Semi-Quantitative Risk Matrix Analysis

A purely qualitative judgment uses words like 'low' or 'high' with no numeric meaning. A semi-quantitative matrix anchors each ordinal level to a quantitative band — a frequency range for likelihood and a monetary or impact range for consequence — so the categories carry approximate numeric content. This anchoring, emphasized in ISO/IEC 31010, gives more discipline and comparability than verbal scales while stopping short of computing an actual probability or expected loss, which is the province of fully quantitative methods.

They are reliable for what they are designed to do — fast screening and ordinal ranking — provided they are built carefully. Cox showed that badly designed matrices can rank risks in the wrong order, compress very different risks into one cell, and perform worse than random for risks with negatively correlated frequency and severity. The remedy is not to abandon the tool but to design scales and cell colorings that satisfy weak consistency, avoid range compression, and to escalate closely ranked or high-stakes risks to quantitative analysis rather than relying on the grid.

There is no universal answer, but the number of levels trades discrimination against false precision. Too few levels compress distinct risks together; too many imply a precision the underlying judgments cannot support and can introduce ordering inconsistencies. ISO/IEC 31010 leaves the choice to the user but stresses anchoring each level to a defined band. In practice three-by-three to five-by-five grids are common, and the design should be checked against consistency criteria rather than chosen by habit, since the level count directly affects whether the matrix can rank risks correctly.