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In this paper, a tree-like structure of Key Performance Indicators (KPIs) is proposed to describe the Performance Measurement System (PMS) of a lean production system. The KPIs and their supporting measurement elements are identified and categorized in a multi-level hierarchy designed to give answers at strategic, tactical, and operational level. Examples of the dependencies between high-level decision variables, KPIs, and their measurement elements are presented with reference to the Bosch Production System (BPS) of a multinational manufacturer leader in the automotive industry. Moreover, the role and the impact of the KPIs selection in supporting, addressing, and evaluating the implementation of smart manufacturing projects in the fourth industrial revolution (I4.0) is shown.