Optimal Control of a Partially Observable Failing System with Costly Multivariate Observations

Kim, Michael Jong; Makiš, Viliam

doi:10.1080/15326349.2012.726039

Cited by 7 publications

(3 citation statements)

References 40 publications

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“…and the downtime costs C p (i) and C r (i) are obtained via (16) and (17), respectively. SettingV (0) = 0, we have for each i ∈ L ,V…”

Section: Solution Techniquesmentioning

confidence: 99%

“…The replacement model is formulated as an optimal stopping problem, and the long‐run expected replacement cost per unit time is minimized. That work was extended in to include multivariate observations that are normally distributed with mean and covariance matrices determined by the degradation state. A similar model was used by Jiang et al to maximize the component's long‐run expected availability per unit time.…”

Section: Introductionmentioning

confidence: 99%

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Optimal replacement of continuously degrading systems in partially observed environments

Flory

Kharoufeh

Abdul-Malak

2015

Naval Research Logistics

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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

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“…and the downtime costs C p (i) and C r (i) are obtained via (16) and (17), respectively. SettingV (0) = 0, we have for each i ∈ L ,V…”

Section: Solution Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal replacement of continuously degrading systems in partially observed environments

Flory

Kharoufeh

Abdul-Malak

2015

Naval Research Logistics

View full text Add to dashboard Cite

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“…In the maintenance optimization literature, one of the key structural properties to establish is convexity of the value function (see, e.g., Dayanik et al 2008, Kim and Makis 2012, Maillart 2006, Makis 2008). In the current setting however, it is not clear that the robust value function W defined in (14) will preserve such a convex structure in the presence of positional and transitional model ambiguity.…”

Section: Structure Of the Decision-maker's Optimal Policymentioning

confidence: 99%

Robust Control of Partially Observable Failing Systems

Kim

2016

Operations Research

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This paper is concerned with optimal maintenance decision making in the presence of model misspecification. Specifically, we are interested in the situation where the decision maker fears that a nominal Bayesian model may be miss-specified or unrealistic, and would like to find policies that work well even when the underlying model is flawed. To this end, we formulate a robust dynamic optimization model for condition-based maintenance in which the decision maker explicitly accounts for distrust in the nominal Bayesian model by solving a worst-case problem against a second agent, "nature," who has the ability to alter the underlying model distributions in an adversarial manner. The primary focus of our analysis is on establishing structural properties and insights that hold in the face of model miss-specification. In particular, we prove (i) an explicit characterization of nature's optimal response through an analysis of the robust dynamic programming equation, (ii) convexity results for both the robust value function and the optimal robust stopping region, (iii) a general robustness result for the preventive maintenance paradigm, and (iv) the optimality of a robust control limit policy for the important subclass of Bayesian change point detection problems. We illustrate our theoretical result on a real-world application from the mining industry.

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Optimal condition-based maintenance policy for a partially observable system with two sampling intervals

Makiš

2014

Int J Adv Manuf Technol

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In this paper, we propose an optimal Bayesian control policy with two sampling intervals minimizing the long-run expected average maintenance cost per unit time for a partially observable deteriorating system. Unlike the previous optimal Bayesian approaches which used periodic sampling models with equidistant intervals, a novel sampling methodology is proposed which is characterized by two sampling intervals and two control thresholds. The deterioration process is modeled as a 3-state continuous time hidden-Markov process with two unobservable operatingstates and an observable failure state. At each sampling epoch, the multivariate observation data provides only partial information about the actual state of the system. We start observing the system with a longer sampling interval. If the posterior probability that the system is in the warning state exceeds a warning limit, observations are taken more frequently, i.e., the sampling interval changes to a shorter one, and if the posterior probability exceeds a maintenance limit, the full inspection is performed, followed possibly by preventive maintenance. We formulate the maintenance control problem in a partially observable Markov decision process (POMDP) framework to find the two optimal control limits and two sampling intervals. Also, the mean residual life (MRL) of the system is calculated as a function of the posterior probability. A numerical example is provided and comparison of the proposed scheme with several alternative sampling and maintenance control strategies is carried out.F. Naderkhani ZG · V. Makis ( ) Mechanical and Industrial Engineering

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Optimal Control of a Partially Observable Failing System with Costly Multivariate Observations

Cited by 7 publications

References 40 publications

Optimal replacement of continuously degrading systems in partially observed environments

Optimal replacement of continuously degrading systems in partially observed environments

Robust Control of Partially Observable Failing Systems

Optimal condition-based maintenance policy for a partially observable system with two sampling intervals

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