The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift

Several variations of stochastic processes have been studied in the literature to obtain reliability estimations of products and systems from degradation data. As the degradation trajectories may have different degradation rates, it is necessary to consider alternatives to characterize their individ...

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Autores: Luis Carlos Méndez-González, Luis Pérez Domínguez, Hector Eduardo Tovanche-Picón, Luis Alberto Rodriguez Picon
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:México
Institución:Universidad Autónoma de Ciudad Juárez
Repositorio:Repositorio Institucional de la Universidad Autónoma de Ciudad Juárez
OAI Identifier:oai:uacj.mx:oai:cathi.uacj.mx:20.500.11961ir-28746
Acceso en línea:https://doi.org/10.3390/math12172613
Access Level:acceso abierto
Palabra clave:Proceso Wiener
Tasa de riesgo
Efectos aleatorios
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spelling The Wiener Process with a Random Non-Monotone Hazard Rate-Based DriftLuis Carlos Méndez-GonzálezLuis Pérez DomínguezHector Eduardo Tovanche-PicónLuis Alberto Rodriguez PiconProceso WienerTasa de riesgoEfectos aleatoriosinfo:eu-repo/classification/cti/7Several variations of stochastic processes have been studied in the literature to obtain reliability estimations of products and systems from degradation data. As the degradation trajectories may have different degradation rates, it is necessary to consider alternatives to characterize their individual behavior. Some stochastic processes have a constant drift parameter, which defines the mean rate of the degradation process. However, for some cases, the mean rate must not be considered as constant, which means that the rate varies in the different stages of the degradation process. This poses an opportunity to study alternative strategies that allow to model this variation in the drift. For this, we consider the Hjorth rate, which is a failure rate that can define different shapes depending on the values of its parameters. In this paper, the integration of this hazard rate with the Wiener process is studied to individually identify the degradation rate of multiple degradation trajectories. Random effects are considered in the model to estimate a parameter of the Hjorth rate for every degradation trajectory, which allows us to identify the type of rate. The reliability functions of the proposed model is obtained through numerical integration as the function results in a complex form. The proposed model is illustrated in two case studies based on a crack propagation and infrared LED datasets. It is found that the proposed approach has better performance for the reliability estimation of products based on information criteria.Luis Carlos Méndez-GonzálezLuis Pérez DomínguezHector Eduardo Tovanche-Picón2024info:eu-repo/semantics/articleArtículoinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.3390/math12172613reponame:Repositorio Institucional de la Universidad Autónoma de Ciudad Juárezinstname:Universidad Autónoma de Ciudad Juárezinstacron:UACJen_USinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc/4.0oai:uacj.mx:oai:cathi.uacj.mx:20.500.11961ir-287462025-11-26T19:48:41Z
dc.title.none.fl_str_mv The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift
title The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift
spellingShingle The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift
Luis Carlos Méndez-González
Proceso Wiener
Tasa de riesgo
Efectos aleatorios
info:eu-repo/classification/cti/7
title_short The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift
title_full The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift
title_fullStr The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift
title_full_unstemmed The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift
title_sort The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift
dc.creator.none.fl_str_mv Luis Carlos Méndez-González
Luis Pérez Domínguez
Hector Eduardo Tovanche-Picón
Luis Alberto Rodriguez Picon
author Luis Carlos Méndez-González
author_facet Luis Carlos Méndez-González
Luis Pérez Domínguez
Hector Eduardo Tovanche-Picón
Luis Alberto Rodriguez Picon
author_role author
author2 Luis Pérez Domínguez
Hector Eduardo Tovanche-Picón
Luis Alberto Rodriguez Picon
author2_role author
author
author
dc.contributor.none.fl_str_mv Luis Carlos Méndez-González
Luis Pérez Domínguez
Hector Eduardo Tovanche-Picón
dc.subject.none.fl_str_mv Proceso Wiener
Tasa de riesgo
Efectos aleatorios
info:eu-repo/classification/cti/7
topic Proceso Wiener
Tasa de riesgo
Efectos aleatorios
info:eu-repo/classification/cti/7
description Several variations of stochastic processes have been studied in the literature to obtain reliability estimations of products and systems from degradation data. As the degradation trajectories may have different degradation rates, it is necessary to consider alternatives to characterize their individual behavior. Some stochastic processes have a constant drift parameter, which defines the mean rate of the degradation process. However, for some cases, the mean rate must not be considered as constant, which means that the rate varies in the different stages of the degradation process. This poses an opportunity to study alternative strategies that allow to model this variation in the drift. For this, we consider the Hjorth rate, which is a failure rate that can define different shapes depending on the values of its parameters. In this paper, the integration of this hazard rate with the Wiener process is studied to individually identify the degradation rate of multiple degradation trajectories. Random effects are considered in the model to estimate a parameter of the Hjorth rate for every degradation trajectory, which allows us to identify the type of rate. The reliability functions of the proposed model is obtained through numerical integration as the function results in a complex form. The proposed model is illustrated in two case studies based on a crack propagation and infrared LED datasets. It is found that the proposed approach has better performance for the reliability estimation of products based on information criteria.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
Artículo
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status_str publishedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.3390/math12172613
url https://doi.org/10.3390/math12172613
dc.language.none.fl_str_mv en_US
language_invalid_str_mv en_US
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc/4.0
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc/4.0
dc.source.none.fl_str_mv reponame:Repositorio Institucional de la Universidad Autónoma de Ciudad Juárez
instname:Universidad Autónoma de Ciudad Juárez
instacron:UACJ
instname_str Universidad Autónoma de Ciudad Juárez
instacron_str UACJ
institution UACJ
reponame_str Repositorio Institucional de la Universidad Autónoma de Ciudad Juárez
collection Repositorio Institucional de la Universidad Autónoma de Ciudad Juárez
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