Optimal replacement of continuously degrading systems in partially observed environments

Abstract

Motivated by wind energy applications, we consider the problem of optimally replacing a stochastically degrading component that resides and operates in a partially observable environment. The component's rate of degradation is modulated by the stochastic environment process, and the component fails when it is accumulated degradation first reaches a fixed threshold. Assuming periodic inspection of the component, the objective is to minimize the long‐run average cost per unit time of performing preventive and reactive replacements for two distinct cases. The first case examines instantaneous replacements and fixed costs, while the second considers time‐consuming replacements and revenue losses accrued during periods of unavailability. Formulated and solved are mixed state space, partially observable Markov decision process models, both of which reveal the optimality of environment‐dependent threshold policies with respect to the component's cumulative degradation level. Additionally, it is shown that for each degradation value, a threshold policy with respect to the environment belief state is optimal if the environment alternates between two states. The threshold policies are illustrated by way of numerical examples using both synthetic and real wind turbine data. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 395–415, 2015

Optimizing usage and maintenance decisions for k‐out‐of‐n systems of moving assets

“…In the last two decades, several condition‐based maintenance models have been developed for phased‐mission systems (see, e.g., Refs. ). Our work is closely related to that of Refs.…”

Integrated maintenance and spare part optimization for moving assets

“…They showed that there exists an optimal threshold-type replacement policy for each environment. Considering similar degradation dynamics, Flory et al (2015) extended the work of Ulukus et al (2012) to partially observable environments. Çekyay and Özekici (2012) defined both the mission process and the degradation process as finite-state Markov processes where the generator of the degradation process depends on the phases of the mission.…”

Continuous-Observation Partially Observable Semi-Markov Decision Processes for Machine Maintenance

“…Another common choice is to directly model conditioning monitoring data by a stochastic process, e.g., the gamma process, [4], [5], [6]; failure is defined as the process exceeding a (random) threshold. However, in many practical applications, the physical condition of a machine 1 is characterized by a discrete set of states; see, e.g., [7] for road maintenance, [8] for power system management, [9] for production scheduling, and [10] for optimal replacement of wind turbines. Moreover, in many cases we are not permitted exact observations of the state of the machine.…”

“…Propositions 1 and 2 indicate that value iteration is a promising method for policy optimization. Equations (10) and 11…”