Generalized Renewal Process as an Adaptive Probabilistic Model

The model denominated generalized renewal process (GRP) is patented of the Maryland University. It is based on a probabilistic function that depends on the operation time from the last time, the previous times (historical data) and three parameters: shape, scale and effectiveness. This model is adjusted to the data considering the magnitude and the occurrence order, which is not possible using the traditional models; this property is denominated adaptability. Although the model was created originally to estimate the repairable systems reliability (it is adjusted using the successive corrective maintenances, and it measures its effectiveness), it is possible to apply it to any probabilistic process as: eolic and lightning. For performing this, a MAPLE language coded algorithm was designed. This paper suggests to simplify the PGR model to the three parameters Weibull distribution, applying the least square estimation. The model functionality is verified, applying it to an electrical and eolic system