Abstract
The failure events for a system constitute a marked point process, with severity marks defined by the consequences of failure. In this paper the process is summarized with the triplet: {failure rate, severity mean, severity exceedance}. Those component measures locate the process status in a 3 - dimensional probability consequence diagram. If the dimensions are stratified into intervals, the diagram is displayed as a risk cube. Composite risk measures, which are consistent with orders of stochastic dominance, are defined by integration of the risk process. The composite measures will determine equivalence classes of risk processes, and benchmarks for the measures mark regions of high/low risk on the cube. The risk cube methodology is applied to incident data for an airport navigation system. The location of an individual airport triplet on a risk cube, with regions determined by a family of airports, illustrates the potential for identifying unusual performance in terms of failure events.
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