Optimal maintenance policies under deterministic deterioration and stochastic failure

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.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example.

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.

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

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

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.

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

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.

Optimal maintenance policy for a system subject to damage in a discrete time process

International audience

This paper presents a methodology for maintenance optimisation for heterogeneous infrastructure systems, i.e., systems composed of multiple facilities with different characteristics such as environments, materials, and deterioration processes. We present a bottom-up approach: facility-level optimal maintenance policies are first found; these policies are then combined with budget constraints in the system-level optimisation. In the first step, optimal and near-optimal maintenance policies for each facility are found and used as inputs for the system-level optimisation. In the second step, the problem is formulated as a constrained combinatorial optimisation problem, where the best combination of facility-level optimal and near-optimal solutions is identified. Two heuristics, pattern search heuristic (PSH) and evolutionary algorithm (EA), are adopted to solve the combinatorial optimisation problem. Their performance is evaluated using a hypothetical system of pavement sections. Comparison result with real optimal solutions for 20 facilities showed that both algorithms give near-optimal solutions (within less than 0.1% difference from the optimal solution) in 978 (PSH) and 966 (EA) cases out of 1000 executions. The EA performs better in terms of processing time than the PSH. Numerical experiments show the potential of the proposed algorithms to solve the maintenance optimisation problem for realistic heterogeneous systems.

Joint production and maintenance optimization in flexible hybrid Manufacturing–Remanufacturing systems under age-dependent deterioration

In this study, an optimal maintenance policy is developed for a k-out-of-n: G system subject to two types of maintenance services, preventive maintenance and corrective maintenance. We investigate the optimal replacement age when a component failure is not detected immediately until a k-out-of-n: G system fails. The optimal maintenance policy is determined to minimize the expected total system cost when a generalized block replacement model is developed using downtime period. It is assumed that component failures are not monitored until a system failure, thus, a k-out-of-n: G system failure occurs. The downtime period of each failed component using order statistics for life time and age distributions for a k-out-of-n: G system is investigated. Numerical examples are discussed in order to demonstrate the applicability of the methodology derived from this paper.

With the popularization of service-oriented manufacturing, the current operation & maintenance (O&M) has shifted from traditional in-house maintenance to proactive outsourcing maintenance. It is paramount for an original equipment manufacturer (OEM) to provide timely and cost-effective maintenance schemes to geographically distributed customer enterprises. Interestingly, transportation theories could be combined to facilitate multi-location O&M management. In this paper, a transportation-oriented cross-regional opportunistic maintenance (TCOM) policy is developed for solving O&M optimizations and planning real-time schemes for the multi-center service network. The optimization model of this TCOM policy addresses several inter-related decisions: (1) most suitable maintenance times for each leased machine, (2) cost-effective arrangements of technician teams to perform maintenance tasks, and (3) optimal service routes for required teams. We not only integrate maintenance grouping and technician routing, but also investigate the new issues arising from the collaborative sharing of technician teams belonging to different maintenance centers. Numerical examples show that this TCOM policy can achieve significant cost-saving in cross-regional maintenance grouping and multi-location routing optimization for OEMs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the critical problem of computing an optimal maintenance policy for the multi-center service network of geographically distributed production systems to achieve a timely and cost-effective O&M management. We consider individual machine degradations, complex maintenance opportunities and network logistics optimization to establish a global maintenance scheme for the multi-center service network. The existing approaches are to schedule the preventive maintenance (PM) for a single machine or multi-unit leased system, which is unilateral and cannot be applied to multi-location production systems. Although the network opportunistic maintenance policy has been proposed in the literature for maintenance grouping and technician routing problem, it still does not consider the limited workforce resource and the collaborative sharing of technician teams from different maintenance centers. To fill this literature gap, in this paper, we develop the TCOM policy to determine the optimal maintenance timetable for leased machines, as well as the cost-effective service route of technician teams belonging to multiple maintenance centers, so as to conduct timely and cost-effective PM on multi-location production systems. Compared with the conventional maintenance policy, our adaptive policy greatly reduces the total outsourcing maintenance cost in long-term O&M services.