A variance-based sensitivity index function for factor prioritization

Among the many uses for sensitivity analysis is factor prioritization—that is, the determination of which factor, once fixed to its true value, on average leads to the greatest reduction in the variance of an output. A key assumption is that a given factor can, through further research, be fixed to some point on its domain. In general, this is an optimistic assumption, which can lead to inappropriate resource allocation. This research develops an original method that apportions output variance as a function of the amount of variance reduction that can be achieved for a particular factor. This variance-based sensitivity index function provides a main effect sensitivity index for a given factor as a function of the amount of variance of that factor that can be reduced. An aggregate measure of which factors would on average cause the greatest reduction in output variance given future research is also defined and assumes the portion of a particular factors variance that can be reduced is a random variable. An average main effect sensitivity index is then calculated by taking the mean of the variance-based sensitivity index function. A key aspect of the method is that the analysis is performed directly on the samples that were generated during a global sensitivity analysis using rejection sampling. The method is demonstrated on the Ishigami function and an additive function, where the rankings for future research are shown to be different than those of a traditional global sensitivity analysis. & 2011 Elsevier Ltd. All rights reserved.