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

• Published in: Applied stochastic models in business and industry 2024-07, Vol.40 (4), p.1182-1201
• Main Authors: Pereira, Edilenia Queiroz, Junior, Oilson Alberto Gonzatto, Tomazella, Vera Lucia Damasceno, Morita, Lia Hanna Martins, Mota, Alex L., Louzada Neto, Francisco
• Format: Article
• Language: English
• Subjects: accelerated testing; Failure times; Frailty; Laplace transforms; Modelling; Parameter estimation; Recurrent events; regression model; Regression models; weighted Lindley distribution
• ISSN: 1524-1904; 1526-4025
• DOI: 10.1002/asmb.2864

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.