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Performance analysis in process mining aims to provide insights on the performance of a business process by using a process model as a formal representation of the process. Such insights are reliably interpreted by process analysts in the context of a model with formal semantics. Existing techniques for performance analysis assume that a single case notion exists in a business process (e.g., a patient in healthcare process). However, in reality, different objects might interact (e.g., order, item, delivery, and invoice in an O2C process). In such a setting, traditional techniques may yield misleading or even incorrect insights on performance metrics such as waiting time. More importantly, by considering the interaction between objects, we can define object-centric performance metrics such as synchronization time, pooling time, and lagging time. In this work, we propose a novel approach to performance analysis considering multiple case notions by using object-centric Petri nets as formal representations of business processes. The proposed approach correctly computes existing performance metrics, while supporting the derivation of newly-introduced object-centric performance metrics. We have implemented the approach as a web application and conducted a case study based on a real-life loan application process.