Two kinds of design ideation process may be distinguished in terms of the problems addressed: (i) solution-focused, i.e. generating solutions to address a fixed problem specifying a desired output; and (ii) exploratory, i.e. considering different interpretations of an openended problem and generating associated solutions. Existing systematic analysis approaches focus on the former; the literature is lacking such an approach for the latter. In this paper, we provide a means to systematically analyse exploratory ideation for the first time through a new approach: Analysis of Exploratory Design Ideation (AEDI). AEDI involves: (1) open-ended ideation tasks; (2) coding of explored problems and solutions from sketches; and (3) evaluating ideation performance based on coding. We applied AEDI to 812 concept sketches from 19 open-ended tasks completed during a neuroimaging study of 30 professional product design engineers. Results demonstrate that the approach provides: (i) consistent tasks that stimulate problem exploration; (ii) a reliable means of coding explored problems and solutions; and (iii) an appropriate way to rank/compare designers' performance. AEDI enables the benefits of systematic analysis (e.g. greater comparability, replicability, and efficiency) to be realised in exploratory ideation research, and studies using open-ended problems more generally. Future improvements include increasing coding validity and reliability.