Frailty Modeling for Repairable Systems with Minimum Repair: An Application to Dump Truck Data of a Brazilian Mining Company

Amanda Morales Eudes D’Andrea¹, Cirdêmia Costa Feitosa¹, Vera Lucia Damasceno Tomazella², Afrânio Márcio Corrêa Vieira²

1. Universidade Federal de São Carlos, Departamento de Estatística, São Carlos, SP, Brasil e Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, São Carlos, SP, Brasil.
2. Universidade Federal de São Carlos, Departamento de Estatística, São Carlos, SP, Brasil.

Abstract: In repairable system data analysis it is common to many components of the same type are studied and in these cases it is relevant to verify the heterogeneity between systems. Proschan [1] pointed out that the unobserved heterogeneity may explain increasing failure rates, which is often found in reliability analysis. The unobserved heterogeneity may be estimated from models of frailty. This model is characterized by using a random effect, that is, a non-observable random variable that represents the information that could not or were not observed. However, according with Vaupel et al. [2], the standard methods in repairable system data analysis ignore the unobserved heterogeneity. Thus, this work will explore the frailty models. The inferential method for estimation of the parameters will be displayed for models with minimal repair. Finally, an application to real data set [3] was taken, in which the models with and without frailty are compared. These real data set involving failures in trucks was collected in a Brazilian mining company.

Keywords: Repairable systems, minimal repair, Power Law Process, frailty.

Pages: 179 – 198 | Full PDF Paper