Modern implementations of industrial robots require the use of extensive knowledge and novel concepts. To bring real benefits, robotized processes must be analyzed in detail. One can now observe an increasing use of Lean Robotics, a concept that is primarily intended to simplify processes and eliminate inefficient activities. In the research, a new method for predictive cobot programming was presented. Firstly, the main idea of the Lean Robotics approach was outlined. Secondly, the problem of part location prediction and the cobot predictive programming issue were discussed. Moreover, the proposed method utilizing ARIMA model was presented. The developed solution has been verified in the simulation environment, where the results have proven the effectiveness of the proposed approach. The use of the method results in improved efficiency in the analyzed process. The research proved that it is crucial to reduce the time waste in modern robotic processes.