Modelagem da confiabilidade de equipamentos por combinações ou extensões de distribuições de Weibull - Barbosa, João Paulo (2008)
In this work we are going to model the reliability of the failure process of repairable equipments whose failure rate presents a bathtub type behavior. We are going to purpose two models. The first studied model is that of the combination of two Weibull distributions to represent the failure rate function, one represents the softening phase and to another the wear phase. Several methods are considered to be applied in a preliminary phase with the purpose of substituting a graphical solution, aiming to generate a solution that effectively describes initially a data set of failures. The application of maximum likelihood method in connection with the optimization procedure, having as starting points the parameters obtained in this preliminary phase, are used for the optimization of the parameters used in the considered model. Numerical examples are developed to illustrate the estimation procedure. In the second model we use a new extension of the Weibull function, called in this way because it has a distribution of Weibull as a special and asymptotic case. A solution is obtained by the adjustment of a straight line using the least squares method in a set of failure data for the determination of the necessary parameters for an initial modeling. Before the application of the least squares method, this data set goes through a mathematical treatment. Again, we are going to apply the method of the maximum likelihood in connection with the optimization procedure, taking as starting points the parameters obtained in this preliminary phase, to be used in the determination of the parameters of the considered model. Numerical examples are developed to illustrate the estimation procedure. The results obtained in the two modeling processes were satisfactory, both in the visual part illustrated by the graphs, and in the mathematical analysis. The parameters that were obtained by the modeling processes proposed in this work are going to be useful for a possible taking decision on the best time of maintenance for each equipment