Production planning in maintenance facilities that rely on the availability of certified operators is a challenging task. This is primarily attributed to the need for the integration of workforce training with the operations schedule, in addition to the uncertain repair time of some components. We confine our attention to the repair and overhaul of advanced technological devices that are composed of several components. In this context, this study proposes a novel approach to embedding uncertain repair times of faulty components and develops a multi-stage stochastic programming model for integrated production and workforce planning in such facilities under independent random repair time. Our numerical experiments conducted on a range of problem instances expose the significant value of incorporating repair time uncertainty in this problem.