How to Design Rating Schemes of Risk Matrices: A Sequential Updating Approach

Risk matrices have been widely used as a risk evaluation tool in many fields due to their simplicity and intuitive nature. Designing a rating scheme, i.e., determining the number of ratings used in a risk matrix and assigning different ratings to different cells, is an essential part of risk matrix construction. However, most of the related literature has focused on applying a risk matrix to various fields, instead of researching how to design risk matrices. Based on the analysis of several current rules, we propose a new approach, namely, the sequential updating approach (SUA), to design the rating scheme of a risk matrix in a reliable way. In this article, we propose three principles and a rating algorithm based on these principles. The three principles, namely, adjusted weak consistency, consistent internality, and continuous screening, characterize a good rating scheme. The resulting rating scheme has been proven to be unique. A global rating algorithm is then proposed to create the design that satisfies the three principles. We then explore the performance of the SUA. An illustrative application is first given to explain the feasibility of our approach. The sensitivity analysis shows that our method captures a resolution-reliability tradeoff for decisionmakers in choosing an appropriate rating scheme for a risk matrix. Finally, we compare the designs based on the SUA and Cox's axioms, highlighting the advantages of the SUA.