A review on condition-based maintenance optimization models for stochastically deteriorating system

© 2016 Elsevier Ltd Condition-based maintenance (CBM) is a maintenance strategy that collects and assesses real-time information, and recommends maintenance decisions based on the current condition of the system. In recent decades, research on CBM has been rapidly growing due to the rapid development of computer-based monitoring technologies. Research studies have proven that CBM, if planned properly, can be effective in improving equipment reliability at reduced costs. This paper presents a review of CBM literature with emphasis on mathematical modeling and optimization approaches. We focus this review on important aspects of the CBM, such as optimization criteria, inspection frequency, maintenance degree, solution methodology, etc. Since the modeling choice for the stochastic deterioration process greatly influences CBM strategy decisions, this review classifies the literature on CBM models based on the underlying deterioration processes, namely discrete- and continuous-state deterioration, and proportional hazard model. CBM models for multi-unit systems are also reviewed in this paper. This paper provides useful references for CBM management professionals and researchers working on CBM modeling and optimization

Condition-Based Production for Stochastically Deteriorating Systems: Optimal Policies and Learning

Production systems deteriorate stochastically due to usage and may eventually break down, resulting in high maintenance costs at scheduled maintenance moments. This deterioration behavior is affected by the system's production rate. While producing at a higher rate generates more revenue, the system may also deteriorate faster. Production should thus be controlled dynamically to trade-off deterioration and revenue accumulation in between maintenance moments. We study systems for which the relation between production and deterioration is known and the same for each system as well as systems for which this relation differs from system to system and needs to be learned on-the-fly. The decision problem is to find the optimal production policy given planned maintenance moments (operational) and the optimal interval length between such maintenance moments (tactical). For systems with a known production-deterioration relation, we cast the operational decision problem as a continuous-time Markov decision process and prove that the optimal policy has intuitive monotonic properties. We also present sufficient conditions for the optimality of bang-bang policies and we partially characterize the structure of the optimal interval length, thereby enabling efficient joint optimization of the operational and tactical decision problem. For systems that exhibit variability in their production-deterioration relations, we propose a Bayesian procedure to learn the unknown deterioration rate under any production policy. Our extensive numerical study indicates significant profit increases of our approaches compared to the state-of-the-art

Integrated production quality and condition-based maintenance optimisation for a stochastically deteriorating manufacturing system

This paper investigates the problem of optimally integrating production quality and condition-based maintenance in a stochastically deteriorating single- product, single-machine production system. Inspections are periodically performed on the system to assess its actual degradation status. The system is considered to be in ‘fail mode’ whenever its degradation level exceeds a predetermined threshold. The proportion of non-conforming items, those that are produced during the time interval where the degradation is beyond the specification threshold, are replaced either via overtime production or spot market purchases. To optimise preventive maintenance costs and at the same time reduce production of non-conforming items, the degradation of the system must be optimally monitored so that preventive maintenance is carried out at appropriate time intervals. In this paper, an integrated optimisation model is developed to determine the optimal inspection cycle and the degradation threshold level, beyond which preventive maintenance should be carried out, while minimising the sum of inspection and maintenance costs, in addition to the production of non-conforming items and inventory costs. An expression for the total expected cost rate over an infinite time horizon is developed and solution method for the resulting model is discussed. Numerical experiments are provided to illustrate the proposed approach

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

Joint optimization of dynamic lot-sizing and condition-based maintenance

This study investigates the dynamic lot-sizing problem integrated with Condition-based maintenance (CBM) for a stochastically deteriorating production system. The main difference of this work and the previous literature on the joint optimization of lot-sizing and CBM is the relaxation of the constant demand assumption. In addition, the influence of the lot-size quantity on the evolution of the equipment degradation is considered. To optimally integrate production and maintenance, a stochastic dynamic programming model is developed that optimizes the total expected production and maintenance cost including production setup cost, inventory holding cost, lost sales cost, preventive maintenance cost and corrective maintenance cost. The algorithm is run on a set of instances and the results show that the joint optimization model provides considerable cost savings compared to the separate optimization of lot-sizing and CBM

Applications of maintenance optimisation models: a review and analysis

In this paper we give an overview of applications of maintenance optimization models published so far. We analyze the role of these models in maintenance and discuss the factors which may have hampered applications. Finally, we discuss future prospects

When to Initiate, When to Switch, and How to Sequence HIV Therapies: A Markov Decision Process Approach

HIV and AIDS are major health care problems throughout the world,with 40 million people living with HIV by the end of 2005. Inthat year alone, 5 million people acquired HIV, and 3 millionpeople died of AIDS. For many patients, advances in therapies overthe past ten years have changed HIV from a fatal disease to achronic, yet manageable condition. The purpose of thisdissertation is to address the challenge of effectively managingHIV therapies, with a goal of maximizing a patient's totalexpected lifetime or quality-adjusted lifetime.Perhaps the most important issue in HIV care is when a patientshould initiate therapy. Benefits of delaying therapy includeavoiding the negative side effects and toxicities associated withthe drugs, delaying selective pressures that induce thedevelopment of resistant strains of the virus, and preserving alimited number of treatment options. On the other hand, the risksof delayed therapy include the possibility of irreversible damageto the immune system, development of AIDS-related complications,and death. We develop a Markov decision process (MDP) model thatexamines this question, and we solve it using clinical data.Because of the development of resistance to administered therapiesover time, an extension to the initiation question arises: whenshould a patient switch therapies? Also, inherent in both theinitiation and switching questions is the question of whichtherapy to use each time. We develop MDP models that consider theswitching and sequencing problems, and we discuss the challengesinvolved in solving these models