Algorithms for bottom-up maintenance optimisation for heterogeneous infrastructure systems

Thompson1 considers a linear control model to ascertain the optimal preventive maintenance policy for production equipment and, simultaneously, its optimal sale date. He assumes age‐dependent deterministic continuous deterioration, production rate and linear efficiency of maintenance expenditures. In the present paper we first consider a linear maintenance model under a budget constraint. The impact of such a restriction is an earlier switch in the optimal bang‐bang policy. Then a non‐linear, non‐autonomous generalization of Thompson's model is analysed by the maximum principle. The optimal maintenance policy is shown to be downward sloping provided that in each time period the production rate is greater than the sum of interest and deterioration rate. The monotonicity of the optimal rate of preventive maintenance holds also under the additional possibility of random machine failure provided the production rate is greater than the sum of the rate of interest, the rate of deterioration and the rate of stochastic failure at each age. Moreover, it is shown that the higher the failure rate the smaller the optimal expenditures for preventive maintenance at any fixed age of the machine. In particular, the optimal maintenance rate at age t in a model without random failure is greater than those in any case including stochastic failure at the same age.

Burn-in is a widely used method to eliminate the initial failures. Preventive maintenance policy such as age replacement is often used in field operation. In this paper burn-in and maintenance policy are taken into consideration at the same time. The properties of the corresponding optimal burn-in times and optimal maintenance policy are discussed.

Different type of maintenance problems have been investigated during the past decades. With the growth in complexity of modern systems, the cost of purchasing new systems becomes higher ever than before. Surprisingly, very little attention in the literature has been paid to the failure replacement in these preventive maintenance models. However, in practice most systems incur increasingly expensive down time costs when the systems suffer the unexpected failures. The major changes to the standard maintenance model in this research are the addition of a failure replacement cost for a failed system and the reliability limit for which system has to be replaced. The overall objective of this research is to propose an efficient algorithm to obtain the optimal maintenance policy. The optimal preventive maintenance policy is investigated with incorporating the costs of minimal repair, imperfect preventive maintenance, failure replacement and preventive replacement. The specific maintenance actions for a repairable system are when to perform an imperfect preventive maintenance or to replace the system while the system is in the operating condition. In another case, the specific maintenance actions for a repairable system are whether to replace the system, or to perform a minimal repair when the system fails. The number of imperfect preventive maintenance and the control limits of the optimal maintenance policy are calculated under the expected average cost rate criterion.

Optimal maintenance policy and residual life estimation for a slowly degrading system subject to condition monitoring

This paper considers a Bayesian approach to determine an optimal maintenance policy following the expiration of combination warranty. The combination warranty policies can be divided by the renewing combination warranty and the non-renewing combination warranty. Given the cost structure to the user during the cycle of the system, we derive the mathematical formula for the expected cost rate per unit time. When the failure time is Weibull distribution with uncertain parameters, a Bayesian approach is established to formally express and update the uncertain parameters for determining an optimal maintenance policy. We show that there exists a unique optimal maintenance period following the expiration of combination warranty such that the expected cost rate per unit time is minimized. Some numerical examples are presented for illustrative purpose.

Joint optimization of maintenance and spares inventory policy for a series-parallel system considering dependent failure processes

Optimal rearrangement and preventive maintenance policies for heterogeneous balanced systems with three failure modes

Optimal preventive maintenance policy for leased equipment using failure rate reduction

This paper proposes a maintenance policy for a k-out-of-n: F system operating to fulfil several jobs without interruptions. The system is replaced when the Nth job completes or at the kth failure, whichever occurs first. So, there are some non-failed components when a replacement is done. These components can be sold as second-hand products to continue working in other systems for a while. The price of them is also considered in the proposed maintenance policy. An optimal maintenance policy is studied to minimise long-run average cost under the constraint of relative mean operating time. Comprehensive numerical studies are done to assess the effect of the model parameters on the optimal solutions. Also, to demonstrate the applicability of the proposed plan, a data set related to wind turbine generator failures is considered as a case study.

A special game against nature is examined in this paper, in which nature controls timings of repairable and non-repairable failures of a system of equipment, and preventive maintenance, repairs and preventive replacement policies are the countermeasures. We optimize the imperfect preventive maintenance policy for a multi-unit system with different initial virtual age units. We develop a binary integer programming problem, where the management decides on the optimal preventive maintenance policy to minimize the total expected maintenance cost not to exceed a given budget. The mathematical formulation is developed for a multi-unit system, considering different preventive maintenance levels for each unit. Numerical examples with sensitivity analysis are performed to illustrate the performance and efficiency of the proposed model. Also, the model is examined for a real case study from railway industry. The results determine the optimal preventive maintenance policy and provide managerial insights based on computational analysis.

With the enhancement of hardware and software engineering, the effectiveness and correctness of software is less and less doubted and customers are more aware about whether software services are available or not when needed. Software maintenance is one of the main reasons that make software unavailable and it is often very expensive to perform maintenance tasks. Common approaches of studying software maintenance are to consider it as a static by‐product of software operation and only the maintenance cost is covered. In this paper, software maintenance policies are studied with the consideration of unavailable service time. A non‐homogeneous continuous Markov chain is adopted for modeling the software operation and maintenance process, and the cost of software unavailability that is brought in by software maintenance is investigated and analyzed for searching the optimal maintenance policy, which aims at minimizing the average maintenance time cost. The optimality of our proposed policy is shown and checked by numerical examples with discussions of its possible application perspectives. Copyright © 2010 John Wiley & Sons, Ltd.

An Efficient Jaya Algorithm for Joint Optimization of Preventive Maintenance and Quality Policy in Production Systems

This paper proposes optimal maintenance policies for multi-deteriorating product considering its remanufacturability so as to reduce maintenance cost. It is assumed that all the failures can be repaired and the repair time can be considered. A maintenance model is established for diverse health index based on long-run average cost rate. In the model, discrete Markov process is adopted to depict the system deteriorating. Once a failure occurs, the system's health index can be identified immediately. Then the system's remanufacturability and continuing using capability through repairs are evaluated to determine the maintenance policy. The optimal maintenance policies can be obtained by a policy-iteration algorithm. Finally, the proposed approach is applied to an automotive engine. The results show that the model can describe the multi-degradation repair process effectively, and can be used to optimize the maintenance policies.

Operating a system for optimum availability is a key aspect in many a complex system. Failure of the system can have serious consequences both in monetary terms as well as in loss of production or disruption of service. Optimal control theory provides a convenient tool to obtain the optimal maintenance policies of maintainable systems. These optimal policies are obtained by applying the generalized maximum principle of Gamkrelidze. The prescribed objective function is represented in terms of the cost of repair as well as the downtime cost. The models considered are Markov in that their present state provides sufficient information about the system. Constant as well as time-varying optimal maintenance policies during the planning or operating period can be considered by the proposed method. The optimal maintenance policy very much depends on the failure rates of the individual system components.

ABSTRACTIn reliability mathematics, the optimization of a maintenance policy is derived based on reliability indexes, such as the reliability or its derivatives (e.g., the cumulative failure intensity or the renewal function) and the associated cost information. The reliability indexes, also referred to as models in this article, are normally estimated based on either failure data collected from the field or lab data. The uncertainty associated with them is sensitive to several factors, including the sparsity of data. For a company that maintains a number of different systems, developing maintenance policies for each individual system separately and then allocating the maintenance budget may not lead to optimal management of the model uncertainty and may lead to cost-ineffective decisions. To overcome this limitation, this article uses the concept of risk aggregation. It integrates the uncertainty of model parameters in the optimization of maintenance policies and then collectively optimizes maintenance policies for a set of different systems, using methods from portfolio theory. Numerical examples are given to illustrate the application of the proposed methods.