Accelerated failure time frailty model for modeling multiple systems subject to minimal repair

IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Edilenia Queiroz Pereira, Oilson Alberto Gonzatto Junior, Vera Lucia Damasceno Tomazella, Lia Hanna Martins Morita, Alex L. Mota, Francisco Louzada Neto
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引用次数: 0

Abstract

This article presents accelerated failure time models with and without frailty for modeling multiple systems subject to minimal repair. The study considers the conventional accelerated failure time model, the accelerated failure time model with Gamma frailty, and proposes the accelerated failure time model with weighted Lindley frailty, which has attractive properties such as a closed-form Laplace transform. The proposed model extends the accelerated failure time model with the intensity function of a power law process. It retains the direct physical interpretation of the original accelerated failure time model, in which the role of covariates is to accelerate or decelerate the time to each repair. This framework includes parametric approaches to model fitting, which we consider for estimating the vector of regression parameters under this model and the parameter in the baseline intensity functions. The methodology is illustrated with a simulation study and a toy example to demonstrate the applicability of these models in the industrial context.

用于模拟受最小修复影响的多系统的加速故障时间虚弱模型
本文提出了有脆性和无脆性的加速失效时间模型,用于对受到最小修复的多系统建模。研究考虑了传统的加速失效时间模型、带伽马虚弱的加速失效时间模型,并提出了带加权林德利虚弱的加速失效时间模型,该模型具有闭式拉普拉斯变换等吸引人的特性。所提出的模型利用幂律过程的强度函数扩展了加速失效时间模型。它保留了原始加速故障时间模型的直接物理解释,其中协变量的作用是加速或减速每次修复的时间。这个框架包括模型拟合的参数方法,我们考虑用这种方法来估计该模型下的回归参数向量和基线强度函数中的参数。我们通过一个模拟研究和一个玩具示例对该方法进行了说明,以展示这些模型在工业环境中的适用性。
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来源期刊
CiteScore
2.70
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.
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