A0343
Title: Statistical modeling and reliability analysis of repairable systems with dependent failure times under imperfect repair
Authors: Paulo Ferreira - Federal University of Bahia (Brazil) [presenting]
Eder Brito - Federal Institute of Education Science and Technology of Goias (Brazil)
Vera Tomazella - Federal University of Sao Carlos (Brazil)
Francisco Louzada - University of Sao Paulo (Brazil)
Oilson Gonzatto-Junior - University of Sao Paulo (Brazil)
Abstract: Imperfect repairs (IRs) are widely applicable in reliability engineering since most equipment is not completely replaced after failure. In this sense, it is necessary to develop methodologies that can describe failure processes and predict the reliability of systems under this type of repair. One of the challenges in this context is to establish reliability models for multiple repairable systems considering the dependency and/or unobserved heterogeneity between systems and the times of their respective failures after performing IRs. Thus, frailty models are proposed to identify these failure processes' statistical dependence and unobserved heterogeneity. In this context, we consider the arithmetic reduction of age (ARA) and arithmetic reduction of intensity (ARI) classes of IR models, with constant repair efficiency, a power-law process distribution to model failure times, and a shared gamma distributed frailty by all systems. Classical inferential methods are used to estimate the parameters and reliability predictors of systems under IRs. An extensive simulation study is carried out under different scenarios to investigate the suitability of the models and the asymptotic consistency and efficiency properties of the maximum likelihood estimators. We illustrate the practical relevance of the proposed models on two real data sets.
