Análise transversal de tempos entre intervenções de processos de renovação generalizados via distribuição Weibull

Abstract

A Generalized Renewal Process (PRG) is a process of counting events of interest in a system, considering a certain time interval. The PRGs belong to a class of probabilistic models, which deal with repair actions, according to the change that provide the real age of the system. Thus, it is possible to evaluate the quality of the interventions, as well as to predict the occurrence of undesirable events, in systems that are in particular repairable, since the system can return to a satisfactory condition of operation, through some process of repair / intervention , rather than replacing the entire system. This is important, due to the high cost of the system itself and / or difficulty obtaining another system, for example. The study is carried out traditionally, considering the total operational history of a system, over a certain period of time, in the past or in the future, that is, they are longitudinal. With this, a single level of repair is characterized for the system, and the focus of this analysis is the system itself. From the literature on PRGs, the challenge of a new type of study, regarding the analysis of times between interventions, characterizes the level of repair in the system to each specific intervention. This thesis proposes the transversal analysis to be introduced in the PRG’s. For this, it will need a system formed by several atomic individuals and independent of each other, and the focus of the analysis becomes the interventions of the system. From the literature, a data adherence test was adapted for the most used PRG cross-sectional study, based on the Weibull distribution, PRGW, thus obtaining PRGW-Transversal. In the study of the performance of the adhesion test for PRGW-Transversal, the simulated results are analyzed by means of random sampling. The usefulness of the new model is verified, applying in a real world case, which involves failure times of tractor engines. Due to the lack of a real database with complete information in the literature, the study of imputation of gaps was done. It was possible to verify, by means of simulated realizations, that the imputations of the gaps by means of the average value of the column of each time, among the studied ones, has smaller Average Absolute Error (EAM), and therefore was chosen in the format of the base of actual data. This research allows us to classify the progress or decline of the repairable system over time and the interventions that are carried out, making it possible to improve decision making in order to make the operational life of the system longer and also contribute to the current studies of PRGs.