Context: Exploratory testing plays an important role in the continuous integration and delivery pipelines of large-scale software systems, but a holistic and structured approach is needed to realize efficient and effective exploratory testing. Objective: This paper seeks to address the need for a structured and reliable approach by providing a tangible model, supporting practitioners in the industry to optimize exploratory testing in each individual case. Method: The reported study includes interviews, group interviews and workshops with representatives from six companies, all multi-national organizations with more than 2,000 employees. Results: The ExET model (Excellence in Exploratory Testing) is presented. It is shown that the ExET model allows companies to identify and visualize strengths and improvement areas. The model is based on a set of key factors that have been shown to enable efficient and effective exploratory testing of large-scale software systems, grouped into four themes: "The testers knowledge, experience and personality", "Purpose and scope", "Ways of working" and "Recording and reporting". Conclusions: The validation of the ExET model showed that the model is novel, actionable and useful in practice, showing companies what they should prioritize in order to enable efficient and effective exploratory testing in their organization. (C) 2021 Elsevier Inc. All rights reserved.