A Classification Scheme for Importance Measures

Importance measures are playing a valuable role in the transitioning strategy to risk-informed regulation. In this report the basic mathematical elements, the F(.) parameters, used in defining importance measures will be further analyzed to bring their properties into the open. The F(.) parameters are used throughout this paper to define the six importance measures used in the SAPHIRE code, to show relationships among these measures, to describe differences among these measures, to make comparisons among these measures, and to introduce and define a classification scheme for these measures. Overlapping, related, and nearly equivalent information is prevalent among these six importance measures, thus some importance measures are nearly equal in value and in rank ordering. The Birnbaum Importance Measure [1, 2] can be uniquely expressed in all three possible pair-wise combinations of the three F(.) parameters, which means that the Birnbaum Importance Measure can be easily compared with the definitions of all of the other interval measures, making the Birnbaum Importance Measure a very important importance measure with an important structure. A FORTRAN program was written to perform an inverse engineering process on two examples in order to look at the values of the three F(.) parameters for learning more about the interactions between and among the importance measures. Besides the F(.) parameters, other tools such as a classification scheme and some inequality flags are developed to help select component importance. Page 2