In survival analysis, the most frequently used parametric survival models are the exponential and the Weibull distribution. A random effects model based on a generalized Weibull distribution is proposed for censored correlated observations. The specific individual effects play the role of the random effects part. A conceptually simple and very useful algorithm using the generalized linear model is given, to apply random effects Weibull models to data, and calculate the asymptotic variance-covariance matrix. The model is applied to two real data sets and the results are compared with previous work.