The Fukushima-Daiichi Accident demonstrated the need of assessing and strengthening institutions involved in nuclear safety, including the accountability of regulators. There are a few problems hindering the path towards a greater understanding of accountability systems, the ensemble of mechanisms holding to account the nuclear regulator on behalf of the public. There is no consensus on what it should deliver and no systematic assessment method exists. This article proposes a method of assessing institutions based on defence in depth concepts and inspired from risk-assessment techniques used for nuclear safety. As a first step in testing the proposal, it presents a simple Monte-Carlo simulation, illustrating some of the workings of the method of assessment and demonstrating the kind of results it will be able to supply. This on-going work will assist policy-makers take better informed decisions about the size, structure and organisation of a nuclear regulator and the cost-effective funding of its accountability system. It will assist in striking a balance between efficiency and resilience of regulatory decision-making processes. It will also promote the involvement of stakeholders and allow them to have a more meaningful impact on regulatory decisions, thereby enhancing the robustness of the regulatory system and potentially trust and confidence.