A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems

We define and study a four-parameter model called the generalized odd log-logistic flexible Weibull distribution. The new distribution can be used effectively in the context of reliability since it accommodates different hazard rate forms such as monotone, unimodal, bathtub-shaped, increasing-decreasing-increasing, among possible others. We provide an extensive study of the quantile function. Further, we present a parametric regression model based on the new distribution as an alternative to the location-scale regression model. An important property of this new regression model is that it does not need the assumption of proportional risks. We use the method of maximum likelihood for estimating the model parameters and perform various simulations for different parameter settings, sample sizes and censoring percentages. Applications in real engineering data sets illustrate the flexibility of the proposed models.