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

Imperfect Preventive Maintenance Policies With Unpunctual Execution.

Traditional maintenance planning problems usually presume that preventive maintenance (PM) policies will be executed exactly as planned. In reality, however, maintainers often deviate from the intended PM policy, resulting in unpunctual PM executions that may reduce maintenance effectiveness. This article studies two imperfect PM policies with unpunctual executions for infinite and finite planning horizons, respectively. Under the former policy, imperfect PM actions are periodically performed and the system is preventively replaced at the last PM instant. The objective is to determine the optimal number of PM actions and associated PM interval so as to minimize the long-run average cost rate. While the latter policy specifies that a system is subject to periodic PM activities within a finite planning horizon and there is no PM activity at the end of the horizon. The aim is then to identify the optimal number of PM activities to minimize the expected total maintenance cost. We discuss the modeling and optimization of the two unpunctual PM policies, and then explore the impact of unpunctual executions on the optimal PM decisions and corresponding maintenance expenses in an analytical or numerical way. The resulting insights are helpful for practitioners to adjust their PM plans when unpunctual executions are anticipated

A unified methodology of maintenance management for repairable systems based on optimal stopping theory

This dissertation focuses on the study of maintenance management for repairable systems based on optimal stopping theory. From reliability engineering’s point of view, all systems are subject to deterioration with age and usage. System deterioration can take various forms, including wear, fatigue, fracture, cracking, breaking, corrosion, erosion and instability, any of which may ultimately cause the system to fail to perform its required function. Consequently, controlling system deterioration through maintenance and thus controlling the risk of system failure becomes beneficial or even necessary. Decision makers constantly face two fundamental problems with respect to system maintenance. One is whether or when preventive maintenance should be performed in order to avoid costly failures. The other problem is how to make the choice among different maintenance actions in response to a system failure. The whole purpose of maintenance management is to keep the system in good working condition at a reasonably low cost, thus the tradeoff between cost and condition plays a central role in the study of maintenance management, which demands rigorous optimization. The agenda of this research is to develop a unified methodology for modeling and optimization of maintenance systems. A general modeling framework with six classifying criteria is to be developed to formulate and analyze a wide range of maintenance systems which include many existing models in the literature. A unified optimization procedure is developed based on optimal stopping, semi-martingale, and lambda-maximization techniques to solve these models contained in the framework. A comprehensive model is proposed and solved in this general framework using the developed procedure which incorporates many other models as special cases. Policy comparison and policy optimality are studied to offer further insights. Along the theoretical development, numerical examples are provided to illustrate the applicability of the methodology. The main contribution of this research is that the unified modeling framework and systematic optimization procedure structurize the pool of models and policies, weed out non-optimal policies, and establish a theoretical foundation for further development

The establishment of the time interval between inspections for a cold standby system with component repair

The time interval between inspections of cold standby systems is a crucial decision to ensure the appropriated system reliability and the lowest costs possible. This paper presents a model developed to establish the optimal time interval between inspections for a two-unit cold standby system with component repair and subject to periodic inspection, considering reliability and costs. A Markov chain is used to define possible states, their transition probabilities and the mean time to system failure, as a function of the time interval between inspections. Given the mean time to system failure, the steady state availability is determined. Finally, the costs related to the system maintenance are established and a cost function is developed and optimized for the time interval between inspections. Numerical examples are presented and results for different system parameters are compared. Besides optimizing the time interval between inspections, the analyses also reveal the effect of repair time on system availability and mean time to system failure

Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair

We analyze the optimal replacement policy for a system subject to a general failure and repair model. Failures can be of one of two types: catastrophic or minor. The former leads to the replacement of the system, whereas minor failures are followed by repairs. The novelty of the proposed model is that, after repair, the system recovers the operational state but its condition is worse than that just prior to failure (worse than old). Undertrained operators or low quality spare parts explain this deficient maintenance. The corresponding failure process is based on the Generalized Pólya Process which presents both the minimal repair and the perfect repair as special cases. The system is replaced by a new one after the first catastrophic failure, and also undergoes two sorts of preventive maintenance based on age and after a predetermined number of minor failures whichever comes first. We derive the long-run average cost rate and study the optimal replacement policy. Some numerical examples illustrate the comparison between the as bad-as-old and the worse than old conditions

Post-Sale Cost Modeling and Optimization Linking Warranty and Preventive Maintenance

Ph.DDOCTOR OF PHILOSOPH

Optimal maintenance and replacement decisions under technological change with consideration of spare parts inventories

International audienceClassical spare parts inventory models assume that the same vintage of technology will be utilized throughout the planning horizon. However, replacement often occurs in the form of a new technology that renders existing spare parts inventories obsolete. This paper aims to study the impact of spare parts inventory on maintenance and replacement decisions under technological change via a Markov decision process formulation. The replacement decision is complex in that one must decide with which technology available on the market to replace the current asset. Under technological change, the do nothing and repair options have significantly more value as they allow the appearance of even better technologies in the future

An study of cost effective maintenance policies: Age replacement versus replacement after N minimal repairs

In this paper we consider the inspection and maintenance of a system under two types of age-dependent failures, revealed minor failures (R) and unrevealed catastrophic failures (U). Periodic inspections every T units of time are carried out to detect U failures, leading to the system replacement when one is discovered. R failures are followed by a minor repair. In addition the system is preventively replaced at MT or after the Nth R failure whichever comes first. The costs of minimal repair and replacement after N minor failures depend on age and history of failures. Non-perfect inspections are assumed, providing false positives when no U failure has happened or false negatives when a U failure is present. The long-run cost per unit of time along with the optimum policy (T*, M*, N*) are obtained. We explore conditions under which both strategies of preventive maintenance are profitable, comparing with suboptimal policies when only one of them is performed. Maintenance of infrastructures illustrates the model conditions