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Risk analyses applied to radiotherapy treatments have become an undeniable necessity, considering the dangers generated by the combination of using powerful radiation fields on patients and the occurrence of human errors and equipment failures during these treatments. The technique par excellence to execute these analyses has been the risk matrix. This paper presents the development of a new algorithm to execute the task with wide graphic and analytic potentialities, thus transforming it into a very useful option for risk monitoring and the optimization of quality assurance. The system SECURE-MR, which is the basic software of this algorithm, has been successfully used in risk analysis regarding different kinds of radiotherapies. Compared to previous methods, It offers new possibilities of analysis considering risk controlling factors as the robustness of reducers of initiators frequency and its consequences. Their analytic capacities and graphs allow novel developments to classify risk contributing factors, to represent information processes as well as accidental sequences. The paper shows the application of the proposed system to a generic process of radiotherapy treatment using a lineal accelerator. [ABSTRACT FROM AUTHOR]