Abstract
Complex systems are subject to failure with increased use and degradation. The risk process is the stochastic dynamic process of system failures and their severities. This paper considers aggregate risk measures for the risk process of complex systems in the context of stochastic ordering. The aggregation follows from the accumulation of losses from a series of failure events. The emphasis is on second-order risk measures which account for risk aversion as defined by concave utilities. A second-order measure termed the adjusted risk priority number (ARPN) is presented. The measure is constructed from well-known statistics: rate of failures, average severity of failures, and the Gini Index for severity of failures. The ARPN is contrasted with the traditional risk priority number (RPN) defined by the rate and average severity. The computation and use of the measures is illustrated with a spectrum of failure data from commercial aircraft in the USA.
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