A numerical study of Markov decision process algorithms for multi-component replacement problems

Andersen, Jesper Fink; Andersen, Anders Reenberg; Külahçı, Murat; Nielsen, Bo Friis

doi:10.1016/j.ejor.2021.07.007

Cited by 23 publications

(9 citation statements)

References 37 publications

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“…(2) Considering two independent performance indicators If two independent performance indicators are considered, the log-likelihood function based on the degradation data of both performance indicators can be given by Equation (24).…”

Section: Likelihood Function Based On Degradation Datamentioning

confidence: 99%

“…The degradation of two performance indicators is described by the IG process with parameters 1 3   , 1 24   , 1 1.2 q  and 2 2…”

Section: Data Generationmentioning

confidence: 99%

“…Saberzadeh et al [23] used stochastic models and copula function to build a system reliability model. Andersen et al [24] presented replacement optimization framework in multi-component systems. The degradation models for components are described by a multivariate gamma process model and the dependent structure is described by Lévy copula.…”

Section: Introductionmentioning

confidence: 99%

“…As for the likelihood function (24), two stage estimation strategies, which are called the inference functions for the margins (IFM) method, are used to separately estimate the unknown parameters in the IG process and copula function. The likelihood corresponding to the IG process ln L IG Θ IG k D is estimated first.…”

mentioning

confidence: 99%

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Bivariate-Dependent Reliability Estimation Model Based on Inverse Gaussian Processes and Copulas Fusing Multisource Information

et al. 2022

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Reliability estimation for key components of a mechanical system is of great importance in prognosis and health management in aviation industry. Both degradation data and failure time data contain abundant reliability information from different sources. Considering multiple variable-dependent degradation performance indicators for mechanical components is also an effective approach to improve the accuracy of reliability estimation. This study develops a bivariate-dependent reliability estimation model based on inverse Gaussian process and copulas fusing degradation data and failure time data within one computation framework. The inverse Gaussian process model is used to describe the degradation process of each performance indicator. Copula functions are used to capture the dependent relationship between the two performance indicators. In order to improve the reliability estimation accuracy, both degradation data and failure time data are used simultaneously to estimate the unknown parameters in the degradation model based on the likelihood function transformed using the zeros-ones trick. A simulation study and a real application in the reliability estimation of mechanical seal used in airborne hydraulic pump are conducted to validate the effectiveness and accuracy of the proposed model compared with existing reliability models.

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Section: Likelihood Function Based On Degradation Datamentioning

confidence: 99%

“…The degradation of two performance indicators is described by the IG process with parameters 1 3   , 1 24   , 1 1.2 q  and 2 2…”

Section: Data Generationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Bivariate-Dependent Reliability Estimation Model Based on Inverse Gaussian Processes and Copulas Fusing Multisource Information

et al. 2022

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“…Indeed, it is well-known that all the dependence between the marginal processes of a multivariate Lévy process can be captured through a Lévy copula (see [14] for technical details about Lévy copulas). Among the reliability papers using this model, one can quote for instance [1], [16], and [17]. As will be seen later on, if this model allows to catch any range of dependence between the marginal processes of a multivariate Lévy process, its use entails a high technicality.…”

Section: Introductionmentioning

confidence: 99%

On the modeling of dependence between univariate Lévy wear processes and impact on the reliability function

Mercier

Verdier

2022

Appl Stoch Models Bus & Ind

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Univariate Lévy processes have become quite common in the reliability literature for modeling accumulative deterioration. In case of correlated deterioration indicators, several possibilities have been suggested for modeling their dependence. The point of this paper is the study of three different dependence models: use of a regular copula, superposition of independent univariate Lévy processes and use of a Lévy copula. The three methods are first presented and analysed. In this way, it is shown that the multivariate process constructed through an ordinary copula cannot have independent increments in general, that is, it is not a Lévy process. The impact of a wrong choice for the model is next explored, based on data simulated from one model and next adjusted to all three models. It is shown that a wrong model can lead to either overestimate or underestimate the reliability function, which could be problematic in an application context.

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Structured replacement policies for a system subject to random mission types

Zheng

2024

Naval Research Logistics

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This paper optimizes condition‐based replacement policies for a mission‐oriented system. The key challenge in our problem is that the system does not work under a fixed mission type but is subject to an infinite sequence of random types of missions assigned in a Markovian manner, which is realistic in many practical situations. The mission process modulates the deterioration process. Taking advantage of the opportunities when missions are switched, condition monitoring is conducted to support replacement decision‐making. This paper considers two practical scenarios in which the type of the next mission is either available or unavailable at each decision epoch. The objective is to determine the optimal replacement decisions for both scenarios that minimize their long‐run expected average cost rates. The optimization problems are analyzed in the framework of the Markov decision process. The optimal decisions of both scenarios are proven to be of partially monotone control‐limit forms. Near‐optimal policies with multilevel thresholds are provided for more convenient decision‐making. The policy iteration algorithm is modified for efficient optimization. A numerical example is used to demonstrate the feasibility of the proposed approach.

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A numerical study of Markov decision process algorithms for multi-component replacement problems

Cited by 23 publications

References 37 publications

Bivariate-Dependent Reliability Estimation Model Based on Inverse Gaussian Processes and Copulas Fusing Multisource Information

Bivariate-Dependent Reliability Estimation Model Based on Inverse Gaussian Processes and Copulas Fusing Multisource Information

On the modeling of dependence between univariate Lévy wear processes and impact on the reliability function

Structured replacement policies for a system subject to random mission types

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