Retrospective on the risk matrix, part II: Mathematics

We present a review of mathematical and engineering science foundation of the risk matrix (RM). The objective was to locate and evaluate information surrounding its use. RM is governed by number theory, set theory, metrology, and functional analysis, which explains the strengths and weakness of its use. Although incorrectly reported, ordinal multiplication rigidly sets the cell numeric allocation. No scientific support was found for changing the ordinal ranks, although one reduction is introduced. Existing evidence suggests that the RM is unreliable. An example is given. Suggestions for beneficial use of the RM are provided.