New partial ordering of survival functions based on the notion of uncertainty. (English) Zbl 0817.62082
Summary: A new partial ordering among life distributions in terms of their uncertainties is introduced. Our measure of uncertainty is Shannon information applied to the residual lifetime. The relationship between this ordering and various existing orderings of life distributions are discussed. Various properties of our proposed concept are examined. Based on our proposed ordering and various existing orderings, the notion of a ‘better system’ is introduced.
MSC:
62N05 | Reliability and life testing |
60E15 | Inequalities; stochastic orderings |
62B10 | Statistical aspects of information-theoretic topics |
62E10 | Characterization and structure theory of statistical distributions |