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.     

Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break. A list of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme.     

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 imperfect preventive maintenance policy for equipment leased during successive periods

In this paper, we consider randomly failing equipment leased several times during their life cycle with a given warranty period. A mathematical model is developed to determine the optimal efficiency levels of preventive maintenance (PM) to be performed on the equipment between successive lease periods, maximising the expected total profit of the lessor over the equipment life cycle. The model considers the expected leasing revenue as well as the equipment acquisition cost and the average PM and repair costs. PM actions allow reducing the age of the equipment to a certain extent with a corresponding cost depending on the PM level adopted. The efficiency of the PM is determinant of the expected revenue during the next lease period. Given a set of K possible PM levels and the number of lease periods n over the equipment life cycle, K^{n?1 PM} strategies are possible. A genetic algorithm is proposed in order to obtain nearly optimal policies in situations where the number of possibilities K^n?1 is very high. Obtained numerical results are discussed. Small- and big-size instances of the problem are considered in the case of a service company in the oil and gas industry specialised in leasing specific equipment such as separators, to oil companies for production activities with a limited duration of several months like well testing or short production tests.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.     

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.     

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).     

Effects of maintenance policy on an imperfect production system under trade credit

The traditional production model development assumed that all products are perfect quality and did not consider maintenance, which is far from reality. In practice, the production process may shift randomly from an in-control state to an out-of-control state during a production run, i.e. process deterioration. This paper considers both preventive maintenance and corrective maintenance which are used to increase the system reliability. The objective of this paper is to determine the optimal production run time and maintenance frequency while minimising the total cost under process deterioration and trade credit. This paper develops a theorem and an algorithm to solve the problem described, provides numerical analysis to illustrate the proposed solution procedure, and discusses the impact of various system parameters. A real case of hi-tech manufacturer is used to verify the model. It predicts a 10.36% decrease in total cost if the preventive maintenance decision is considered.     

Optimal joint selective imperfect maintenance and multiple repairpersons assignment strategy for complex multicomponent systems

This paper addresses the joint selective maintenance and repairperson assignment problem (JSM–RAP) for complex multicomponent systems. The systems perform consecutive missions separated by scheduled finite duration breaks and are imperfectly maintained during the breaks. Current selective maintenance (SM) models usually assume that only one repair channel is available or that the repairperson assignment optimisation can be done at a subsequent stage. Using a generalised reliability function for k-out-of-n systems, we formulate the JSM–RAP for multicomponent systems more complex than the series-parallel systems commonly used in previous SM models. Two nonlinear formulations and their corresponding binary integer programming models are then proposed and optimally solved. Numerical experiments show the added value of the proposed approach and highlight the benefit of jointly carrying out the selection of the components to be maintained, the maintenance level to be performed and the assignment of the maintenance tasks to repairpersons. It is also shown that the flexibility provided by mixed skill cohorts of repairpersons over uniform cohorts can yield higher performance levels when the skillsets are significantly different.     

Bi-objective optimisation for integrated scheduling of single machine with setup times and preventive maintenance planning

This paper deals with an integrated bi-objective optimisation problem for production scheduling and preventive maintenance in a single-machine context with sequence-dependent setup times. To model its increasing failure rate, the time to failure of the machine is subject to Weibull distribution. The two objectives are to minimise the total expected completion time of jobs and to minimise the maximum of expected times of failure of the machine at the same time. During the setup times, preventive maintenance activities are supposed to be performed simultaneously. Due to the assumption of non-preemptive job processing, three resolution policies are adapted to deal with the conflicts arising between job processing and maintenance activities. Two decisions are to be taken at the same time: find the permutation of jobs and determine when to perform the preventive maintenance. To solve this integrated problem, two well-known evolutionary genetic algorithms are compared to find an approximation of the Pareto-optimal front, in terms of standard multi-objective metrics. The results of extensive computational experiments show the promising performance of the adapted algorithms.     

Multi-phase preventive maintenance policy for leased equipment

This paper proposes a multi-phase preventive maintenance (PM) policy for leased equipment by combining the advantages of both periodic PM and sequential PM. The lease period of the equipment is divided into multiple PM phases. The PM activities within each phase are performed periodically with the convenience of implementation, while the frequency of PM for each phase is different and it gives a gradual increase because of the imperfect effect of PM. A multi-phase PM model is built up based on the age reduction method for imperfect PM with the penalty for equipment failures and overtime of repair involved. The optimal PM intervals for every PM phases are achieved by minimising the cumulative maintenance cost throughout the lease period from the perspective of the lessor. Numerical example shows that the cumulative maintenance cost under the proposed multi-phase PM policy is lower than that under periodic PM policy.     

Optimal preventive maintenance strategy using two repair crews having different efficiencies: a quasi renewal process based modelling approach

This paper considers randomly failing, single-unit equipment subject to a periodic preventive maintenance (PM) policy. In case of failure between successive perfect PM actions (renewals), imperfect repairs are performed following a decreasing quasi-renewal process. One of two different maintenance crews can perform the repairs. One team is more experienced, and consequently more efficient than the other, but more costly. A mathematical model is developed in order to determine the PM period, T, and the kth repair, during a PM period, after which the repair team should be changed, minimising the average total cost per time unit over an infinite time span. It is also proved that an optimal solution in terms of the PM period always exists for any given system lifetime distribution and any set of maintenance costs. Numerical examples are presented and the obtained results are discussed.     

Analysing event data from a repairable machine subject to imperfect preventive maintenance

A machine is minimally repaired on failure and imperfect preventive maintenance (PM) is also carried out from time to time, not necessarily at regular intervals. A simple point process model is proposed for the sequence of corresponding failure times, and estimates of the machine lifetime parameters and the degree of age rejuvenation at PMs are obtained using maximum likelihood techniques. These results are then applied to real event data. © 1997 John Wiley & Sons, Ltd.     

A two-dimensional preventive maintenance strategy for items sold with warranty

Conventional preventive maintenance (PM) strategies under two-dimensional (2D) warranties are usually age-based or usage-based, which means that the implementation of PM activities is based solely on item age or usage. In this paper, a new PM strategy, called 2D PM strategy, is proposed for items sold with a 2D warranty. Under this strategy, the item is preventively maintained every K units of age or L units of usage, whichever occurs first. The marginal approach is used to describe the effect of age and usage on item reliability by treating usage as a random function of age. Besides, the effect of PM is characterised by the reduction of virtual age. The objective of this study is to identify the optimal 2D PM strategy under fixed warranty terms so as to minimise the total expected warranty servicing cost from the manufacturer’s perspective. A numerical example is provided to demonstrate the effectiveness of the proposed PM strategy. It is shown that the 2D PM strategy contains the age-based and usage-based strategies as special cases, and outperforms them in terms of warranty servicing cost. Finally, how to implement the proposed PM strategy in practice is discussed with an illustrative case.     

Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.     

A methodology for simultaneous optimisation of design parameters for the preventive maintenance and quality policy incorporating Taguchi loss function

The performance of a production system depends on the breakdown-free operation of equipment and processes. Maintenance and quality control play an important role in achieving this goal. In addition to deteriorating with time, equipment may experience a quality shift (i.e. process moves to out-of-control state), which is characterised by a higher rejection rate and a higher tendency to fail. This paper develops an integrated model for joint optimisation of preventive maintenance interval and control parameters incorporating the Taguchi loss function. We consider two types of maintenance policies: minimal corrective maintenance that maintains the state of the equipment without affecting the age and imperfect preventive maintenance that upgrades the equipment in between ‘as good as new’ and ‘as bad as old’ condition. The proposed model enables the determination of the optimal value of each of the four decision variables, i.e. sample size (n), sample frequency (h), control limit coefficient (k), and preventive maintenance interval (t _PM) that minimises the expected total cost of the integration per unit time. A numerical example is presented to demonstrate the effect of the cost parameters on the joint economic design of preventive maintenance and process quality control policy. The sensitivity of the various parameters is also examined.     

Generalized non‐stationary preventive maintenance model for deteriorating repairable systems

This paper deals with a practical approach for the analysis and modelling of preventive maintenance (PM) data for repairable systems which have an increasing failure frequency and/or increasing severity. The concept and testing for the trend of severity of corrective work (CO) and PM are discussed. A framework for statistical analysis of interarrival times and downtimes due to CO/PM is proposed. A generalized non‐stationary model for scheduling PM to maximize availability is suggested. The effect of severity on scheduling PM activities is shown through sensitivity analysis. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimal multi-level classification and preventive maintenance policy for highly reliable products

Highly reliable products are widely used in aerospace, automotive, integrated manufacturing and other fields. With increasing market demand and competition, product classification for different segment market segments has become more and more critical. Leading manufacturers are always searching and designing classification policies for highly reliable products. On the other hand, preventive maintenance can improve the operation efficiency of the product, extend the service life and reduce enormous losses brought by failures. These two factors are taken into account by many large enterprises when making sound economical and operational decisions. Therefore, this research proposes a joint multi-level classification and preventive maintenance model (JMCPM model) under age-based maintenance. Different preventive maintenance policies are developed for corresponding level units. Accordingly, the optimal joint policy of multi-level classification and preventive maintenance can be obtained by JMCPM. In this model, degradation-based burn-in is utilised to eliminate defective units and collect degradation data. The degradation data are the basis of classification and can be used to estimate the residual life. Then, for making full use of these data, linear discriminant analysis is employed to design classification rules. The objective of the JMCPM model is to minimise the average cost per unit time by properly choosing the settings of classification and preventive maintenance intervals simultaneously. Finally, a simulation study is carried out for evaluating the performance of the JMCPM model. For an illustration of the proposed model and the methods of inference developed here, a real case involving degradation data from electrical connectors is analysed.     

A trade-off between productivity and cost for the integrated part quality inspection and preventive maintenance planning under uncertainty

This paper proposes a robust possibilistic and multi-objective mixed-integer linear programming mathematical model to concurrently plan part quality inspection and Preventive Maintenance (PM) activities for a serial multi-stage production system. This system contains the deteriorating stages and faces the uncertainty about estimated cost components and demand amount. The integrated model reaches two significant decisions which are the right time and place for performing the part quality inspection and PM. These decisions are made while the model is to simultaneously optimise the implied system productivity and total cost. To measure the implied system productivity, a new piecewise utility function for the ratio of produced conforming products to input workpieces is developed. A real case study and a numerical example are explored to validate and verify the developed model. The results prove the significance and effectiveness of considering the uncertainty and conflicting practical objectives for the problem.     

Availability and cost-centered preventive maintenance scheduling of continuous operating series systems using multi-objective genetic algorithm: A case study

This article presents a multi-objective (maximization of availability and minimization of maintenance cost) preventive maintenance (PM) scheduling model for a continuous operating series system (COSS) which do not provide an off-working period for PM. The objective functions are optimized by using a Multi-Objective Genetic Algorithm (MOGA). The effectiveness of the model is demonstrated through a coal-fired boiler-tube. The case study shows that the model can improve the availability along with profound reduction of the maintenance cost, i.e., increases the profit of the plant.