optimization based on unavailability and cost criteria and considering epistemic uncertainty in the imperfect maintenance modelling. It is framed as a multiple criteria decision making problem where unavailability and cost act as uncertain and conflicting decision criteria. A tolerance interval based approach is used to address uncertainty with regard to effectiveness parameter and imperfect maintenance model embedded within a multiple-objective genetic algorithm. A case of application for a stand-by safety related system of a nuclear power plant is presented. The results obtained in this application show the importance of considering uncertainties in the modelling of imperfect maintenance, as the optimal solutions found are associated with a large uncertainty that influences the final decision making depending on, for example, if the decision maker is risk averse or risk neutral.     

Modelling and optimizing sequential imperfect preventive maintenance

This paper deals with the problem of scheduling imperfect preventive maintenance (PM) of some equipment. It uses a model due to Kijima in which each application of PM reduces the equipment's effective age (but without making it as good as new). The approach presented here involves minimizing a performance function which allows for the costs of minimal repair and eventual system replacement as well as for the costs of PM during the equipment's operating lifetime. The paper describes a numerical investigation into the sensitivity of optimum schedules to different aspects of an age-reduction model (including the situation when parts of a system are non-maintainable—i.e., unaffected by PM).     

Optimal inspection and preventive maintenance of units with revealed and unrevealed failures

The maintenance of a single unit system that alternates operating and idle periods is studied. In the former case the failures are detected as soon as they occur and only by special testing or inspection in the latter. This paper aims at minimizing the cost per unit of time for an infinite time span by selection of a unique interval, for both inspection and maintenance. A special feature of this model is the possibility of a less than perfect testing as the inspections may fail and give a wrong result. It is further assumed that both preventive and corrective maintenance make the unit as good as new with the durations of inspections and maintenances being negligible. The existence of an optimum interval and how it depends on both the cost parameters and the reliability characteristics of the unit is discussed.     

Modelling imperfect maintenance and the reliability of complex systems using superposed renewal processes

In problems of maintenance optimization, it is convenient to assume that repairs are equivalent to replacements and that systems or objects are, therefore, brought back into an as good as new state after each repair. Standard results in renewal theory may then be applied for determining optimal maintenance policies. In practice, there are many situations in which this assumption cannot be made. The quintessential problem with imperfect maintenance is how to model it. In many cases it is very difficult to assess by how much a partial repair will improve the condition of a system or object and it is equally difficult to assess how such a repair influences the rate of deterioration. In this paper, a superposition of renewal process is used to model the effect of imperfect maintenance. It constitutes a different modelling approach than the more common use of a virtual age process.     

Preventive maintenance and replacement policies for deteriorating production systems subject to imperfect repairs

This paper presents a special case of integration of the preventive maintenance into the repair/replacement policy of a failure-prone system. The machine of the considered system exhibits increasing failure intensity and increasing repair times. To reduce the failure rate and subsequent repair times following a failure, there is an incentive to perform preventive maintenance on the machine before failure. When a failure occurs, the machine can be repaired or replaced by a new one. Thus the machine's mode at any time can be classified as either operating, in repair, in replacement or in preventive maintenance. The decision variables of the system are the repair/replacement switching age or number of failures at the time of the machine's failure and the preventive maintenance rate. The problem of determining the repair/replacement and preventive maintenance policies is formulated as a semi-Markov decision process and numerical methods are given in order to compute optimal policies which minimise the average cost incurred by preventive maintenance, repair and replacement over an infinite planning horizon. As expected, the decisions to repair or to replace the machine upon a failure are modified by performing preventive maintenance. A numerical example is given and a sensitivity analysis is performed to illustrate the proposed approach and to show the impact of various parameters on the control policies thus obtained.     

Multi-objective imperfect preventive maintenance optimisation with NSGA-II

Maintenance optimisation is a multi-objective problem in nature, and it usually needs to achieve a trade-off among the conflicting objectives. In this study, a multi-objective maintenance optimisation (MOMO) model is proposed for electromechanical products, where both the soft failure and hard failure are considered, and minimal repair is performed accordingly. Imperfect preventive maintenance (IPM) is carried out during the preplanned periods, and modelled with a hybrid failure rate model and quasi-renewal coefficient. The initial IPM period and the total number of IPM periods are set as the decision variables, and a MOMO model is developed to optimise the availability and cost rate concurrently. The fast elitist non-dominated sorting genetic algorithm (NSGA-II) is applied to solve the model. A case study of wind turbine’s gearbox is provided. The results show that there are 30 optimal solutions in the MOMO’s Pareto frontier that can maximise the availability and minimise the cost rate simultaneously. Compared with the single-objective maintenance optimisation, it can provide more choices for maintenance decision, and better satisfy the resource constraints and the customer’s preference. The results of the sensitivity analysis show that the effect of age reduction factor on optimisation results is greater than that of failure rate increase factor.     

Simultaneous determination of preventive maintenance and replacement policies in a queue-like production system with minimal repair

This paper addresses the joint effects of preventive maintenance and replacement policies on a queue-like production system with minimal repair at failures. We consider a policy which calls for a preventive maintenance operation whenever N parts have been processed. If a failure occurs and at least K preventive maintenance operations have been carried out, the system is replaced by a new one. Otherwise, a failure is handled by minimal repair. An analytical model is developed and the argument of renewal–reward theory is used to provide long-run expected profit per unit time for a given maintenance and replacement policy. Numerical examples are given to provide some managerial insights.     

A new modeling approach to the safety evaluation of N-modular redundant computer systems in presence of imperfect maintenance

A large number of safety-critical control systems are based on N-modular redundant architectures, using majority voters on the outputs of independent computation units. In order to assess the compliance of these architectures with international safety standards, the frequency of hazardous failures must be analyzed by developing and solving proper formal models. Furthermore, the impact of maintenance faults has to be considered, since imperfect maintenance may degrade the safety integrity level of the system. In this paper, we present both a failure model for voting architectures based on Bayesian networks and a maintenance model based on continuous time Markov chains, and we propose to combine them according to a compositional multiformalism modeling approach in order to analyze the impact of imperfect maintenance on the system safety. We also show how the proposed approach promotes the reuse and the interchange of models as well the interchange of solving tools.     

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.     

Preventive maintenance and optimal buffer inventory for products sold with warranty in an imperfect production system

This paper deals with an imperfect production system with allowable shortages due to regular preventive maintenance for products sold with free minimal repair warranty. Preventive maintenance is an essential factor of the just-in-time structure that results in a shutdown of the production process for a certain period of time. During such an interruption, a buffer stock is needed to adjust the market demand. The study includes the possibility of imperfect production and determines the optimum buffer level and production run time by trading off the holding cost, shortage cost, rework cost, repair cost for warranty, labour/energy costs, material cost and cost for maintenance so that the cost per unit product is minimised.     

Optimization for condition-based maintenance with semi-Markov decision process

The semi-Markov decision model is a powerful tool in analyzing sequential decision processes with random decision epochs. In this paper, we have built the semi-Markov decision process (SMDP) for the maintenance policy optimization of condition-based preventive maintenance problems, and have presented the approach for joint optimization of inspection rate and maintenance policy. Through numerical examples, the improvement of this method is compared with the scheme, which optimizes only over the inspection rate. We also find that under a special case when the deterioration rate at each failure stage is the same, the optimal policy obtained by SMDP algorithm is a dynamic threshold-type scheme with threshold value depending on the inspection rate.     

A maintenance policy for two-unit parallel systems based on imperfect monitoring information

In this paper a maintenance policy is optimised for a two-unit system with a parallel structure and stochastic dependences. Monitoring problems are taken into account in the optimisation scheme: the failure time of each unit can be not detected with a given probability. Conditions on the system parameters (unit failure rates) and on the non-detection probabilities must be verified to make the optimisation scheme valid. These conditions are clearly identified. Numerical experiments allow to show the relevance of taking into account monitoring problems in the maintenance model.     

Online maintenance policy for a deteriorating system with random change of mode

Most of maintenance policies proposed in the literature for gradually deteriorating systems, consider a stationary deterioration process. This paper is an attempt to take into account stochastically deteriorating systems which are subject to a sudden change in their degradation process. A technical device subject to gradual degradation is considered. It is assumed that the level of degradation can be resumed by a single scalar variable. An online maintenance decision rule is proposed, which makes it possible to take into account in real time the online information available on the operating mode of the system as well as its actual deterioration level. We show the efficiency of considering online decision rules for maintenance with respect to traditional maintenance policies based on a static alarm threshold. Numerical simulations are given, to assess and optimize the performance of the maintained system from its asymptotic unavailability point of view. It is compared to the results obtained with classical control-limit maintenance policies.     

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.     

Age-dependent reliability model considering effects of maintenance and working conditions

Nowadays, there is some doubt about building new nuclear power plants (NPPs). Instead, there is a growing interest in analyzing the possibility to extend current NPP operation, where life management programs play an important role. The evolution of the NPP safety depends on the evolution of the reliability of its safety components, which, in turn, is a function of their age along the NPP operational life. In this paper, a new age-dependent reliability model is presented, which includes parameters related to surveillance and maintenance effectiveness and working conditions of the equipment, both environmental and operational. This model may be used to support NPP life management and life extension programs, by improving or optimizing surveillance and maintenance tasks using risk and cost models based on such an age-dependent reliability model. The results of the sensitivity study in the example application show that the selection of the most appropriate maintenance strategy would directly depend on the previous parameters. Then, very important differences are expected to appear under certain circumstances, particularly, in comparison with other models that do not consider maintenance effectiveness and working conditions simultaneously.