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.     

A condition-based maintenance policy for stochastically deteriorating systems

We focus on the analytical modeling of a condition-based inspection/replacement policy for a stochastically and continuously deteriorating single-unit system. We consider both the replacement threshold and the inspection schedule as decision variables for this maintenance problem and we propose to implement the maintenance policy using a multi-level control-limit rule.In order to assess the performance of the proposed maintenance policy and to minimize the long run expected maintenance cost per unit time, a mathematical model for the maintained system cost is derived, supported by the existence of a stationary law for the maintained system state.Numerical experiments illustrate the performance of the proposed policy and confirm that the maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the maintenance structure thresholds, or equivalently by a joint optimization of a system replacement threshold and the aperiodic inspection schedule.     

Genetic algorithm optimisation of the maintenance scheduling of generating units in a power system

A new method for optimisation of the maintenance scheduling of generating units in a power system is developed. Maintenance is scheduled to minimise the risk through minimisation of the yearly value of the loss of load expectation (LOLE) taken as a measure of the power system reliability. The proposed method uses genetic algorithm to obtain the best solution resulting in a minimal value of the annual LOLE value for the power system in the analysed period. The operational constraints for generating units are included in the method. The proposed algorithm was tested on a Macedonian power system and the obtained results were compared with the results received from the approximate methodology. The results show the improved reliability of a power system with the maintenance schedule obtained by the new method compared to the results from the approximate methodology.     

A Bayesian approach to an adaptive preventive maintenance model

In this paper we consider a Bayesian theoretic approach to determine an optimal adaptive preventive maintenance policy with minimal repair. By incorporating minimal repair, maintenance and replacement, the mathematical formulas of the expected cost per unit time are obtained. When the failure density is Weibull with uncertain parameters, a Bayesian approach is established to formally express and update the uncertain parameters for determining an optimal adaptive preventive maintenance policy. Furthermore, various special cases of our model are discussed in detail.     

A survey of the application of gamma processes in maintenance

This article surveys the application of gamma processes in maintenance. Since the introduction of the gamma process in the area of reliability in 1975, it has been increasingly used to model stochastic deterioration for optimising maintenance. Because gamma processes are well suited for modelling the temporal variability of deterioration, they have proven to be useful in determining optimal inspection and maintenance decisions. An overview is given of the rich theoretical aspects as well as the successful maintenance applications of gamma processes. The statistical properties of the gamma process as a probabilistic stress-strength model are given and put in a historic perspective. Furthermore, methods for estimation, approximation, and simulation of gamma processes are reviewed. Finally, an extensive catalogue of inspection and maintenance models under gamma-process deterioration is presented with the emphasis on engineering applications.     

Optimal condition based maintenance with imperfect information and the proportional hazards model

Condition based maintenance (CBM) is based on collecting observations over time, in order to assess equipment's state, to prevent its failure and to determine the optimal maintenance strategies. In this paper, we derive an optimal CBM replacement policy when the state of equipment is unknown but can be estimated based on observed condition. We use a proportional hazards model (PHM) to represent the system's degradation. Since equipment's state is unknown, the optimization of the optimal maintenance policy is formulated as a partially observed Markov decision process (POMDP), and the problem is solved using dynamic programming. Practical advantages of combining the PHM with the POMDP are shown.     

A study of a two-phase inspection policy for a preparedness system with a defective state and heterogeneous lifetime

This paper considers an inspection policy for a single component protection or preparedness system, in which the component arises from a heterogeneous population. At any point in time, the system may be in one of three states, good, defective or failed. The system is only required in an emergency, and in order to ensure high availability of the system on-demand, the system undergoes a sequence of inspections. Inspection determines the system state, so that if a transition from the good state occurs between inspections it is not revealed until subsequent inspection. When a defect or failure is revealed, the component is replaced. At the final inspection the component is replaced. We suppose that a component may be either weak or strong, so that the time in the good state has a distribution that is a mixture. In these circumstances, the efficacy of a two-phase inspection policy, with an anticipated high inspection frequency in early life and low inspection frequency in later life, is considered using availability and cost criteria. The policy is investigated in the context of a valve in a natural gas supply network. If the lifetime distributions in the mixture are quite distinct, then cost savings of the order of 5% can be achieved by using the two-phase policy in place of the simpler single phase policy. Furthermore, only if the mean time in the defective state is small or the required availability is very high does the two-phase policy tend to mimic a burn-in policy.     

A geometric process repair model for a repairable cold standby system with priority in use and repair

In this paper, a deteriorating cold standby repairable system consisting of two dissimilar components and one repairman is studied. For each component, assume that the successive working times form a decreasing geometric process while the consecutive repair times constitute an increasing geometric process, and component 1 has priority in use and repair. Under these assumptions, we consider a replacement policy N based on the number of repairs of component 1 under which the system is replaced when the number of repairs of component 1 reaches N. Our problem is to determine an optimal policy N^* such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit equation of the average cost rate of the system is derived and the corresponding optimal replacement policy N^* can be determined analytically or numerically. Finally, a numerical example with Weibull distribution is given to illustrate some theoretical results in this paper.     

A modified particle swarm optimisation algorithm to solve the part feeding problem at assembly lines

The Assembly Line Part Feeding Problem (ALPFP) is a complex combinatorial optimisation problem concerned with the delivery of the required parts to the assembly workstations in the right quantities at the right time. Solving the ALPFP includes simultaneously solving two sub-problems, namely tour scheduling and tow-train loading. In this article, we first define the problem and formulate it as a multi-objective mixed-integer linear programming model. Then, we carry out a complexity analysis, proving the ALPFP to be NP-complete. A modified particle swarm optimisation (MPSO) algorithm incorporating mutation as part of the position updating scheme is subsequently proposed. The MPSO is capable of finding very good solutions with small time requirements. Computational results are reported, demonstrating the efficiency and effectiveness of the proposed MPSO.     

A prognostics-based spare part ordering and system replacement policy for a deteriorating system subjected to a random lead time

Prognostics-based spare part ordering and system replacement (PSOSR) policies are at the forefront of the prevalent prognostics and health management discipline. However, almost all of the existing researches in this domain ignore the stochasticity of the lead time. With this in mind, this paper proposes a PSOSR policy based on the real-time health condition of a deteriorating system subjected to a random lead time. In doing so, the degradation path of the interested system is modelled by a Wiener process, and the associated life distributions can be predicted recursively according to the real-time health condition of the system. In turn, the proposed policy can also be updated dynamically based on these real-time obtained life distributions. The policy, which – in addition to incorporating the stochasticity of the lead time – integrates the decision-making issues of both spare part ordering and system replacement – is finally applied to a case study of an inertial navigation system served in a type of aircraft. The experimental results validate the policy’s effectiveness and superiority.     

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.     

A model for preventive maintenance planning by genetic algorithms based in cost and reliability

This work has two important goals. The first one is to present a novel methodology for preventive maintenance policy evaluation based upon a cost-reliability model, which allows the use of flexible intervals between maintenance interventions. Such innovative features represents an advantage over the traditional methodologies as it allows a continuous fitting of the schedules in order to better deal with the components failure rates. The second goal is to automatically optimize the preventive maintenance policies, considering the proposed methodology for systems evaluation.Due to the great amount of parameters to be analyzed and their strong and non-linear interdependencies, the search for the optimum combination of these parameters is a very hard task when dealing with optimizations schedules. For these reasons, genetic algorithms (GA) may be an appropriate optimization technique to be used. The GA will search for the optimum maintenance policy considering several relevant features such as: (i) the probability of needing a repair (corrective maintenance), (ii) the cost of such repair, (iii) typical outage times, (iv) preventive maintenance costs, (v) the impact of the maintenance in the systems reliability as a whole, (vi) probability of imperfect maintenance, etc. In order to evaluate the proposed methodology, the High Pressure Injection System (HPIS) of a typical 4-loop PWR was used as a case study. The results obtained by this methodology outline its good performance, allowing specific analysis on the weighting factors of the objective function.     

A Bayesian model for the joint optimization of quality and maintenance decisions

We develop a model for the economic design of a Bayesian control chart for monitoring a process mean. The process may randomly suffer failures that result in a non‐operating state, and thus call for an immediate corrective maintenance action, as well as assignable causes that shift the process mean to an undesirable level. Quality shifts, apart from poorer quality outcome and higher operational cost, also result in higher failure rate. Consequently, their removal, besides improving the outcome quality and reducing the quality‐related cost, is also a preventive maintenance action since it reduces the probability of a failure. The proposed Bayesian model allows the determination of the design parameters that minimize the total expected quality and maintenance cost per time unit. The effectiveness of the proposed model is evaluated through the comparison of its expected cost against the optimum expected cost of the simpler variable‐parameter Shewhart chart. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

A cost minimisation model for joint production and maintenance planning under quality constraints

In this paper, integrated planning of production, imperfect maintenance and process inspections in a multi-machine system is investigated. This system consists of parallel machines which deteriorate with time and they may shift from a primarily in-control state to a degraded state with a higher defective rate or to a failed state. Maintenance scheduling corresponds to a discrete time age-based imperfect maintenance with a large number of maintenance alternatives. Process inspections are considered to detect the current state of the system. Detecting a deteriorated condition initiates the quality check of the related sub-lots, rework of defective items and a process adjustment that brings the machine in its normal conditions. Production planning includes a capacitated lot-sizing problem with multiple products. We propose a joint approach that coordinates the decisions of the three functions, where the objective function minimises the total cost. Evaluation of costs and interacting factors is presented and two heuristic methods are proposed to solve the problem. The results of the joint model are compared to a non-integrated method and a sensitivity analysis is conducted.     

A case study of machinery maintenance protocols and procedures within the UK utilities sector

Failure to conduct periodic fixed-time-to (or scheduled) maintenance on off-highway plant and equipment represents a significant health and safety hazard and major litigation risk for utility contractors completing service excavation and reinstatement works on public highways. Mini-excavators are a ubiquitous mobile plant item used for such tasks and have recently been responsible for several major injuries and fatalities involving workers and members of the public in the United Kingdom (UK). The research utilises the method of triangulation to examine the maintenance practices of utility contractors in the UK. Findings from the research reveal that a combination of prevailing market forces and internal ‘company’ pressures have inadvertently removed knowledgeable and trained operators, site foremen and managerial supervisors from hands-on maintenance inspections. Rather, ‘virtual’ maintenance protocols and procedures are adopted by head office but rarely fully implemented on-site. The research concludes with pragmatic recommendations and direction for future research.     

On the availability of a k-out-of-N system given limited spares and repair capacity under a condition based maintenance strategy

This paper considers a k-out-of-N system with identical, repairable components. Maintenance is initiated when the number of failed components exceeds some critical level. After a possible set-up time, all failed components are replaced by spares. A multi-server repair shop repairs the failed components. The system availability depends on the spare part stock level, the maintenance policy and the repair capacity. We present a mathematical model supporting the trade-off between these three parameters. We present both an exact and an approximate approach to analyse our model. In some numerical experiments, we provide insight on the impact of repair capacity, number of spares and preventive maintenance policy on the availability.     

A durability model incorporating safe life methodology and damage tolerance approach to assess first inspection and maintenance period for structures

This paper outlines a new durability model to assess the first inspection and maintenance period for structures. Practical scatter factor formulae are presented to determine the safe fatigue crack initiation and propagation lives from the results of a single full-scale test of a complete structure. New theoretical solutions are proposed to determine the s_a−s_m−N surfaces of fatigue crack initiation and propagation. Prediction techniques are then developed to establish the relationship equation between safe fatigue crack initiation and propagation lives with a specific reliability level using a two-stage fatigue damage cumulative rule. A new durability model incorporating safe life and damage tolerance design approaches is derived to assess the first inspection and maintenance period. Finally, the proposed models are applied to assess the first inspection and maintenance period of a fastening structure at the root of helicopter blade.     

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.     

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.