Key performance indicators (KPIs) are critical for manufacturing operation management and continuous improvement (CI). In modern manufacturing systems, KPIs are defined as a set of metrics to reflect operation performance, such as efficiency, throughput, availability, from productivity, quality and maintenance perspectives. Through continuous monitoring and measurement of KPIs, meaningful quantification and identification of different aspects of operation activities can be obtained, which enable and direct CI efforts. A set of 34 KPIs has been introduced in ISO 22400. However, the KPIs in a manufacturing system are not independent, and they may have intrinsic mutual relationships. The goal of this paper is to introduce a multi-level structure for identification and analysis of KPIs and their intrinsic relationships in production systems. Specifically, through such a hierarchical structure, we define and layer KPIs into levels of basic KPIs, comprehensive KPIs and their supporting metrics, and use it to investigate the relationships and dependencies between KPIs. Such a study can provide a useful tool for manufacturing engineers and managers to measure and utilize KPIs for CI.