Risk Matrix Analysis Using Copulas Open Access
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In this research, a framework is developed to determine the best design of risk matrices based on Cox's (2008) approach, where the performance of a risk matrix is evaluated through the probability of elimination error value. The development of research requires extension of Cox's (2008) approach to 3×3, 4×4, 5×5 matrices and up to four vice three risk priority levels. Analyses of risk matrices with equally and non-equally spaced breakpoint designs for both likelihood and consequence are provided. In the course of the research, all possible colorings are determined for difference sized risk matrices which adhere to Cox's basic rules. Next, the joint distribution of consequence and likelihood is generated using a generalized diagonal band (GDB) copula, where the dependence parameter of the GDB copula is estimated through expert elicitation. Finally, given the copula selection, the optimal coloring with the minimal probability of elimination error value is determined after the calculation of the probability of elimination error for all possible colorings. The comparison between theoretical and numerical results is provided for the 2×2 risk matrix, and numerical analyses are provided for the 3×3, 4×4, 5×5 risk matrices.