Several models aim to measure how demographic, professional, and labour market factors influence unemployment duration, which has a compelling social and economic interest. Nevertheless, this quest still appear challenging in both interpretations and solutions, due to various difficulties. Among others, a relevant issue is the accurate measurement of unemployment, which is often biased by the presence of unknown errors. In this paper, we consider the measurement error as a latent variable and derive an Expectation-Maximization (EM) algorithm in the context of aWeibull regression model. The proposed methodology allows to estimate at the same time: (i) the effect of the covariates of interest on unemployment duration and (ii) the measurement error.