Summary and Discussion

There are many problems of probability and statistics in which characterizing a large and awkward space of objects by a simpler index of the space facilitates analysis and makes the identification of optimal or at least rational solutions possible. The notion of a sufficient statistic, one that can reduce the data to a simple summary measure without loss of information about the unknown features of the model involved, is perhaps the quintessential example of this phenomenon. In linear model theory, results on dimension reduction have the same aim, though the possibility of such reduction without some (at least minor) loss of information is rarely possible. In this latter case, the compromise is generally deemed to be worth making. The theory and applications of system signatures can be thought of in the same way. The signature of a system is a characteristic of the system’s design which captures an essential feature of that design. Specifically, it provides a measure of how component failures influence system failures when the components are independent and have the same lifetime distributions. As mentioned earlier, this leveling of the playing field among the components’ theoretical performance allows one to focus exclusively on system design. Signatures are deterministic measures that are properly classified as tools within the field of Structural Reliability, providing information solely about the design of the corresponding system.